Control System Pune University MCQs

This set of Control Systems Interview Questions and Answers focuses on “Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms”.

1. Consider a simple mass spring friction system as given in the figure K1, K2 are spring constants f-friction, M-Mass, F-Force, x-Displacement. The transfer function X/F of the given system will be :

control-systems-interview-questions-answers-q1

a) 1/(Ms 2 +fs+K1.K2)

b) 1/(Ms 2 +fs+K1+K2)

c) 1/(Ms 2 +fs+K1.K2/K1+K2)

d) K2/(Ms 2 +fs+K1)

Answer: b

Explanation: Force balance equations are formed where force from both the springs will be balanced by the mass system.

2. The output of an first order hold between two consecutive sampling instants is:

a) Constant

b) Quadratic Function

c) Ramp Function

d) Exponential Function

Answer: c

Explanation: Inverse Laplace of the equation of first order hold gives the ramp function and hence the output of an first order hold between two consecutive sampling is ramp function.

3. Which of the following is an example of an open loop system?

a) Household Refrigerator

b) Respiratory system of an animal

c) Stabilization of air pressure entering into the mask

d) Execution of program by computer

Answer: d

Explanation: Execution of a program by a computer is an example of an open loop system as the feedback mechanism is not taken by the computer program and set programs are used to get the set output.

4. A tachometer is added to servomechanism because:

a) It is easily adjustable

b) It can adjust damping

c) It reduces steady state error

d) It converts velocity of the shaft to a proportional Dc voltage

Answer: b

Explanation: A tachometer is a device to control the speed and adjust damping and it is used in servomechanism to adjust damping and mainly is used in AC servomotors.

5. A synchro Transmitter is used with control transformer for:

a) Feedback

b) Amplification

c) Error detection

d) Remote sensing

Answer: c

Explanation: Synchro transmitter is used as the error detector to get the desired speed and it is accompained with the synchro transformer which is used as an amplifier.

6. The below figure represents:

control-systems-interview-questions-answers-q6

a) Lead network

b) Lag network

c) PI controller

d) PD controller

Answer: b

Explanation: The equations of performance are

B1+k1=k2X0

T=k1/k1+k2

X0/X1=1/a.

7. Backlash in a stable control system may cause:

a) Under damping

b) Over damping

c) High level oscillations

d) Low level oscillations

Answer: d

Explanation: In a servo system, the gear backlash may cause sustained oscillations or chattering phenomenon and the system may even turn unstable for large backlash.

8. Tachometer feedback in a D.C. position control system enhances stability?

a) True

b) False

Answer: a

Explanation: Tachometer feedback is derivative feedback and hence increases the stability and speed of response, so tachometer adds zero at origin.

9. For a tachometer, if a is the rotor displacement, e is the output voltage and K is the tachometer constant, then the transfer function is given by:

a) Ks 2

b) K/s

c) K s

d) K

Answer: c

Explanation: e=K w

E=K sa 

E/a=K s .

10. Gear train in the motor is used to reduce the gear ratio?

a) True

b) False

Answer: b

Explanation: Gear ratio refers to the ratio of the number of teeths in the respective gears and gear train in the motor is specifically used to increase the gear ratio.

11. Assertion : Servomotors have heavier rotors and lower R/X ratio as compared to ordinary motors of similar ratings.

Reason : Servomotor should have smaller electrical and mechanical time constants for faster response.

a) Both A and R are true and R is the correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: d

Explanation: Ac servomotors are essentially induction motor with low X/R ratio for the rotor which has very low inertia.

12. Assertion : DC servomotors are more commonly used in armature controlled mode than field controlled mode.

Reason : Armature controlled Dc motors have higher starting torque than fiels controlled motors.

a) Both A and R are true and R is the correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: a

Explanation: To get higher speed in field controlled dc motor, field current is decreased with decrease in torque.

13. In case of DC servomotor, the back emf is equivalent to an “electric friction” which tends to:

a) Slowly decrease the stability of the system

b) Improve stability of the system

c) Very rapidly decrease the stability of the system

d) Have no effect of stability

Answer: b

Explanation: As Back emf in dc servomotors provides necessary centrifugal force to control the speed of the motor that increases the stability of the system.

14. The lagrangian is defined as:

a. Sum of kinetic energy and hydraulic energy

b. Mechanical energy

c. Difference of kinetic and potential energy

d. None of these

Answer: c

Explanation: By definition lagrangian is defined as difference of kinetic and potential energy.

L=K-P.

15. A gantry robot consists of a manipulator mounted on an overhead system that allows movement only in ________ plane.

a) Horizontal

b) Inclined

c) Vertical

d) None of the mentioned

Answer: a

Explanation: Gantry robot allows motion only in horizontal plane and this is made in this geometry to fulfill the respective work.

Answer: b

Explanation: An object stationary or moving in a uniform motion w.r.t A will appear to be traveling in a curved path w.r.t B. This apparent path curvature is attributed to Coriolis acceleration.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Transfer Functions”.

1. Which of the following is not the feature of modern control system?

a) Quick response

b) Accuracy

c) Correct power level

d) No oscillation

Answer: d

Explanation: For a good control system the speed of response and stability must be high and for the slow and sluggish response is not used and undesirable.

2. The output of the feedback control system must be a function of:

a) Reference input

b) Reference output

c) Output and feedback signal

d) Input and feedback signal

Answer: d

Explanation: Feedback control system has the property of reducing the error and that is by differencing the output with the desired output and as the equation of the output of the system is C=GR/1+GH.

3. The principle of homogeneity and superposition are applied to:

a) Linear time invariant systems

b) Nonlinear time invariant systems

c) Linear time variant systems

d) Nonlinear time invariant systems

Answer: c

Explanation: Superposition theorem states that for two signals additivity and homogeneity property must be satisfied and that is applicable for the LTI systems.

4. In continuous data systems:

a) Data may be continuous function of time at all points in the system

b) Data is necessarily a continuous function of time at all points in the system

c) Data is continuous at the inputs and output parts of the system but not necessarily during intermediate processing of the data

d) Only the reference signal is continuous function of time

Answer: b

Explanation: Continuous signals are the signals having values for the continuous time and if impulse response decays to zero as time approaches infinity, the system is stable.

5. A linear system at rest is subject to an input signal r=1-e -t . The response of the system for t>0 is given by c=1-e -2t . The transfer function of the system is:

a) /

b) /

c) 2/

d) /2

Answer: c

Explanation: c=1-e -2t

R=1/s-1/s+1

C=1/s-1/s+2

Tf=2/.

6. In regenerating the feedback, the transfer function is given by

a) C/R=G/1+GH

b) C/R=GH/1-GH

c) C/R=G/1+GH

d) C/R=G/1-GH

Answer: d

Explanation: Regenerating feedback is positive feedback and it increases the infinitely and hence the speed of response of the system reduces.

7. A control system whose step response is -0.5(1+e -2t ) is cascaded to another control block whose impulse response is e -t . What is the transfer function of the cascaded combination?

a) 1/

b) 1/s

c) 1/

d) 0.5/

Answer: a

Solution: Laplace transform is the transformation that transforms the time domain into frequency domain and of both the cascaded systems are 1/.

8. A transfer function has two zeroes at infinity. Then the relation between the numerator and the denominator degree of the transfer function is:

a) N=M+2

b) N=M-2

c) N=M+1

d) N=M-1

Answer: b

Explanation: Zeroes at infinity implies two poles at origin hence the type of the system is two and degree of denominator is M=N+2.

9. When deriving the transfer function of a linear element

a) Both initial conditions and loading are taken into account

b) Initial conditions are taken into account but the element is assumed to be not loaded

c) Initial conditions are assumed to be zero but loading is taken into account

d) Initial conditions are assumed to be zero and the element is assumed to be not loaded

Answer: c

Explanation: When deriving the transfer function of a linear element only initial conditions are assumed to be zero, loading cannot be assumed to be zero.

Answer: c

Explanation: A system with zero initial condition is said to be at rest since there is no stored energy.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Block diagram Algebra”.

1. Consider the block diagram shown below:

control-systems-questions-answers-block-diagram-algebra-q1

If the transfer function of the system is given by T=G1G2+G2G3/1+X. Then X is:

a) G2G3G4

b) G2G4

c) G1G2G4

d) G3G4

Answer: b

Explanation: Use the technique of making two different block diagram by dividing two summers and use the approaches of shifting take off point and blocks.

2. For the block diagram given in the following figure, the expression of C/R is:

control-systems-questions-answers-block-diagram-algebra-q2

a) G1G2G3/1-G2G1

b) G1G2/1-G1G2G3

c) G1G2G3/1-G1G2G3

d) G1G2/G3

Answer: a

Explanation: Block diagram is being converted into signal flow graphs by considering each take off point as a node and each forward transfer function as forward gain.

3. The transfer function from D to Y is :

control-systems-questions-answers-block-diagram-algebra-q3

a) 2/3s+7

b) 2/3s+1

c) 6/3s+7

d) 2/3s+6

Answer: a

Explanation: Y/D=2/3s+1/1+3*=2/3s+7.

4. The closed loop gain of the system shown in the given figure is :

control-systems-questions-answers-block-diagram-algebra-q4

a) -9/5

b) -6/5

c) 6/5

d) 9/5

Answer: b

Explanation: C/R=-3/1+3/2=-6/5.

5. The advantage of block diagram representation is that it is possible to evaluate the contribution of each component to the overall performance of the system.

a) True

b) False

Answer: a

Explanation: The advantage of the block diagram is that it is possible to get the contribution of each block to the overall performance of the system.

6. The overall transfer function from block diagram reduction for cascaded blocks is :

a) Sum of individual gain

b) Product of individual gain

c) Difference of individual gain

d) Division of individual gain

Answer: b

Explanation: Gain of block get multiplied when they are cascaded where cascaded means that the blocks are in series combination with no summer in between.

7. The overall transfer function of two blocks in parallel are :

a) Sum of individual gain

b) Product of individual gain

c) Difference of individual gain

d) Division of individual gain

Answer: a

Explanation: The gains get added as the blocks are connected in parallel with the summer in between and they are connected with the same sign.

8. Transfer function of the system is defined as the ratio of Laplace output to Laplace input considering initial conditions________

a) 1

b) 2

c) 0

d) infinite

Answer: c

Explanation: By definition transfer function is the ratio of the laplace output to the input but the initial conditions mainly the stored energy is zero.

9. In the following block diagram, G1=10/s G2=10/s+1 H1=s+3, H2=1. The overall transfer function is given by :

control-systems-questions-answers-block-diagram-algebra-q9

a) 10/11s 2 +31s+10

b) 100/11s 2 +31s+100

c) 100/11s 2 +31s+10

d) 100/11s 2 +31s

Answer: b

Explanation: C/R=G2G1/1+G2H2+G1G2H2

C/R=100/11s 2 +31s+100.

Answer: a

Explanation: Oscillations are the unwanted sinuoidal signals with high gain in positive feedback and s the damping factor is absent in the positive feedback system entirely oscillations are present.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Signal Flow Graphs”.

1. A signal flow graph is the graphical representation of the relationships between the variables of set linear algebraic equations.

a) True

b) False

Answer: a

Explanation: By definition signal flow graphs are the graphical representation of the relationships between the variables of set linear algebraic equations.

2. A node having only outgoing branches.

a) Input node

b) Output node

c) Incoming node

d) Outgoing node

Answer: a

Explanation: Nodes are the point by which the branches are outgoing or ingoing and this can be input or output node and input node is the node having only outgoing branches.

3. Use mason’s gain formula to find the transfer function of the given signal flow graph:

control-systems-questions-answers-signal-flow-graphs-q3

a) abd/1-

b) abdeg/1-+bcef

c) abd/1-+bcef

d) adcdef/1-+bcef

Answer: b

Explanation: Using mason’s gain formula transfer function from signal flow graph can be calculated which relates the forward path gain to the various paths and loops.

4. Use mason’s gain formula to find the transfer function of the following signal flow graph:

control-systems-questions-answers-signal-flow-graphs-q4

a) abcd+efg/1-cd-fg-cdfg

b) acdfg+bcefg/1-cd-fg-cdfg

c) abef+bcd/1-cd-fg-cdfg

d) adcdefg/1-cd-fg-cdfg

Answer: b

Explanation: Using mason’s gain formula transfer function from signal flow graph can be calculated which relates the forward path gain to the various paths and loops.

5. Loop which do not possess any common node are said to be ___________ loops.

a) Forward gain

b) Touching loops

c) Non touching loops

d) Feedback gain

Answer: c

Explanation: Loop is the part of the network in which the branch starts from the node and comes back to the same node and non touching loop must not have any node in common.

6. Signal flow graphs:

a) They apply to linear systems

b) The equation obtained may or may not be in the form of cause or effect

c) Arrows are not important in the graph

d) They cannot be converted back to block diagram

Answer: a

Explanation: Signal flow graphs are used to find the transfer function of control system by converting the block diagrams into signal flow graphs or directly but cannot be used for nonlinear systems.

7. Signal flow graphs are reliable to find transfer function than block diagram reduction technique.

a) True

b) False

Answer: a

Explanation: As one set technique and formula is used here but in block diagram technique various methods are involved which increases complexity.

8. The relationship between an input and output variable of a signal flow graph is given by the net gain between the input and output node is known as the overall______________

a) Overall gain of the system

b) Stability

c) Bandwidth

d) Speed

Answer: a

Explanation: The relationship between input and output variable of a signal flow graph is the overall gain of the system.

9. Use mason’s gain formula to calculate the transfer function of given figure:

control-systems-questions-answers-signal-flow-graphs-q9

a) G1/1+G2H

b) G1+G2/1+G1H

c) G2/1+G1H

d) None of the mentioned

Answer: b

Explanation: Use mason’s gain formula to solve the signal flow graph and by using mason’s gain formula transfer function from signal flow graph can be calculated which relates the forward path gain to the various paths and loops.

Answer: c

Explanation: Using mason’s gain formula transfer function from signal flow graph can be calculated which relates the forward path gain to the various paths and loops.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Feedback and Non-feedback Systems”.

1. The mechanism of control of body temperature is non feedback system?

a) True

b) False

Answer: b

Explanation: It is feedback system as the temperature of our body is regulated periodically and being warm blooded we regulate our body temperature w.r.t. to the climate.

2. Benefits of feedback:

a) Performance of system is greater.

b) Need for system much larger path gain and system instability.

c) Controlled variable accurately follows the desired value

d) Affected by parameter variations

Answer: d

Explanation: Closed loop system is the system with the feedback and this can be positive or negative feedback and having feedback have less dependence on parameter variation.

3. Feedback always increases the gain?

a) True

b) False

Answer: b

Explanation: It cannot always increase gain it can also reduce the gain as gain of Open loop control system is more as compared to it.

4. Effect of feedback on sensitivity is minimum in:

a) Open loop control system

b) Closed loop control system

c) None of the mentioned

d) Both of the mentioned

Answer: b

Explanation: Sensitivity is defined as the change in output with respect to change in parameter or input and for a good control system the sensitivity must be less and in closed loop control system it gets reduced by the factor of 1/.

5. Feedback control systems are:

a) Insensitive to both forward and feedback path parameter changes

b) Less sensitive to feedback path parameter changes than to forward path parameter changes

c) Less sensitive to forward path parameter changes that to feedback path parameter changes

d) Equally sensitive to forward feedback path parameter changes

Answer: c

Explanation: Feedback control system can be positive and negative but positive feedback systems less widely used as the positive feedback systems are more sensitive to parameter variations but negative feedback are less sensitive to change in G than change in H.

6. Consider the following statements with respect to the feedback of the control systems:

1. Feedback can improve stability or be harmful to stability if it is not properly applied.

2. Feedback can always improve stability

3. In many situations the feedback can reduce the effect of noise and disturbance on system performance.

4. In general the sensitivity of the system gain of a feedback system of a parameter variation depends on where the parameter is located.

a) 1,2 and 3 only

b) 1,3 and 4 only

c) 1,2 and 4 only

d) 1,2,3 and 4 only

Answer: b

Explanation: Negative feedback increases stability but not positive positive feedback reduces the stability and for this reason negative feedback systems are used .

7. The closed system has higher ________ than open loop control system, this implies increased speed of response.

a) Gain

b) Bandwidth

c) Frequency

d) Speed

Answer: b

Explanation: As transient response of the system is improved by the use of feedback and it causes the settling time to reduce and closed loop system has higher bandwidth than open loop systems and this implies increase in speed of response.

8. Feedback can always reduce the effects of noise and disturbance on system performance?

a) True

b) False

Answer: a

Explanation: Feedback has many advantages as it can reduces the effects of noise and disturbance on system performance by increasing speed of response.

9. Multiple signals as input can be used in which systems:

a) Feedback systems

b) Non feedback systems

c) Feedforward systems

d) None of the mentioned

Answer: a

Explanation: As in feedback system output can be obtained for more than one input as output can be generated for both the reference input and also for the disturbance input.

Answer: d

Explanation: Feedback can either make a system stable if not stable previously or may be it can cause instability as it reduces the gain of the system and hence the system can become stable if unstable or vice versa.

This set of Control Systems Questions and Answers for Freshers focuses on “Control of the Effects of Disturbance Signals by Use of Feedback”.

1. Regenerative feedback implies feedback with

a) Oscillations

b) Step input

c) Negative sign

d) Positive sign

Answer: d

Explanation: Regenerative feedback that is the positive feedback implies feedback with Positive sign and for complementary root locus is for the regenerative feedback.

2. The output of a feedback control system must be a function of

a) Reference and output

b) Reference and input

c) Input and feedback signal

d) Output and feedback signal

Answer: d

Explanation: The response of the control system is the output of the control system that depends upon the transfer function of the system and feedback system and also upon the input of the system.

3. A control system with excessive noise, is likely to suffer from

a) Saturation in amplifying stages

b) Loss of gain

c) Vibrations

d) Oscillations

Answer: a

Explanation: Noise is defined as the unwnated output due to the input and this is due to the excessive bandwidth and control system with excessive noise is likely to suufer from saturation in amplifying stages.

4. Zero initial condition for a system means

a) Input reference signal is zero

b) Zero stored energy

c) Initial movement of moving parts

d) System is at rest and no energy is stored in any of its components

Answer: d

Explanation: Zero initial condition means that the system is at rest and no energy is stored in any of its component.

5. Transfer function of a system is used to calculate which of the following?

a) The order of the system

b) The time constant

c) The output for any given input

d) The steady state gain

Answer: c

Explanation: Transfer function of a system is that ratio of Laplace output to the Laplace input at zero initial conditions and which is used to calculate the output for any given input.

6. The band width, in a feedback amplifier.

a) Remains unaffected

b) Decreases by the same amount as the gain increase

c) Increases by the same amount as the gain decrease

d) Decreases by the same amount as the gain decrease

Answer: c

Explanation: The bandwidth is defined as the difference in the higher frequency to the input frequency and increase in the bandwidth leads to the noise and in a feedback amplifier increases by the same amount as the gain decreases.

7. On which of the following factors does the sensitivity of a closed loop system to gain changes and load disturbances depend?

a) Frequency

b) Loop gain

c) Forward gain

d) All of the mentioned

Answer: d

Explanation: Sensitivity is defined as the change in the output with respect to the change in the parameter variations and the change in the input and load disturbances depends upon frequency loop gain and forward gain.

8. The transient response, with feedback system,

a) Rises slowly

b) Rises quickly

c) Decays slowly

d) Decays quickly

Answer: d

Explanation: Transient response is the response that is between time t=0 and at any time and behaviors depends upon the value of damping factor and maximum peak overshoot.

Answer: d

Explanation: The time constant is the time required to attain the final value of the steady state and the value if less then the speed of response will be more and second derivative input signals modify suppress the oscillations.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Linearizing Effect and Regenerative Feedback”.

1. The effect of adding feedback makes the system__________

a) Linear

b) Non-linear

c) Time variant

d) Time invariant

Answer: a

Explanation: Consider the single loop system with forward path transfer function as the square function then the response generated is nonlinear if system is open loop but will be approximately linear if closed loop.

2. The relation between output response and input signal in closed loop system is :

a) Exponential

b) Parabolic

c) Linear

d) Nonlinear

Answer: c

Explanation: Due to the linearizing effect of the feedback the relation between output response and the input signal in closed loop system is linear.

3. Assertion : Practical systems must be closed loop system.

Reason : This is due to the fact that closed loop systems are least affected by parameter variations, stable, higher bandwidth, linear and more speed of response.

a) Both A and R are true and R is the correct explanation of A.

b) Both A and R are true but R is not the correct explanation of A.

c) A is true but R is false.

d) A is false but R is true.

Answer: a

Explanation: Practically systems used must be linear to avoid error, ease of calibration and also to get accurate results but the systems used are non-linear to avoid the error due to the linearity they are approximated.

4. Regenerative feedback is also called as_________________

a) Negative feedback

b) Positive feedback

c) No feedback

d) Negative and Positive Feedback

Answer: b

Explanation: As the name implies that is regenerates the oscillations hence by name it can be positive.

5. Which of the following are the characteristics of regenerative feedback:

a) Zero damping

b) Stable

c) Least sensitive to parameter variations

d) None of the mentioned

Answer: a

Explanation: Output response is slow and sluggish and transient time is more due to the oscillations.

6. Which of the following are true:

a) Sensitivity of regenerative feedback is more than negative feedback but less than non-feedback system

b) Sensitivity of regenerative feedback is more non-feedback system but less than negative feedback system

c) Sensitivity of regenerative feedback is less than both

d) Sensitivity of regenerative feedback is more than both

Answer: c

Explanation: Sensitivity of the positive feedback system is even more than non-feedback system and it is more by a factor of 1/1-GH.

7. Loop gain provided by the regenerative feedback makes the closed loop transfer function insensitive to G.

a) True

b) False

Answer: a

Explanation: As if the positive feedback loop gain is nearly considered to be unity then transfer function becomes insensitive to G.

Answer: c

Explanation: Closed loop systems are the systems with positive and negative feedback and for standard test signals error constants are defined and for one of the inputs one of the static error co-efficient has a finite non-zero value.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Linear Approximation of the Nonlinear System”.

1. Due to which of the following reasons excessive band width in control systems should be avoided?

a) It leads to slow speed of response

b) It leads to low relative stability

c) Noise is proportional to bandwidth

d) Presence of feedback

Answer: c

Explanation: Excessive Bandwidth causes increases in the noise with the same proportion as the bandwidth and hence noise is not good for any signal therefore the excessive bandwidth is not desirable.

2. In a stable control system backlash can cause which of the following?

a) Underdamping

b) Overdamping

c) Poor stability at reduced values of open loop gain

d) Low-level oscillations

Answer: d

Explanation: In stable control systems backlash is the form of the error which may cause low level of the oscillations and hence can be useful sometimes as it increases the damping.

3. In an automatic control system which of the following elements is not used?

a) Error detector

b) Final control element

c) Sensor

d) Oscillator

Answer: d

Explanation: In an automatic control system oscillator is not used because the oscillator increases the oscillations but our aim is to reduce the oscillations and hence oscillator is not used.

4. In a control system the output of the controller is given to

a) Final control element

b) Amplifier

c) Comparator

d) Sensor

Answer: a

Explanation: In control system the output of the controller is given to the final control element it may be the plant or any other controller which-ever is used in the control circuit.

5. A controller, essentially, is a

a) Sensor

b) Clipper

c) Comparator

d) Amplifier

Answer: c

Explanation: A controller is essentially the comparator which compares the given input with the reference input and generates the error signal.

6. Which of the following is the input to a controller?

a) Servo signal

b) Desired variable value

c) Error signal

d) Sensed signal

Answer: c

Explanation: Error signal is the input to the controller and it causes the output to be the desired output.

7. The on-off controller is a _____ system.

a) Digital

b) Linear

c) Non-linear

d) Discontinuous

Answer: d

Explanation: The on-off controller is discontinuous at the point when the system changes its state from on to off.

8. The capacitance, in force-current analogy, is analogous to

a) Momentum

b) Velocity

c) Displacement

d) Mass

Answer: d

Explanation: The capacitance in the force current is analogous to the mass and this analogy is also called parallel analogy as mostly all the elements are parallel.

9. The temperature, under thermal and electrical system analogy, is considered analogous to

a) Voltage

b) Current

c) Capacitance

d) Charge

Answer: a

Explanation: The temperature under thermal and electrical system analogy is considered analogous to the voltage and is similar to the Force voltage analogy.

10. In electrical-pneumatic system analogy the current is considered analogous to

a) Velocity

b) Pressure

c) Air flow

d) Air flow rate

Answer: d

Explanation: In electrical-pneumatic system analogy the current is analogous to the air-flow rate.

11. The use of feedback element in the feedback loop is:

a) It converts the output variable ‘c’ to another suitable feedback variable ‘b’ to compare with the input command signal.

b) It is the actuating element

c) To increase the stability

d) None of the mentioned

Answer: a

Explanation: The feedback can be positive and negative and so applied is to produce the error signal so as to get the desired output.

12. The major components of a controller are:

a) Control element

b) Error detector and control element

c) Feedback element

d) Error detector and feedback element

Answer: b

Explanation: Controller is the extra block used in the system to get the desired characteristics and consists of two major components as the error detector and control element in the forward path.

13. Practically all the elements are:

a) Linear

b) Non-linear

c) Exponential

d) None of the mentioned

Answer: b

Explanation: It is not practically possible to achieve linear elements as there is some error present so practically all the elements present are non-linear but can be made linear only to some extent.

14. The need of assuming non-linear element as linear:

a) Simplicity of analysis and accuracy of results

b) Ease of calculations

c) Less time consuming

d) Mathematical tool available

Answer: d

Explanation: All the mathematical tools are available as per ideal cases so it is necessary to make assumptions for non-ideal to be nearly ideal and hence do the necessary calculations as needed.

Answer: a

Explanation: It is possible to make non-linear elements linear to make necessary calculations as practically non-linear elements are present and we make certain assumptions to make them linear.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Controller Components – I”.

1. Low power transducers called sensors prefer:

a) Linear relationship between controlled variable and output variable

b) Non-functional relationship between controlled variable and output variable

c) Non-linear relationship between controlled variable and output variable

d) Not related with each other

Answer: a

Explanation: Sensors are different from transducers as in transducers the energy is converted from one form to another while in sensors only the energy is sensed not converted and it is possible to get the accurate results in less time.

2. The chief advantage offered by the electronics is:

a) Differencing and stable amplification by Op-Amp

b) Stable amplification of power level by use of power transistor and SCR’s

c) Differencing and stable amplification of power level by Op-Amp

d) No amplification with the Op-Amp

Answer: c

Explanation: Advantage of electronics is that every type of energy is converted into measurable and storage energy and electronically differencing to get the error signal and its amplifier.

3. Which of the motions in actuators are preferred:

a) Translator

b) Rotary

c) Stationary

d) Non-Stationary

Answer: b

Explanation: An actuator in a control systems perform variety of task in hydraulic, pneumatic and electrical system but majorly they are all controlling rotary motions.

4. Assertion : Electric actuators are used control system for high torque applications.

Reason : Due to linear speed-Torque characteristics.

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: a

Explanation: Electric actuators are the devices that are used to convert non measurable form of energy into measurable and are used in high torque applications due to linear speed torque characteristics but not used in low speed where hydraulic actuators are still used.

5. Low power DC and AC motors are also known as _________

a) Servomotors

b) Tachogenerators

c) A.C. generators

d) D.C. generators

Answer: a

Explanation: Electric actuators are of two kinds’ ac and dc motors and with low power rating they are called ac servomotors.

6. The torque developed by the motor when stationary with the full applied voltage__________

a) Stalled torque

b) Torque

c) Force

d) Couple

Answer: a

Explanation: Stalled torque is the important figure of merit of Servomotor which is important for linearity characteristics.

7. High torque/inertia ratio means:

a) Stalled torque

b) Stalled inertia

c) Stalled toque/inertia ratio

d) Lower motor time constant

Answer: d

Explanation: High torque/inertia ratio means the ration of torque to the inertia should be high as for higher torque the inertia must be very low and this indicates lower time constant as it leads to dynamic response.

8. Electric actuators for stepped motion are known as stepper motor.

a) True

b) False

Answer: a

Explanation: Stepper motors are the motors in which the motion generated is in the form of steps with respect to the time and works on the same principle as electric actuators but with stepped motion.

9. DC motors can be modeled as:

a) Armature controlled

b) Field Controlled

c) Both a and b

d) None of the mentioned

Answer: c

Explanation: DC motors are the motors that work o the direct current and commutators are replaced by slip rings and can be classified based on the construction as armature controlled or field controlled.

10. Assertion : Pneumatic actuators are not as messy as hydraulic ones.

Reason : Pneumatic suffer from leakages and inherent inaccuracies.

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: b

Explanation: Pneumatic actuators are the devices that convert the motion of air into measurable form of the energy and can also be used in low speed applications but they suffer leakages and inherent in accuracies.

11. DC motors are constructed using:

a) Permanent Magnet

b) Electromagnet.

c) Magnets are not used

d) Plastics

Answer: a

Explanation: DC motors are are the motors that work o the direct current and commutators are replaced by slip rings and now constructed using permanent magnets having high flux density.

Answer: c

Explanation: Permanent magnets are hard magnets with the area og B-H curve more and they are less used at core of the magnet and are used for DC servomotors as they have high residual flux density and high coercivity.

This set of Control Systems Interview Questions and Answers for freshers focuses on “Controller Components – II”.

1. Different type of construction in permanent type DC magnet are :

a) Slotted armature type

b) Surface wound armature type

c) Surface wound rotating armature, stationary wound type.

d) All of the mentioned

Answer: d

Explanation: Permanent magnet are the hard magnets that have broad B-H curve and can not be used as the core of the transformer due to their high retentivity and can be constructed by various ways as described above.

2. Assertion : Slotted armature type in this armature is placed in slotted armature with DC windings placed inside the slots.

Reason : The construction is highly reliable and rugged but has high torque.

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: b

Explanation: Slotted armature as the name indicates in which armature is paced in slots but high inertia is present causing higher torque and less used.

3. A much lower inertia in Surface wound armature type is obtained by placing the winding on a non-magnetic cylinder which rotates in annular space between permanent magnet stator and stationary rotor.

a) True

b) False

Answer: a

Explanation: Because of larger air gap strong permanent magnets are needed and much lower inertia is obtained by placing non-magnetic cylinder which rotates in annular space between permanent magnet stator and stationary rotor.

4. Lower inertia is obtained due to much larger gap and hence stronger magnets are used for this purpose.

a) True

b) False

Answer: a

Explanation: Stronger permanent magnets are used so as to cause lower inertia as in Surface wound rotating armature and stationary wound type.

5. PMDC when coupled to a rotating shaft would generate a voltage proportional to speed and thus would serve as____________

a) Tachometer

b) Servomotor

c) D.C. motor

d) A.C. motor

Answer: a

Explanation: Tachometer is a device that has relationship between voltage and speed and this is used in the controller to enhance the gain of the control system.

6. PMDC device is commonly employed for:

a) Speed feedback in speed control system

b) Internal velocity feedback loop of a position control system

c) This device is used in both speed feedback and internal velocity feedback control

d) None of the mentioned

Answer: c

Explanation: The current rating of this type of device is very small and it is to be connected to the input end of the OP-AMP.

7. Commutation process of a DC motor can be accomplished by solid devices .

a) True

b) False

Answer: a

Explanation:Commutation process refers to the process in the alternating current is used as input in the DC motor and in case of a DC motor this can be accomplished by solid devices as the IC’s and transistors.

8. DC motors are constructed using Permanent Magnet resulting in:

a) Higher torque/inertia ratio

b) Higher operating frequency

c) No filed losses

d) All of the mentioned

Answer: d

Explanation: DC motors are extensively using Permanent Magnets for its construction as they provide higher torque/inertia ratio, higher operating frequency, no field losses.

9. Speed of a permanent magnet DC motor:

a) It is directly proportional to the armature voltage at a given load torque

b) The speed torque characteristics are more flat than in a wound field motor

c) It depends upon armature voltage and are more flat than in a wound field motor

d) None of the mentioned

Answer: c

Explanation: Speed of a permanent magnet DC motor is directly proportional to the armature voltage at a given load torque and speed torque characteristics are more flat than in a wound field motor as the effect of armature reaction is less pronounced in a PM motor.

Answer: a

Explanation: AC servomotors are replaced by DC servomotors as frictional losses and higher torque/inertia ratios have been achieved.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Stepper Motors”.

1. A variable reluctance stepper motor is constructed of ______________ material with salient poles.

a) Paramagnetic

b) Ferromagnetic

c) Diamagnetic

d) Non-magnetic

Answer: b

Explanation: A variable reluctance stepper motor is the motor that has motion in steps with respect to increase in time and constructed of ferromagnetic material with salient poles.

2. In a three-stack 12/8-pole VR motor, the rotor pole pitch is

a) 15º

b) 30º

c) 45º

d) 60º

Answer: c

Explanation: Pole pitch is defined as the number of armature slots to the pole pitch and here this has been converted into degrees.

3. A stepper motor having a resolution of 300 steps/rev and running at 2400 rpm has a pulse rate of- pps.

a) 4000

b) 8000

c) 6000

d) 10,000

Answer: c

Explanation: Pulse per second is mathematically given as PPS = *.

4. If a hybrid stepper motor has a rotor pitch of 36º and a step angle of 9º, the number of its phases must be

a) 4

b) 2

c) 3

d) 6

Answer: a

Explanation: Step angle is defined as =(N s -N r )/(N s +N r )*360.

5. The rotor of a stepper motor has no

a) Windings

b) Commutator

c) Brushes

d) All of the mentioned

Answer: d

Explanation: The rotor is the rotatory part of the motor of a stepper motor and has no windings, commutator and brushes.

6. A stepping motor is a ____________ device.

a) Mechanical

b) Electrical

c) Analogue

d) Incremental

Answer: d

Explanation: A stepping motor is a motor in which the motion in the form of steps and is a incremental device i which as the time increases the steps are increased.

7. The rotational speed of a given stepper motor is determined solely by the

a) Shaft load

b) Step pulse frequency

c) Polarity of stator current

d) Magnitude of stator current.

Answer: b

Explanation: The stator part of a motor is the stationary part of the motor and rotational speed of a given stepper motor is given by the step pulse frequency.

8. Which of the following phase switching sequence represents half-step operation of a VR stepper motor ?

a) A, B, C,A……..

b) A, C, B,A…….

c) AB, BC, CA, AB……..

d) A, AB, B, BC……..

Answer: d

Explanation: In the half step operation of a Variable reluctance motor physical step resolution is multiplied by 2 and control signals appear to be digital rather than analog.

9. A stepper motor may be considered as a ____________ converter.

a) Dc to dc

b) Ac to ac

c) Dc to ac

d) Digital-to-analogue

Answer: d

Explanation: A stepper motor is a motor in which the motion is in steps and it is an increemental device and may be considered as a digital to analog converter.

Answer: b

Explanation: Step angle is defined as =/*360 where Ns is the number of stator poles and Nr is the number of rotor poles.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Hydraulic Systems”.

1. Heavy lifting work is often accomplished by shifting fluids in big machines. The power system of such machines can be described as

a) Reciprocating

b) Pneumatic

c) Hydraulic

d) Hybrid

Answer: c

Explanation: The power system of heavy and big machines can be described by hydraulic systems and heavy lifting work is often accomplished by shifting fluids in big machines.

2. The scientific principle that makes hydraulic systems possible is

a) Pascal’s principle

b) Boyle’s law

c) Bernoulli’s principle

d) The fluid flow principle

Answer: a

Explanation: Pascal’s principle is the basis of hydraulic system which states that the water exerts pressure in all direction.

3. Pneumatic and other power systems can support three kinds of motion; they are

a) Linear, reciprocating, and random motion

b) Linear, flowing, and rotary motion

c) Linear, zigzag, and spiral motion

d) Linear, reciprocating, and rotary motion

Answer: d

Explanation: Pneumatic systems are the systems that control the process where the motion is in air and can support linear, reciprocating, and rotary motion.

4. A single acting cylinder can be pressurized externally from one direction only.

a) True

b) False

Answer: a

Explanation: Pressure variation is possible only if the force is acting from one direction if the force will be acting from multiple directions then the force cancellation is also possible.

5. A one-way valve that lets air into the reservoir of a compressor, but doesn’t let it out, is a

a) Check valve

b) Receiver valve

c) Control valve

d) Three way valve

Answer: a

Explanation: Check valve is a one-way valve that lets air into the reservoir of a compressor, but doesn’t let it out as the name indicates it allows air to enter as it has one entrance.

6. Series circuits work on both hydraulic and pneumatic actuators.

a) True

b) False

Answer: a

Explanation: Series circuits are the circuits where the components are connected in series and the component is called lumped component and work for both hydraulic and pneumatic error detectors.

7. 5/2 way single solenoid valve has:

a) 2 ports 2 positions

b) 5 ports 2 positions

c) 5 ports 5 positions

d) 2 ports 5 positions

Answer: b

Explanation:5/2 way single solenoid valve is the valve in which the valve is in the shape of solenoid has 5 ports equally spaced and 2 flow positions.

8. The ____________________ converts the compressed air energy into mechanical energy in the form of linear movement in one direction only.

a) Piston cylinders

b) Double acting cylinders

c) Single acting cylinders

d) Hydraulic pumps

Answer: c

Explanation:Single acting cylinders converts the compressed air energy into mechanical energy in the form of linear movement in one direction only.

9. A _____________ restricts air flow.

a) Throttle valve

b) Shuttle valve

c) Directional control valve

d) Single acting cylinder

Answer: a

Explanation: Air valve is restricted by the valve it allows only that entry as desired and throttle valve restricts the airflow.

Answer: a

Explanation: Piston is the part in the cylinder that is used to create the pressure difference and in case of single-acting cylinder it is pressed by the spring to the cylinder center .

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Pneumatic Systems”.

1. Fluid power circuits use schematic drawings to:

a) Simplify component function details

b) Make it so only trained persons can understand the functions

c) Make the drawing look impressive

d) Make untrained person to understand

Answer: a

Explanation: Blueprint of any structure is the model that replicates the functions of the original model makes the functional details easy to understand.

2. A pneumatic symbol is:

a) Different from a hydraulic symbol used for the same function

b) The same as a hydraulic symbol used for the same function

c) Not to be compared to a hydraulic symbol used for the same function

d) None of the mentioned

Answer: a

Explanation: The representation for hydraulic and pneumatic systems are different and for creating the easy readability and symbols for both used for the same function.

3. Pneumatic systems usually do not exceed:

a) 1 hp

b) 1 to 2 hp

c) 2 to 3 hp

d) 4 to 5 hp

Answer: a

Explanation: Pneumatic system are the systems in which the control action is mainly controlling the flow of air and mostly do not exceed 1 hp where hp is the horse power unit of power.

4. Most hydraulic circuits:

a) Operate from a central hydraulic power unit

b) Use air-over-oil power units

c) Have a dedicated power unit

d) Does not have dedicated power unit

Answer: a

Explanation: Hydraulic circuits are the circuits where the operation involves conversion of the hydel power into the electrical energy so that it can be stored and used and these operate from a central hydraulic power unit.

5. Hydraulic and pneumatic circuits:

a) Perform the same way for all functions

b) Perform differently for all functions

c) Perform the same with some exceptions

d) Does not perform all the functions

Answer: c

Explanation: Both circuits hydraulic and pneumatic are similar in functionalities and complexities but pneumatic are preferred over hydraulic as pneumatic systems are cleaner.

6. The lubricator in a pneumatic circuit is the:

a) First element in line

b) Second element in line

c) Last element in line

d) Third element in line

Answer: c

Explanation: The lubricator is the fluid that is used to lubricate the parts of the pneumatic circuits to reduce the friction and lubricator in a pneumatic circuit is the last element.

7. Series circuits work on both hydraulic and pneumatic actuators.

a) True

b) False

Answer: b

Explanation: Series circuits are the circuits that in which the elements are connected in series and do not work on both hydraulic and pneumatic actuators.

8. When comparing first cost of hydraulic systems to pneumatic systems, generally they are:

a) More expensive to purchase

b) Less expensive to purchase

c) Cost is same

d) Cost is not required

Answer: b

Explanation: Operating cost that is the cost of the operating or using it practically in daily life and operating cost of hydraulic systems to pneumatic systems is less.

9. When comparing operating cost of hydraulic systems to pneumatic systems, generally they are.

a) More expensive to operate

b) Less expensive to operate

c) Cost is same to operate

d) Cost is not required

Answer: b

Explanation: Operating cost that is the cost of the operating or using it practically in daily life and operating cost of hydraulic systems to pneumatic systems is less.

Answer: c

Explanation: Hydraulic fluid is the fluid that is causing conversion process and used in control action which is chemically inert and readily available.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Classification of Control Systems”.

1. What is the algebraic sum of the reference input and feedback?

a) Error Signal

b) Error Detector

c) Controlled system

d) Controlled output

Answer: a

Explanation: In the block diagram of a basic control system we see that the reference input is passed through Error detector or Comparator. The signal which leaves the same is the algebraic sum of reference input and feedback as the feedback wire is connected to the detector, so we call it error signal.

control-systems-questions-answers-classification-control-systems-q1

2. Feedback control systems are referred to as closed loop systems.

a) True

b) False

Answer: a

Explanation: Feedback control systems are also referred to as closed loop systems. In a closed loop, the actuating error signals, which is the difference between the input signal and the feedback signal is fed to the controller so as to reduce the error and bring the output of the system to the desired value.

3. Which principle does the linear system follow?

a) Principle of energy conservation

b) Principle of mass conservation

c) Principle of electromagnetism

d) Principle of superposition

Answer: d

Explanation: A linear system is one who obeys the principle of superposition. The principle of superposition states that the response produced by simultaneous application of two different forcing functions is equal to the sum of individual responses.

4. ______ control systems have unpredictable & non-repeatable.

a) Static

b) Dynamic

c) Deterministic

d) Stochastic

Answer: d

Explanation: Stochastic control systems are those who have unpredictable and non-repeatable response due to involvement of random parameters. Static systems is the system whose current output depends only on current input, dynamic system is a time dependent system and deterministic system’s response is predictable and repeatable.

5. The pressure inside the furnace is measured by _______

a) Gauge

b) Thermometer

c) Manometer

d) Barometer

Answer: a

Explanation: The pressure inside the furnace is measured by pressure gauge. In case the pressure increases or decreases beyond the desired value, the controller and the actuator will cause a change in the position of the damper.

6. On what difference does the pneumatic system works?

a) Speed

b) Pressure

c) Area

d) Length

Answer: b

Explanation: A pneumatic system works due to pressure difference of air or any other gas. Air at a pressure, pi is injected through the input manifold. It also consists of mass, coefficient of viscous friction and spring constant and the pressure difference created due to that, gives rise to pneumatic system.

7. In a thermal system, the temperature of the medium is ______

a) increasing

b) decreasing

c) zero

d) uniform

Answer: d

Explanation: To analyze a thermal system and determine its transfer function the temperature of the medium should be uniform. If the temperature is varying or zero the analysis will not be proper and a legitimate transfer function will not be the result.

8. How many parameters does process control refer to?

a) 1

b) 3

c) 5

d) 7

Answer: c

Explanation: Process control refers to control of five parameters which are level, flow, pressure, temperature, acidity of the process variable. A particular parameter has only one desired value.

9. What is the effect of feedback in the overall gain of the system?

a) Increases

b) Decreases

c) Zero

d) No change

Answer: b

Explanation: The feedback reduces the overall gain of the system. As soon as we introduce feedback in the system to make the system stable, gain is reduced.

10. In a temperature control system, what conversion in signal takes place?

a) Digital to Analog

b) Analog to Digital

c) Error to Digital

d) Error to Analog

Answer: b

Explanation: In a temperature control system, analog to digital conversion of signals take place. Automatic systems don’t understand analog signals as they only take digital inputs in the form of 0 & 1 so we use a analog to digital converter which converts the signal.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Standard Test Signals”.

1. A feedback control systems has the inherent capability that its parameter can be adjusted to alter both its transient and steady state responses.

a) True

b) False

Answer: a

Explanation: Feedback’s inherent capability is that its parameter can be adjusted to alter both transient and steady state responses as together they are referred to as time responses.

2. Transient response analysis is done for_________ systems.

a) Unstable

b) Stable

c) Conditionally stable

d) Marginally stable

Answer: b

Explanation: In case the system happens to be unstable, we need not proceed with its transient response analysis.

3. The input signals to control systems are not known fully ahead of time, the characteristics of control system which suddenly strain a control system are:

a) Sudden shock

b) Sudden change

c) Constant velocity and acceleration

d) All of the mentioned

Answer: d

Explanation: System dynamic behavior for analysis and design is therefore judged and compared under standard test signals.

4. Standard test signals in control system are:

a) Impulse signal

b) Ramp signal

c) Unit step signal

d) All of the mentioned

Answer: d

Explanation: Standard test signals are impulse, ramp and unit step all of the above to test the dynamic behavior of the control system.

5. The nature of transient response is revealed by ______________

a) Sine wave

b) Cos wave

c) Tan wave

d) Test signals

Answer: d.

Explanation: The nature is dependent on system poles not on the dynamic inputs.

6. It is generally used to analyze the transient response to one of the standard test signals.

a) True

b) False

Answer: a

Explanation: For analyzing transient response mainly step is used and also other signals mainly ramp and parabolic are not used for this analysis but they are used for steady state analysis.

7. Step signal is the signal whose values is :

a) 1 for all values greater than zero

b) Indeterminate at zero

c) It is zero for time less than zero

d) All of the mentioned

Answer: d

Explanation: Step signal is the signal whose value varies from zero to level in zero time.

8. Ramp input :

a) Denotes constant velocity

b) Value increases linearly with time

c) It denotes constant velocity and varies linearly with time

d) It varies exponentially with time

Answer: c

Explanation: Ramp signal denotes constant velocity and also basic definition states that its value increases linearly with time.

9. A perfect impulse has one value at zero time instant but otherwise zero elsewhere.

a) True

b) False

Answer: b

Explanation: A perfect impulse signal has infinite value at zero but mathematically only a small pulse is taken with finite limits.

Answer: d.

Explanation: Impulse response of a system is the inverse Laplace transfer function of its Laplace function.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Time Response of First Order Systems”.

1. First order system is defined as :

a) Number of poles at origin

b) Order of the differential equation

c) Total number of poles of equation

d) Total number of poles and order of equation

Answer: d

Explanation: First order system is defined by total number of poles and also which is same as the order of differential equation.

2. A unit step is applied at t=0 to a first order system without time delay. The response has the value of 1.264 units at t=10 mins, and 2 units at steady state. The transfer function of the system is_____________

a) 3/

b) 2/

c) 5/

d) 2/

Answer: d

Explanation: a= k[1-e ^ -t/T] K=2

0.632= 1-e ^ -10/T

T=600 sec

G=2/.

3. The transfer function of the system is G =100/ . For a unit step input to the system the approximate settling time for 2% criterion is:

a) 100 sec

b) 4 sec

c) 1 sec

d) 0.01 sec

Answer: b

Explanation: G =100/ 

Taking the dominant pole consideration,

S=-100 pole is not taken.

G= 100/s+1

Now it is first order system, ts=4T=4 sec.

4. If a first order system and its time response to a unit step are as shown below, the gain K is :

control-systems-questions-answers-time-response-first-order-systems-q4

control-systems-questions-answers-time-response-first-order-systems-q4a

a) 0.25

b) 0.8

c) 1

d) 4

Answer: d

Explanation: Y/R=K/1+sT+K

By, use of partial fraction, K/T/s+

Taking inverse Laplace transform on both the sides

Y=K/K+1[1-e ^ t] K=4

5. The unit impulse response of a system having transfer function K/ is shown below. The value of a is :

control-systems-questions-answers-time-response-first-order-systems-q5

a) t1

b) t2

c) 1/t1

d) 1/t2

Answer: d

Explanation: G = K/s+a

C =K/ Since R =1

C =Ke ^ -at

T=1/a

C =0.37K

T= t2=1/a.

6. A system with transfer function 1/Ts+1, subjected to a step input takes to seconds to reach 50% of step height. The value of t is :

a) 6.9s

b) 10s

c) 14.4s

d) 20s

Answer: c

Explanation: The response of a first order system is:

A=a[1-e^-t/T] ½= 1-e^-10/t

T= 14.43 sec.

7.A first order system and its response to a unit step input are shown in figure below. The system parameters are____________

a) a=5 and k=12

b) a=10 and k=5

c) a=5 and k=10

d) a=8 and k=9

Answer: c

Explanation: time constant=0.2 sec.

1/a=0.2

a=5

final value=lim s→0 sC =K/a

K/a=2

K=10.

8. Assertion : It is observed that step function is first derivative of a ramp function and impulse function is first derivative of a step function.

Reason : From the derived time response expression it is concluded that the output time response also follows the same sequence as that of input functions.

a) Both A and R are true and R is the correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) Both A is True but R is false

d) Both A is False but R is true

Answer: b

Explanation: If response due to one standard signal is known then response due to other signals can also be derived.

9. Laplace transform of unit impulse signal is :

a) A/s

b) A

c) 1

d) 1/s

Answer: c

Explanation: Laplace response of impulse signal is one which implies Laplace response is systems response.

Answer: a

Explanation: In first order systems the time response during steady state the output velocity matches.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Time Response of Second Order Systems – I”.

1. Which of the following transfer function will have the greatest maximum overshoot?

a) 9/(s 2 +2s+9)

b) 16/(s 2 +2s+16)

c) 25/(s 2 +2s+25)

d) 36/(s 2 +2s+36)

Answer: d

Explanation: Comparing the characteristic equation with the standard equation the value of the damping factor is calculated and the value for the option d is minimum hence the system will have the maximum overshoot .

2. A system generated by control-systems-questions-answers-time-response-second-order-systems-i-q2 The ramp component in the forced response will be:

a) t u

b) 2t u

c) 3t u

d) 4t u

Answer: b

Explanation: control-systems-questions-answers-time-response-second-order-systems-i-q2

Laplace transforming

sY + 2Y=4/s 2

Taking the inverse Laplace transform the forced term is 2t u.

3. The system in originally critically damped if the gain is doubled the system will be :

a) Remains same

b) Overdamped

c) Under damped

d) Undamped

Answer: c

Explanation: control-systems-questions-answers-time-response-second-order-systems-i-q3 hence due to this G lies between 0 and 1.

4. Let c be the unit step response of a system with transfer function K/. If c = 2 and c = 10, then the values of a and K are respectively.

a) 2 and 10

b) -2 and 10

c) 10 and 2

d) 2 and -10

Answer: c

Explanation: Applying initial value theorem which state that the initial value of the system is at time t =0 and this is used to find the value of K and final value theorem to find the value of a.

5. The damping ratio and peak overshoot are measures of:

a) Relative stability

b) Speed of response

c) Steady state error

d) Absolute stability

Answer: b

Explanation: Speed of response is the speed at which the response takes the final value and this is determined by damping factor which reduces the oscillations and peak overshoot as the peak is less then the speed of response will be more.

6. Find the type and order of the system given below:

control-systems-questions-answers-time-response-second-order-systems-i-q6

a) 2,3

b) 2,2

c) 3,3

d) None of the mentioned

Answer: Type = 2 which is the number of poles at the origin and order is the highest power of the characteristic equation.

7. A system has a complex conjugate root pair of multiplicity two or more in its characteristic equation. The impulse response of the system will be:

a) A sinusoidal oscillation which decays exponentially; the system is therefore stable

b) A sinusoidal oscillation with a time multiplier ; the system is therefore unstable

c) A sinusoidal oscillation which rises exponentially ; the system is therefore unstable

d) A dc term harmonic oscillation the system therefore becomes limiting stable

Answer: c

Explanation: Poles are the roots of the denominator of the transfer function and on imaginary axis makes the system stable but multiple poles makes the system unstable.

8. The forward path transfer function is given by G = 2/s. Obtain an expression for unit step response of the system.

a) 1+2e -t +e -2t

b) 1+e -t -2e -2t

c) 1-e -t +2e -2t

d) 1-2e -t +e +2t

Answer: d

Explanation: C/R = s/(s 2 +3s+2)

C = 1/s-2/s+1+1/s+2

c = 1-2e -t +e +2t .

9. Find the initial and final values of the following function:

F = 12/s^2

a) 1,∞

b) 0,∞

c) ∞,1

d) 0,1

Answer: d

Explanation: Using final and initial values theorem directly to find initial and final values but keeping in mind that final value theorem is applicable for stable systems only.

Answer: d

Explanation: Differentiating the equation and getting the impulse response and then taking the inverse Laplace transform and converting the form into time constant form we get K = -7.5.

This set of Control Systems Questions and Answers for Experienced people focuses on ” Time Response of Second Order Systems – II”.

1. What will be the nature of time response if the roots of the characteristic equation are located on the s-plane imaginary axis?

a) Oscillations

b) Damped oscillations

c) No oscillations

d) Under damped oscilaations

Answer: c

Explanation: complex conjugate : oscillatory 

Complex conjugate : unstable .

2. Consider a system with transfer function G = s+6/Ks 2 +s+6. Its damping ratio will be 0.5 when the values of k is:

a) 2/6

b) 3

c) 1/6

d) 6

Answer: c

Explanation: s+6/K[s 2 +s/K+6/K] Comparing with s 2 +2Gw+w 2

w= √6/K

2Gw=1/K

2*0.5*√6/K =1/K

K=1/6.

3. The output in response to a unit step input for a particular continuous control system is c= 1-e -t . What is the delay time Td?

a) 0.36

b) 0.18

c) 0.693

d) 0.289

Answer: c

Explanation: The output is given as a function of time. The final value of the output is lim n->∞ c=1; . Hence Td  is the solution of 0.5=1-e -Td , and is equal to ln 2 or 0.693 sec.

4. Which one of the following is the most likely reason for large overshoot in a control system?

a) High gain in a system

b) Presence of dead time delay in a system

c) High positive correcting torque

d) High retarding torque

Answer: c

Explanation: Large overshoot refers to the maximum peak in the response of the closed loop system and this is mainly due to the high positive correcting torque.

5. For the system 2/s+1, the approximate time taken for a step response to reach 98% of its final value is:

a) 1s

b) 2s

c) 4s

d) 8s

Answer: c

Explanation: C/R = 2/s+1

R = 1/s 

C = 2/s

c = 2[1-e -t ] 1.96 = 2[1-e -T ] T= 4sec.

6. The unit step response of a second order system is = 1-e -5t -5te -5t . Consider the following statements:

1. The under damped natural frequency is 5 rad/s.

2. The damping ratio is 1.

3. The impulse response is 25te -5t .

Which of the statements given above are correct?

a) Only 1 and 2

b) Only 2 and 3

c) Only 1 and 3

d) 1,2 and 3

Answer: d

Explanation: C = 1/s-1/s+5-5/^2

C = 25/s(s 2 +10s+25)

R = 1/s

G = 25/(s 2 +10s+25 )

w= √25

w = 5 rad/sec

G = 1.

7. The loop transfer function of controller Gc is :

a) 1+0.1s/s

b) -1+0.1s/s

c) –s/s+1

d) s/s+1

Answer: a

Explanation: The transfer function of the controller is 0.1s+1/s

Gc = 0.1s+1/s.

8. The peak percentage overshoot of the closed loop system is :

a) 5.0%

b) 10.0%

c) 16.3%

d) 1.63%

Answer: c

Explanation: C/R = 1/s 2 +s+1

C/R = w/ws 2 +2Gws+w 2

Compare both the equations,

w = 1 rad/sec

2Gw = 1

Mp = 16.3 %

9. Consider a second order all-pole transfer function model, if the desired settling time is 0.60 sec and the desired damping ratio 0.707, where should the poles be located in s-plane?

a) -5+j4√2

b) -5+j5

c) -4+j5√2

d) -4+j7

Answer: b

Explanation: G = 1/√2

Gw = 5

s = -5+j5.

Answer: d

Explanation: Maximum overshoot, rise time and delay time are the major factor of the transient behaviour of the system and determines the transient characteristics.

This set of Control Systems Questions and Answers for Experienced people focuses on ” Time Response of Second Order Systems – II”.

1. What will be the nature of time response if the roots of the characteristic equation are located on the s-plane imaginary axis?

a) Oscillations

b) Damped oscillations

c) No oscillations

d) Under damped oscilaations

Answer: c

Explanation: complex conjugate : oscillatory 

Complex conjugate : unstable .

2. Consider a system with transfer function G = s+6/Ks 2 +s+6. Its damping ratio will be 0.5 when the values of k is:

a) 2/6

b) 3

c) 1/6

d) 6

Answer: c

Explanation: s+6/K[s 2 +s/K+6/K] Comparing with s 2 +2Gw+w 2

w= √6/K

2Gw=1/K

2*0.5*√6/K =1/K

K=1/6.

3. The output in response to a unit step input for a particular continuous control system is c= 1-e -t . What is the delay time Td?

a) 0.36

b) 0.18

c) 0.693

d) 0.289

Answer: c

Explanation: The output is given as a function of time. The final value of the output is lim n->∞ c=1; . Hence Td  is the solution of 0.5=1-e -Td , and is equal to ln 2 or 0.693 sec.

4. Which one of the following is the most likely reason for large overshoot in a control system?

a) High gain in a system

b) Presence of dead time delay in a system

c) High positive correcting torque

d) High retarding torque

Answer: c

Explanation: Large overshoot refers to the maximum peak in the response of the closed loop system and this is mainly due to the high positive correcting torque.

5. For the system 2/s+1, the approximate time taken for a step response to reach 98% of its final value is:

a) 1s

b) 2s

c) 4s

d) 8s

Answer: c

Explanation: C/R = 2/s+1

R = 1/s 

C = 2/s

c = 2[1-e -t ] 1.96 = 2[1-e -T ] T= 4sec.

6. The unit step response of a second order system is = 1-e -5t -5te -5t . Consider the following statements:

1. The under damped natural frequency is 5 rad/s.

2. The damping ratio is 1.

3. The impulse response is 25te -5t .

Which of the statements given above are correct?

a) Only 1 and 2

b) Only 2 and 3

c) Only 1 and 3

d) 1,2 and 3

Answer: d

Explanation: C = 1/s-1/s+5-5/^2

C = 25/s(s 2 +10s+25)

R = 1/s

G = 25/(s 2 +10s+25 )

w= √25

w = 5 rad/sec

G = 1.

7. The loop transfer function of controller Gc is :

a) 1+0.1s/s

b) -1+0.1s/s

c) –s/s+1

d) s/s+1

Answer: a

Explanation: The transfer function of the controller is 0.1s+1/s

Gc = 0.1s+1/s.

8. The peak percentage overshoot of the closed loop system is :

a) 5.0%

b) 10.0%

c) 16.3%

d) 1.63%

Answer: c

Explanation: C/R = 1/s 2 +s+1

C/R = w/ws 2 +2Gws+w 2

Compare both the equations,

w = 1 rad/sec

2Gw = 1

Mp = 16.3 %

9. Consider a second order all-pole transfer function model, if the desired settling time is 0.60 sec and the desired damping ratio 0.707, where should the poles be located in s-plane?

a) -5+j4√2

b) -5+j5

c) -4+j5√2

d) -4+j7

Answer: b

Explanation: G = 1/√2

Gw = 5

s = -5+j5.

Answer: d

Explanation: Maximum overshoot, rise time and delay time are the major factor of the transient behaviour of the system and determines the transient characteristics.

This set of Control Systems test focuses on “Time Response of Second Order Systems – IV”.

1. The standard second order system to a unit step input shows the 0.36 as the first peak undershoot, hence its second overshoot is:

a) 0.135

b) 0.216

c) 0.1296

d) 0.116

Answer: b

Explanation: Overshoot and undershoot are calculated from the formula of peak time as odd peaks denote the overshoot and even denotes the under shoot.

2. Consider the input with the inputs 4 u and the impulse response 5 +7 , the time constants of the output are,

a) 0.2, 0.33 and 0.5

b) 4.5 and 7

c) 0.2, 0.4 and 0.7

d) 0.2, 0.1 and 0.25

Answer: a

Explanation: Output response so calculated is the inverse Laplace transform of the input and impulse response and hence converting the resultant form in the time constant form time constant can be directly determined.

3. In a second order feedback control system natural frequency and damping

a) Can be designed by changing the gain of the individual system

b) Cannot be designed by changing the gain of the individual system

c) Are independent on the type of input excitation

d) None of the mentioned

Answer: a

Explanation: Natural frequency and damping can be designed by changing the gain of the individual system.

4. Undamped natural frequency of a second order system has the following influence on the response due to various excitations:

a) Increase in speed of response and decrease sensitivity

b) Decrease in speed of response and increase sensitivity

c) Has no influence in the dynamic response

d) Increase oscillatory behavior

Answer: a

Explanation: Undamped natural frequency is the frequency that has suffered damping and gets affected by the increase in the speed of response and decrease in sensitivity.

5. Normalized response of a dynamic system refers to:

a) Characteristic feature of a response due to specific excitation irrespective of its amplitude

b) Response of dynamic system divided by its maximum value

c) Response of dynamic system divided by a standard value

d) None of the mentioned

Answer: a

Explanation: Normalization refers to the desired to the reference value and normalized response of the dynamic system refers to the characteristic feature of a response due to specific excitation irrespective of its amplitude.

6. The transfer function of a system is G = 100/ . For a unit step input to the system the approximate settling time for 2% criterion is:

a) 100 sec

b) 4 sec

c) 1 sec

d) 0.01 sec

Answer: b

Explanation: Comparing the equation with the characteristic equation and then finding the value of G and w and calculating the value of settling time as 4 sec from 4/Gw.

7. The characteristic equation of a control system is s(s 2 + 6s+13)+K=0. The value of k such that the characteristic equation has a pair of complex roots with real part -1 will be :

a) 10

b) 20

c) 30

d) 40

Answer: b

Explanation: The characteristic equation is considered and the values of G and w are calculated and further the value of k can be calculated.

8. Normalized difference between the time response peak and steady state output is ______________

a) Maximum peak overshoot

b) Damping factor

c) Minimum peak overshoot

d) Undershoot

Answer: a

Explanation: Maximum peak overshoot is the normalized difference between the time response peak and steady state output.

9. Rise time, Peak time, maximum peak overshoot, settling time, and steady state error are mutually dependent.

a) True

b) False

Answer: a

Explanation: Rise time, peak time, settling time and maximum peak overshoot are the prime factors of the time domain analysis and they must be specified in a consistent manner but they are mutually dependent.

Answer: b

Explanation: Practically there are some non-linearity present in the system as friction but in mathematical model these are considered by considering high gain and lower damping.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Steady-state Errors and Error Constants”.

1. The steady state error for a unity feedback system for the input r = Rt^2/2 to the system G = K/s(s 3 +7s 2 +12s) is

a) 0

b) 6R/K

c) ∞

d) 3R/K

Answer: b

Explanation: Ka = 2K/12 = K/6

Ess = 6R/K.

2. A control system is operated with a parabolic input as shown below

control-systems-questions-answers-steady-state-error-constants-q2

If Ka is static error constant of the system, then its dynamic error constant K2 is

a) 0.01

b) 0.02

c) 0.03

d) 0.04

Answer: b

Explanation: Ka = 100/

K2 = 1/50 = 0.02.

3. Find the velocity error constant of the system given below :

control-systems-questions-answers-steady-state-error-constants-q3

a) 0

b) 2

c) 4

d) ∞

Answer: c

Explanation: Comparing with the characteristic equation the values of G and w are calculated as G = 1 and w = 4 and hence the system is critically damped.

4. Consider the unity feedback system with open loop transfer function the minimum value of the steady state error to a ramp input r = 6tu is OLTF = K/s

a) 1

b) 2

c) 3

d) 4

Answer: b

Explanation: Routh-Hurwitz criterion is used to calculate the stability of the system by checking the sign changes of the first row and from Routh-Hurwitz criterion maximum value of K = 6 ess = A/Kv for type-1 system and A = 6then for Kv = K/2, ess = 2.

5. A ramp input applied to a unity feedback system results in 5% steady state error. The type number and zero frequency gain of the system are respectively

a) 1 and 20

b) 0 and 20

c) 0 and 1/20

d) 1 and 1/20

Answer: a

Explanation: Steady state error is the error calculated between the final output and desired output and for the good control system the error must be less and this steady state error is inversely proportional to gain.

6. A particular control system yielded a steady state error of 0.20 for unit step input. A unit integrator is cascaded to this system and unit ramp input is applied to this modified system. What is the value of steady-state error for this modified system?

a) 0.10

b) 0.15

c) 0.20

d) 0.25

Answer: d

Explanation: The integrator is similar to the phase lag systems and it is used to reduce or eleminate the steady state error and when it is cascaded with the ramp input hence the acceleration error constant is calculated which is equal to 0.25.

7. The error constants described are the ability to reduce the steady state errors.

a) True

b) False

Answer: a

Explanation: As the type of the system becomes higher more steady state errors are eliminated.

8. Systems of type higher than 2 are not employed in practice.

a) True

b) False

Answer: a

Explanation: These are more difficult to stabilize and dynamic errors are much larger.

9. Steady state refers to

a) Error at the steady state

b) Error at the transient state

c) Error at both state

d) Precision

Answer: a

Explanation: Steady state errors are the change in the output at the steady state with respect to the change in the input.

Answer: c

Explanation: The disadvantages of the error constants are as they do not give the information of the steady state error when the inputs are other than the three basic types and error constant fail to indicate the exact manner in which the error function change with time.

This set of Control Systems Quiz focuses on “Effect of Adding a Zero to a system and Design Specifications of Second-Order Systems”.

1. Assertion : The zeroes on the real axis near the origin are generally avoided in design.

Reason : In a sluggish system introduction of zeroes can improve the transient response

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: b

Explanation: Zero is defined as the root of the numerator of the transfer function and zero is to introduce a pronounced peak to the system’s response whereby the peak overshoot may increase appreciably.

2. Addition of zero increases the stability.

a) True

b) False

Answer: a

Explanation: Zero is defined as the root of the numerator of the transfer function and addition of zeroes increases the stability as the speed of response increases.

3. Zeroes are defined as:

a) Roots of the denominator of the closed loop transfer function

b) Roots of the numerator of the closed loop transfer function

c) Parts of the numerator

d) Parts of the denominator

Answer: b

Explanation: Zeroes are the roots of the numerator of the closed loop system and addition of the zeroes increases the stability of the closed loop system.

4. As zero moves sufficiently left from the origin the effect of zero becomes less pronounced.

a) True

b) False

Answer: a

Explanation: The effect of zero on transient response will be negligible if the zero moves left from the origin as the zero which is nearer to the origin is more dominant.

5. If number of poles are greater than number of zeroes then the system is known as ______________

a) Stable system

b) Unstable system

c) Minimum phase system

d) Non-minimum phase system

Answer: c

Explanation: Minimum phase system is defined as the perfect system with zeroes greater than poles and also the zeroes and poles lying on the left half of the s plane entirely.

6. A control system is generally met with the time response specifications:

a) Steady state accuracy

b) Damping factor

c) Setting time

d) All of the mentioned

Answer: d

Explanation: Steady state error, damping factor and settling times are the specifications are needed to control the system’s stability and speed of response.

7. Steady state accuracy specified in terms of:

a) Steady state error

b) Damping ratio

c) Natural frequency

d) All of the mentioned

Answer: a

Explanation: Steady state accuracy entirely depends on the accuracy of steady state which is determined by steady state error which is the difference between the final output and desired output.

8. Steady state accuracy is determined by suitable choice of____________

a) Steady error

b) Error constants

c) Damping

d) Transient error

Answer: b

Explanation: Steady state accuracy is determined by suitable choice of error constants Kv, Kp and Ka depending upon the type of the system.

9. Damping factor specifies:

a) Peak overshot to step input.

b) Steady state error

c) Damping ratio

d) Natural frequency

Answer: a

Explanation: Maximum peak overshoot is the maximum peak of the transient response at the resonant frequency and is so calculated as to determine the value of damping factor.

Answer: b

Explanation: Rise time and settling time determine the speed of response as if the values of both these if less then the speed of response will be more and both of these depend on the damping factor and natural frequency.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Effect of Adding a Zero to a System – II”.

1. Which of the following can be measured by the use of a tacho-generator?

a) Acceleration

b) Speed

c) Speed and acceleration

d) Displacement

Answer: b

Explanation: Tacho generator is used to measure the velocity or relative velocity of the system.

2. _____________ is not a final control element.

a) Control valve

b) Potentiometer

c) Electro-pneumatic converter

d) Servomotor

Answer: b

Explanation: Potentiometer among all the options cannot be the final control element as this is responsible to get the output in measurable form.

3. Which of the following is the definition of proportional band of a controller?

a) The range of air output as measured variable varies from maximum to minimum

b) The range of measured variables from set value

c) The range of measured variables through which the air output changes from maximum to minimum

d) All of the mentioned

Answer: c

Explanation: Proportional band controller is the range of measured variables through which the air output changes from maximum to minimum.

4. In pneumatic control systems the control valve used as final control element converts

a) Pressure signal to electric signal

b) Pressure signal to position change

c) Electric signal to pressure signal

d) Position change to pressure signal

Answer: b

Explanation: In pneumatic control systems the control valve is used as the final control element to convert pressure signal to position change.

5. Pressure error can be measured by which of the following?

a) Differential bellows and strain gauge

b) Selsyn

c) Strain gauge

d) Strain gauge and potentiometer

Answer: a

Explanation: Pressure error can be measured by differential bellows and strain gauge.

6. Assertion : Feedback compensation is preferred to series compensation.

Reason : No amplification is required as the energy flows from higher to lower levels.

a) Both assertion and reason are true and R is correct explanation of A

b) Both A and R true but R is not correct explanation of A

c) A is true but R is false

d) A is False but R is true

Answer: a

Explanation: Feedback compensation is preferred to series compensation or cascade compensation because:

In a feedback compensator energy transfer is from higher to a lower one thereby obviating the need for the feedback amplification.

7. Assertion : A PI controller increases the order of the system by units but decreases the steady state error.

Reason : A PI controller introduces a pole at either the origin or at a desired points on the negative real axis.

a) Both assertion and reason are true and R is correct explanation of A

b) Both A and R true but R is not correct explanation of A

c) A is true but R is false

d) A is False but R is true

Answer: a

Explanation: I is proportional +integral controller. Thus integral controller add a pole either at origin or at the desired point on the negative real axis, so order of the system gets increased but it reduces the steady state error of the offset error.

8. Assertion : A derivative controller produces a control action for constant error only.

Reason : The PD controller increases the damping and reduces the peak overshoot.

a) Both assertion and reason are true and R is correct explanation of A

b) Both A and R true but R is not correct explanation of A

c) A is true but R is false

d) A is False but R is true

Answer: d

Explanation: The integral control action produces a control action for error constant not derivative controller. A derivative controller improves the transient state of the control system apart from increasing the bandwidth, overshoot and rise time.

9. A plant is controlled by a proportional controller, if time delay element is introduced in the loop its:

a) Phase margin remains the same

b) Phase margin increases

c) Phase margin decreases

d) Gain margin increases

Answer: c

Explanation: When a delay element is introduces in a control system, it only affects the phase margin of the system and new value of the phase margin is decreased.

Answer: a

Explanation: A lead compensator provides a better gain margin by introducing a positive shift in the phase plot and thus increasing the phase crossover frequency. Thus the system becomes comparatively more stable by using a lead compensator.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Design Considerations for Higher-Order Systems”.

1. Which one of the following statements is correct?

The effects of the phase lead compensator or gain cross over frequency and the bandwidth are:

a) That both are decreased

b) That gain cross over frequency reduces but BW is increased

c) That gain cross over frequency increases but BW is decreased

d) That both are increased

Answer: d

Explanation: Phase lead compensator acts like a high pass filter. So gain crossover frequency and bandwidth both increases.

2. How does cascading an integral controller in the forward path of a control system affect the relative stability  and the steady-state error of that system?

a) RS and SSE are increased

b) RS is reduced nut SSE is increased

c) RS is increased but SSE is reduced

d) RS and SSE are reduced

Answer: d

Explanation: Integral Controller acts like a low pass filter. It reduces the stability as well as steady state error.

3. With regard to the filtering property, the lead compensator and the lag compensator are respectively :

a) Low pass and high pass filters

b) High pass and low pass filters

c) Both high pass filter

d) Both low pass filters

Answer: b

Explanation: Lead compensator is a high pass filter and Lag compensator is a low pass filter.

4. What is the effect of phase-lag compensation on the performance of the servo system?

a) For a given relative stability, the velocity constant is increased

b) For a given relative stability, the velocity constant is decreased

c) The bandwidth of the system is increased

d) The time response is made faster

Answer: a

Explanation: Phase lag compensation is an integrator. It reduces the steady state error. Velocity constant = 1/ . So, the velocity constant is increased.

5. Which one of the following is an advantage of a PD controller in terms of damping and natural frequency?

a) G remains fixed but natural frequency increases

b) G remains fixed but natural frequency decreases

c) Natural frequency fixed but G increases

d) Natural frequency fixed but G decreases

Answer: c

Explanation: Comparing with the characteristic equation natural frequency remains fixed but the value of G that increases hence the transient response is improved.

6. Which one of the following is a disadvantage of proportional controller?

a) It is destabilizes the system

b) It produces offset

c) It makes the response faster

d) It has very simple implementation

Answer: b

Explanation: Main disadvantage of proportional controller is produces the permanent error is called offset error.

7. A process is controlled by PID controller. The sensor has high, measurement noise. How can the effect be reduced?

a) By use of bandwidth limited derivative term

b) By use of proportional and derivative terms in the forward path

c) By use of high proportional band

d) By use of low integral gain

Answer: b

Explanation: The effect of noise can be reduced by the use of proportional and derivative controller in the forward path.

8. Consider the following statements for a PI compensator for control system.

1. It is equivalent to adding a zero at origin

2. It reduces overshoot

3. It improves the steady state error of the system

Which of the statements given above are correct?

a) 1 and 3

b) 1,2 and 3 only

c) 2 and 3

d) 1 only

Answer: c

Explanation: PI compensator adds one open loop pole at origin and open loop zero at negative real axis.

9. The input to a controller is :

a) Sensed signal

b) Error signal

c) Desired variable value

d) Signal of fixed amplitude not dependent on desired value

Answer: b

Explanation: Input to the controller is always the parameter of the system which is to be controlled that is the desirable value.

Answer: In a good control system, output is sensitive to input variations but insensitive to parameter variations.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Performance Indices”.

1. If the performance index of a phase lead compensator is /  and that of a lag compensator is /, then which one of the following sets of conditions must be satisfied?

a) a>b and p<q

b) a>b and p<q

c) a<b and p<q

d) a<b and p>q

Answer: d

Explanation: In phase lead compensator, zero is nearer to origin. In phase lag compensator, pole is nearer to origin.

2. The compensator Gc =5/ would provide a maximum phase shift of:

a) 20°

b) 45°

c) 30°

d) 60°

Answer: c

Explanation: Maximum phase shift sin ^ ⁡ [/] and sin ^ ⁡[1/2] = 30°.

3. The industrial controller having the best steady-state accuracy is:

a) A derivative controller

b) An integral controller

c) A rate feedback controller

d) A proportional controller

Answer: a

Explanation: The best steady state accuracy is of derivative controller and this is due to the fact that derivative controller is only affected by the steady state response not the transient response.

4. Assertion : An on-off controller gives rise to self-sustained oscillation in output.

Reason : Location of a pair of poles on the imaginary axis gives to self-sustained oscillation is output.

a) Both A and R true and R is correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) A is true and R is False

d) A is False and R is True

Answer: a

Explanation: An off-off controller is the initial version of the proportional controller and it gives the self-sustained oscillations and location of poles on the imaginary axis gives the self-sustained oscillations.

5. Consider the following statement:

A proportional plus derivative controller

1. Has high sensitivity

2. Increases the stability of the system

3. Improves the steady state accuracy

Which of these statements are correct?

a) 1,2 and 3

b) 1 and 2

c) 2 and 3

d) 1 and 3

Answer: b

Explanation: A proportional plus derivative controller has the following features as it adds open loop zero on the negative real axis, peak overshoot decreases, bandwidth increases and rise time decreases.

6. Which one of the following compensation is required for improving the transient response of the system?

a) Phase lead compensation

b) Phase lag compensation

c) Gain compensation

d) Both phase lag compensation and gain compensation

Answer: a

Explanation: For increasing or improving the transient response derivative controller is used and which is the phase lead compensation.

7. Pneumatic controller are :

a) Flexible operation

b) High torque high speed operation

c) Fire and explosion proof operation

d) No leakage

Answer: c

Explanation: Pneumatic controllers are fire and explosion proof operation as they require air and gas fuel for its operation.

8. Hydraulic controller :

a) Flexible operation

b) High torque high speed operation

c) Fire and explosion proof operation

d) No leakage

Answer: b

Explanation: Hydraulic controller must have no leakage and also it requires high torque and high speed operation due to high density of the controller.

9. Electronic Controller :

a) Flexible operation

b) High torque high speed operation

c) Fire and explosion proof operation

d) No leakage

Answer: a

Explanation: Flexible in all sense as it does not require heavy components or extra torque or high speed operations.

Answer: c

Explanation: The introduction of a time delay element decreases both the phase and gain margin.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Robotic Control System – I”.

1. Assertion : The servo robot is a closed loop system

Reason: It allows for a feedback

a) Both A and R are true and R is not correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: a

Explanation: A servomechanism, sometimes shortened to servo, is an automatic device that uses error-sensing negative feedback to correct the performance of a mechanism and is defined by its function and the servo robot is a closed loop system as it allows for a feedback.

2. A__________ translates signals from the controller into the motor voltage and current signals.

a) Servo motor

b) Servo amplifier

c) AC motor

d) DC motor

Answer: b

Explanation: A servo amplifier monitors the feedback signal from the servomechanism and continually adjusts for deviation from expected behaviour and translates signals from the controller into the motor voltage and current signals.

3. Motors used for electronic actuator drives :

a) AC servo motors

b) DC servo motors

c) Stepper motors

d) All of the mentioned

Answer: d

Explanation: Motors are the devices that convert the mechnical energy into electrical energy and can be used in many applications and used for electronic actuator drives are AC, DC, and stepper motors.

4. The basic components of hydraulic fluid power system are :

a) Reservoir

b) Pump and lines

c) Actuating devices and control valves

d) All of the mentioned

Answer: d

Explanation: Hydraulic fluid power system are the systems that use the control action in which the control motion is of hydraulic motion and main components are reservoir pump and lines, actuating devices and control valves.

5. Pumps that discharge liquid in a continuous flow are referred to as non-positive displacement.

a) True

b) False

Answer: a

Explanation: Pumps can be classified as non-positive and positive displacement and that discharge liquid in a continuous flow are referred to as non-positive displacement.

6. Connectors and fittings are used in the fluid power system :

a) To connect to various sections of the fluid lines to each other

b) To detach the fluid lines to the components of the system

c) They are used in the high pressure fluid system

d) None of the mentioned

Answer: a

Explanation: Connectors and fittings are used in the fluid power system to connect to various sections of the fluid lines to each other and to attach the fluid lines to the components of the system.

7. ____________ is the back and forth motion of pistons inside of cylinders that provide the flow of fluid.

a) Fluid pump

b) Gravity pump

c) Reciprocating pump

d) Displacement pump

Answer: c

Explanation: Reciprocating Pump is a type of positive pumps which includes the piston pump, plunger pump and diaphragm pump and provides the flow of fluid in the cylinder by back and forth motion of the piston.

8. Assertion : It is all but impossible to design a practical fluid power system without some means of controlling the volume and pressure of the fluid.

Reason : It is controlled and done by valves.

a) Both A and R are true and R is not correct explanation of A.

b) Both A and R are true but R is not correct explanation of A.

c) A is true but R is false

d) A is false but R is true

Answer: a

Explanation: Valves is defined as any device by which the flow of liquid can be controlled by obstructing the flow of liquid and is all but impossible to design a practical fluid power system without some means of controlling the volume and pressure of the fluid.

9. Deciding the method of control by:

a) The purpose of valve

b) Type of fluid

c) Design and purpose of the system

d) All of the mentioned

Answer: d

Explanation: Valves may be controlled manually, electrically, mechanically, pneumatically, hydraulically or by combination of these methods and they are used to control the flow of liquid by onstructing the flow.

Answer: d

Explanation: Valve is a device that is used to control the flow of liquid by obstructing the flow and they can be classified based on their structure and their requirement.

This set of Control Systems MCQs focuses on “Robotic Control System – II”.

1. An automatic apparatus or device that performs functions ordinarily ascribed to humans or operate with what appears to be almost human intelligence is called ________

a) Robot

b) Human

c) Animals

d) Reptiles

Answer: a

Explanation: Robot is an automatic apparatus or device that performs functions ordinarily ascribed to humans or operate with what appears to be almost human intelligence.

2. The laws of Robotics are:

a) A robot may not injure a human being

b) A robot must abbey the order given by human except when conflict with the first law

c) A robot must protect its own existence except when it is violating first and second law

d) Both b and c

Answer: d

Explanation: A robot may not injure a human being or through in action, allow human being to be harmed.

3. The basic components of robot are:

a) The mechanical linkage

b) Sensors and controllers

c) User interface and power conversion unit

d) All of the mentioned

Answer: d

Explanation: The basic components of robot are the mechanical linkage, sensors and controllers, User interface and power conversion unit.

4. Assertion : Degree of freedom is defined as the number of variables to define motion in the body in space.

Reason : Maximum degree of freedom can be six in a robot.

a) Both A and R are true and R is not correct explanation of A.

b) Both A and R are true but R is not correct explanation of A.

c) A is true but R is false

d) A is false but R is true

Answer: b

Explanation: Degree of freedom defines the variables responsible for the motion of the robot and allows robot to reach all positions and orientations.

5. A _________ is connection between parts or links in a robot that allow motion.

a) Hinge

b) Joint

c) Dis joint

d) None of the mentioned

Answer: b

Explanation: A joint is connection between parts or links in a robot that allow motion. It has translator and rotatory motion.

6. Classification of Robot is based on:

a) Geometry and geometric classification

b) Left right classification

c) Based on control system

d) All of the mentioned

Answer: d

Explanation: Robots can be classified on the basis of the movement their structure and geometry as humanoid robots and gantry robots.

7. Assertion : The control system of an industrial robot determine its flexibility and efficiency, within the limits set beforehand by the design of the mechanical structure.

Reason : The control system provides a logical sequence for the robot to follow.

a) Both A and R are true and R is not correct explanation of A.

b) Both A and R are true but R is not correct explanation of A.

c) A is true but R is false

d) A is false but R is true

Answer: a

Explanation: The system provides the theoretical position values for each step and continuously measures the actual position during movement.

8. Hierarchical level control involves :

a) Level 1: Actuator control controls individual robot actuators

b) Level 2: Path control coordinates robot path movement

c) Level 3: Main control high level instruction interpreter

d) All of the mentioned

Answer: d

Explanation: Hierarchy refers to the system where some form of levels are used as higher to lower or vice versa and this level control mainly involves actuator control, path control and main control for various functioning of the parts of the robot.

9. Non servo robots are also called as:

a) Pick and place

b) Fixed stop robot

c) Both of the mentioned

d) None of the mentioned

Answer: c

Explanation: Non servo robots are simplest robots as they are the least complex structures and they are made to do some specific and less jobs and it is an open loop system.

Answer: d

Explanation: Non-servo robots are open loop system and less costly and they are less complex and can be used once or twice for some work and they are less reliable.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “State Variable Analysis – I”.

1. Which among the following is a unique model of a system?

a) Transfer function

b) State variable

c) Block diagram

d) Signal flow graphs

Answer: a

Explanation: Transfer Function is defined as the ratio of the Laplace output to the Laplace input with the zero initial conditions and is a unique model of the system.

2. Which among the following is a disadvantage of modern control theory?

a) Implementation of optimal design

b) Transfer function can also be defined for different initial conditions

c) Analysis of all systems take place

d) Necessity of computational work

Answer: d

Explanation: Modern control theory is also not best suited in every respect it has also some disadvantages and the major disadvantage is that it requires computational work.

3. According to the property of state transition method, e0 is equal to _____

a) I

b) A

c) e -At

d) -e At

Answer: c

Explanation: By definition state transition matrix is defined as e -At and this is the matrix that comes into the picture when the total response is considered that is with the free response and forced response.

4. Which mechanism in control engineering implies an ability to measure the state by taking measurements at output?

a) Controllability

b) Observability

c) Differentiability

d) Adaptability

Answer: b

Explanation: Observability and controllability are the two methods to check the output response characteristics and observability in control engineering implies an ability to measure the state by taking measurements at output.

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5. State model representation is possible using _________

a) Physical variables

b) Phase variables

c) Canonical state variables

d) All of the mentioned

Answer: d

Explanation: State model representation is the representation of the control system is the form of the state variables and state vectors and is possible using physical variables, phase variables and canonical state variables.

6. Which among the following constitute the state model of a system in addition to state equations?

a) Input equations

b) Output equations

c) State trajectory

d) State vector

Answer: b

Explanation: Output Equations constitute the state model of a system in addition to state equations and for the complete state model mainly input model, output model and state models are required.

7. Which among the following plays a crucial role in determining the state of dynamic system?

a) State variables

b) State vector

c) State space

d) State scalar

Answer: a

Explanation: State Variables are the integral part of the state variable analysis and plays a crucial role in determining the state of dynamic system.

8. Which among the following are the interconnected units of state diagram representation?

a) Scalars

b) Adders

c) Integrator

d) All of the mentioned

Answer: d

Explanation: Scalars, adders and integrator are the interconnected units of state diagram representation and this representation helps in determination of the state of the control system.

9. State space analysis is applicable even if the initial conditions are _____

a) Zero

b) Non-zero

c) Equal

d) Not equal

Answer: b

Explanation: State space analysis is the analysis different from the transfer function approach as it has state variables and state vectors used for the analysis and can be used even if initial conditions are non-zero.

Answer: a

Explanation: The major advantage of state space analysis is that it can be applied to MIMO systems also while the conventional control theory that is transfer function approach is applicable to the SISO systems only.

This set of Control Systems Multiple Choice Questions & Answers focuses on “State Variable Analysis – II”.

1. State variable analysis has several advantages overall transfer function as:

a) It is applicable for linear and non-linear and variant and time-invariant system

b) Analysis of MIMO system

c) It takes initial conditions of the system into account

d) All of the mentioned

Answer: d

Explanation: State variable analysis has several advantages overall transfer function as it is applicable for linear and non-linear and variant and time-invariant system, analysis of MIMO system, it takes initial conditions of the system into account.

2. The minimum number of states require to describe the two degree differential equation:

a) 1

b) 2

c) 3

d) 4

Answer: b

Explanation: The number of states required to describe a network is equal to the number of energy storing elements in the electrical network.

3. For a system with the transfer function H = 3/s 3 +4s 2 -2s+1 , the matrix A in the state space form is equal to:

control-systems-multiple-choice-questions-answers-q3

Answer: b

Explanation: Taking the inverse Laplace of the equation and converting it into differential equation and solving the state space by considering various matrices.

4. The transfer function Y/U of a system described by the state equations dx/dt=-2x+2u and y = 0.5x is:

a) 0.5/

b) 1/

c) 0.5/

d) 1/

Answer: d

Explanation: Taking Laplace transform of the equation X = 2U/

Then Y/U =1/.

5. A linear time invariant single input single output system has the state space model given by dx/dt=Fx+Gu, y=Hz, where control-systems-multiple-choice-questions-answers-q5 . Here, x is the state vector, u is the input, and y is the output. The damping ratio of the system is:

a) 0.25

b) 0.5

c) 1

d) 2

Answer: b

Explanation: T = 1/(s 2 +2s+4)

G = 0.5.

6. Given the matrix control-systems-multiple-choice-questions-answers-q6 the Eigen value are___________

a) 1,2,3

b) 1

c) -1,-2,-3

d) 0

Answer: c

Explanation: Solving the characteristic equation|SI-A| =0.

7. A transfer function of control system does not have pole-zero cancellation. Which one of the following statements is true?

a) System is neither controllable nor observable

b) System is completely controllable and observable

c) System is observable but uncontrollable

d) System is controllable but unobservable

Answer: b

Explanation: If the input-output transfer function of a linear time-invariant system has pole-zero cancellation, the system will be neither controllable nor observable.

8. The analysis of multiple input multiple output is conveniently studied by;

a) State space analysis

b) Root locus approach

c) Characteristic equation approach

d) Nicholas chart

Answer: a

Explanation: State space analysis is different from the transfer function approach as this can be used for the analysis of multiple input and multiple output system.

9. The state equation in the phase canonical form can be obtained from the transfer function by:

a) Cascaded decomposition

b) Direct decomposition

c) Inverse decomposition

d) Parallel decomposition

Answer: d

Explanation: The state equation from transfer function by parallel decomposition in the phase canonical form.

Answer: b

Explanation: Unstable focus is a logarithmic spiral extending out of the singular point.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “The Approximation of Higher-Order Systems by Lower-Order”.

1. The output of a feedback control system must be a function of

a) Reference and output

b) Reference and input

c) Input and feedback signal

d) Output and feedback signal

Answer: a

Explanation: The output from the feedback control system must be a function of the reference input and output.

2. A control system with excessive noise, is likely to suffer from?

a) Saturation in amplifying stages

b) Loss of gain

c) Vibrations

d) Oscillations

Answer: a

Explanation: A control system with excessive noise suffers from the saturation due to multiple inputs and outputs present and high gain of the system.

3. Zero initial condition for a system means?

a) Input reference signal is zero

b) Zero stored energy

c) Initial movement of moving parts

d) System is at rest and no energy is stored in any of its components

Answer: d

Explanation: Zero initial condition for a system means it has stored energy and system is at rest.

4. Transfer function of a system is used to calculate which of the following?

a) The order of the system

b) The time constant

c) The output for any given input

d) The steady state gain

Answer: c

Explanation: The output of any given system can be calculated by the transfer function of the system and this is the ratio of Laplace output to the Laplace input considering zero initial conditions.

5. The band width, in a feedback amplifier.

a) Remains unaffected

b) Decreases by the same amount as the gain increase

c) Increases by the same amount as the gain decrease

d) Decreases by the same amount as the gain decrease

Answer: c

Explanation: The bandwidth of closed loop system increases hence increasing the noise due to increased bandwidth.

6. On which of the following factors does the sensitivity of a closed loop system to gain changes and load disturbances depend?

a) Frequency

b) Loop gain

c) Forward gain

d) All of the mentioned

Answer: d

Explanation: The sensitivity depends upon the frequency, loop gain and forward gain of the closed loop control system.

7. The transient response, with feedback system,

a) Rises slowly

b) Rises quickly

c) Decays slowly

d) Decays quickly

Answer: d

Explanation: The transient response of the system is improved with the help of the feedback and hence the transient response decays slowly.

8. The second derivative input signals modify which of the following?

a) The time constant of the system

b) Damping of the system

c) The gain of the system

d) The time constant and suppress the oscillations

Answer: d

Explanation: The second derivative of the input signal modify the time constant and suppress the oscillations.

9. Which of the following statements is correct for any closed loop system?

a) All the co-efficient can have zero value

b) All the co-efficient are always non-zero

c) Only one of the static error co-efficient has a finite non-zero value

d) Only two of the static error co-efficient has a finite non-zero value

Answer: c

Explanation: Closed loop system has one of the static error constant for any input that can be position, velocity or acceleration error constant.

Answer: c

Explanation: The system is highly oscillatory or unstable as the value of phase margin must be finite for the stable system.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Concept of Stability”.

1. Stability of a system implies that :

a) Small changes in the system input does not result in large change in system output

b) Small changes in the system parameters does not result in large change in system output

c) Small changes in the initial conditions does not result in large change in system output

d) All of the above mentioned

Answer: d

Explanation: Stability of the system implies that small changes in the system input, initial conditions, and system parameters does not result in large change in system output.

2. A linear time invariant system is stable if :

a) System in excited by the bounded input, the output is also bounded

b) In the absence of input output tends zero

c) Both a and b

d) System in excited by the bounded input, the output is not bounded

Answer: c

Explanation: A system is stable only if it is BIBO stable and asymptotic stable.

3. Asymptotic stability is concerned with:

a) A system under influence of input

b) A system not under influence of input

c) A system under influence of output

d) A system not under influence of output

Answer: b

Explanation: Asymptotic stability concerns a free system relative to its transient behavior.

4. Bounded input and Bounded output stability notion concerns with :

a) A system under influence of input

b) A system not under influence of input

c) A system under influence of output

d) A system not under influence of output

Answer: a

Explanation: BIBO stability concerns with the system that has input present.

5. If a system is given unbounded input then the system is:

a) Stable

b) Unstable

c) Not defined

d) Linear

Answer: c

Explanation: If the system is given with the unbounded input then nothing can be clarified for the stability of the system.

6. Linear mathematical model applies to :

a) Linear systems

b) Stable systems

c) Unstable systems

d) Non-linear systems

Answer: b

Explanation: As the output exceeds certain magnitude then the linear mathematical model no longer applies.

7. For non-linear systems stability cannot be determined due to:

a) Possible existence of multiple equilibrium states

b) No correspondence between bounded input and bounded output stability and asymptotic stability

c) Output may be bounded for the particular bounded input but may not be bounded for the bounded inputs

d) All of the mentioned

Answer: d

Explanation: For non-linear systems stability cannot be determined as asymptotic stability and BIBO stability concepts cannot be applied, existence of multiple states and unbounded output for many bounded inputs.

8. If the impulse response in absolutely integrable then the system is :

a) Absolutely stable

b) Unstable

c) Linear

d) Stable

Answer: a

Explanation: The impulse response must be absolutely integrable for the system to absolutely stable.

9. The roots of the transfer function do not have any effect on the stability of the system.

a) True

b) False

Answer: b

Explanation: The roots of transfer function also determine the stability of system as they may be real, complex and may have multiplicity of various order.

10. Roots with higher multiplicity on the imaginary axis makes the system :

a) Absolutely stable

b) Unstable

c) Linear

d) Stable

Answer: b

Explanation: Repetitive roots on the imaginary axis makes the system unstable.

11. Roots on the imaginary axis makes the system :

a) Stable

b) Unstable

c) Marginally stable

d) Linear

Answer: c

Explanation: Roots on the imaginary axis makes the system marginally stable.

12. If the roots of the have negative real parts then the response is ____________

a) Stable

b) Unstable

c) Marginally stable

d) Bounded

Answer: d

Explanation: If the roots of the have negative real parts then the response is bounded and eventually decreases to zero.

13. If root of the characteristic equation has positive real part the system is :

a) Stable

b) Unstable

c) Marginally stable

d) Linear

Answer: b

Explanation: The impulse response of the system is infinite when the roots of the characteristic equation has positive real part.

14. A linear system can be classified as :

a) Absolutely stable

b) Conditionally stable

c) Unstable

d) All of the mentioned

Answer: d

Explanation: A system can be stable, unstable and conditionally stable also.

Answer: d

Explanation: Relative Stability may be measured by relative settling times of each root or pair of roots.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Necessary Conditions for Stability and Non-Linear Systems”.

1. The techniques of linear system can be used in the non-linear system entirely:

a) True

b) False

Answer: a

Explanation: The techniques of the linear system cannot be entirely used in the non-linear system as they are differentiated by this way only.

2. The disadvantages of the linear system are:

a) The constraints on the linear operation over wide range demands unnecessarily high quality.

b) The restriction to the linear theory may inhibit the designer’s curiosity to deliberately introduce the non-linear components.

c) Practically systems are non-linear

d) All of the mentioned

Answer: d

Explanation: Linear system impose certain restrictions as the components cost is very high and it will cause restriction to operate the otherwise linear components in non-linear region with a view to improve system response.

3. System non-linearities are taken account by:

a) Analytical

b) Graphical and numerical techniques

c) Both a and b

d) None of the mentioned

Answer: c

Explanation: Systems non-linearities are taken into account by the analytical, graphical and numerical techniques.

4. The superposition theorem is :

a) Homogeneity

b) Additivity

c) Combination of homogeneity and additivity

d) Applied to non-linear systems

Answer: c

Explanation: Superposition theorem applies to linear system only and it refers to the additivity and homogeneity.

5. The standard test signal can be applied to give output to:

a) Linear systems

b) Non-linear systems

c) Time variant systems

d) Time invariant systems

Answer: a

Explanation: For linear systems the standard test signals can be applied to give the desired output.

6. The amplitude of the standard test signal does not matter in linear systems:

a) True

b) False

Answer: a

Explanation: The amplitude of the standard test signal is unimportant since any change in input signal amplitude results simply change in response scale with no change in the basic response characteristics.

7. The non-linear systems:

a) Do not obey superposition theorem

b) May be highly sensitive to the input amplitude

c) Laplace and z transform are not applicable to the non-linear systems

d) All of the mentioned

Answer: d

Explanation: The non-linear systems do not obey superposition theorem and also may be highly sensitive to the input impedance and Laplace and z transform are only applicable to the linear systems.

8. The stability of the linear system:

a) Determined by the location of the poles

b) Dependent entirely of whether or the system is driven

c) The stability of the undriven linear system is dependent on the magnitude of the final initial state.

d) Stability cannot be determined by the open loop poles

Answer: a

Explanation: Linear system’s stability can be determined by the location of poles and also it is independent entirely of whether or the system is driven and the stability of the undriven linear system is independent on the magnitude of the final initial state.

9. In non-linear system stability is :

a) Dependent on the input

b) Independent on initial state

c) Independent on input

d) Dependent on input and initial state.

Answer: d

Explanation: In non-linear system the stability is dependent on the input and initial states.

10. Non-linear elements may exhibit___________

a) Linear systems

b) Non-linear systems

c) Limit cycles

d) Time invariant systems

Answer: c

Explanation: Non-linear elements may exhibit the limit cycles which are self-sustained oscillations of fixed frequency and amplitude. Determination of existence of limit cycles is not an easy task as these may depend upon both the type and amplitude of the excitation signal.

11. The necessary condition of stability are:

a) Coefficient of characteristic equation must be real and have the same sign

b) Coefficient of characteristic equation must be non-zero

c) Both of the mentioned

d) Coefficient of characteristic equation must be zero

Answer: c

Explanation: The necessary condition of stability are coefficient of characteristic equation must be real, non-zero and have the same sign.

12. None of the coefficients can be zero or negative unless one of the following occurs:

a) One or more roots have positive real parts

b) A root at origin

c) Presence of root at the imaginary axis

d) All of the mentioned

Answer: d

Explanation: None of the coefficients can be zero or negative unless one or more roots have positive real parts, root at origin and presence of root at the imaginary axis.

13. The __________ of the coefficients of characteristic equation is necessary as well as sufficient condition for the stability of system of first and second order.

a) Negativeness

b) Positiveness

c) Positiveness and Negativeness

d) None of the mentioned

Answer: b

Explanation: The Positiveness of the coefficients of characteristic equation is necessary as well as sufficient condition for the stability of system of first and second order.

14. The Positiveness of the coefficients of characteristic equation is necessary as well as sufficient condition for:

a) First order system

b) Second order system

c) Third order system

d) None of the mentioned

Answer: c

Explanation: It does not ensure the negativeness of the real parts of the complex roots of the third or higher order systems.

Answer: b

Explanation: Routh criterion is in terms of array formulation which is convenient to handle stability problems of higher order systems.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Routh-Hurwitz Stability Criterion”.

1. Routh Hurwitz criterion gives:

a) Number of roots in the right half of the s-plane

b) Value of the roots

c) Number of roots in the left half of the s-plane

d) Number of roots in the top half of the s-plane

Answer: a

Explanation: Routh Hurwitz criterion gives number of roots in the right half of the s-plane.

2. Routh Hurwitz criterion cannot be applied when the characteristic equation of the system containing coefficient’s which is/are

a) Exponential function of s

b) Sinusoidal function of s

c) Complex

d) Exponential and sinusoidal function of s and complex

Answer: d

Explanation: Routh Hurwitz criterion cannot be applied when the characteristic equation of the system containing coefficient/s which is/are exponential, sinusoidal and complex function of s.

3. Consider the following statement regarding Routh Hurwitz criterion:

a) It gives absolute stability

b) It gives gain and phase margin

c) It gives the number of roots lying in RHS of the s-plane

d) It gives gain, phase margin and number of roots lying in RHS of the s-plane

Answer: d

Explanation: Routh Hurwitz gives the absolute stability and roots on the right of the s plane.

4. The order of the auxiliary polynomial is always:

a) Even

b) Odd

c) May be even or odd

d) None of the mentioned

Answer: a

Explanation: Auxiliary polynomial denotes the derivative of the odd equation which is always even.

5. Which of the test signals are best utilized by the stability analysis.

a) Impulse

b) Step

c) Ramp

d) Parabolic

Answer: a

Explanation: Computational task is reduced to much extent.

6. The characteristic equation of a system is given as3s4+10s3+5s2+2=0. This system is :

a) Stable

b) Marginally stable

c) Unstable

d) Linear

Answer: c

Explanation: There is a missing coefficient so the system is unstable.

7. The characteristic equation of a system is given ass3+25s2+10s+50=0. What is the number of the roots in the right half s-plane and the imaginary axis respectively?

a) 1,1

b) 0,0

c) 2,1

d) 1,2

Answer: b

Explanation: The characteristic equation has no sign changes so number of roots on the right half of s plane is zero.

8. Consider the following statement:

a) A system is said to be stable if its output is bounded for any input

b) A system is said to be stable if all the roots of the characteristic equation lie on the left half of the s plane.

c) A system is said to be stable if all the roots of the characteristic equation have negative real parts.

d) A second order system is always stable for finite values of open loop gain

Answer: a

Explanation: A system is stable if its output is bounded for bounded input.

9. The necessary condition for the stability of the linear system is that all the coefficients of characteristic equation 1+GH =0, be real and have the :

a) Positive sign

b) Negative sign

c) Same sign

d) Both positive and negative

Answer: c

Explanation: The necessary condition for the stability of the linear system is that all the coefficients of characteristic equation 1+GH =0, is they must have same sign.

Answer: b

Explanation: For making an unstable system stable gain of the system should be decreased.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Relative Stability Analysis”.

1. A system with unity feedback having open loop transfer function as G = K/s3+as2+2s+1. What values of ‘K’ and ’a’ should be chosen so that the system oscillates ?

a) K =2, a =1

b) K =2, a =0.75

c) K =4, a =1

d) K =4, a =0.75

Answer: b

Explanation: Solving Routh Hurwitz table whenever row of zero occurs, the roots are located symmetrically on the imaginary axis then the system response oscillates, a =1+K/2+K. If K =2 is consider then a =0.75.

2. The open loop transfer functions with unity feedback are given below for different systems.

Among these systems the unstable system is

a) G =2/s+2

b) G =2/s

c) G =2/s ^ 2

d) G =2/s

Answer: c

Explanation: 1+2/s ^ 2 =0. The coefficient of‘s’ is missing. Hence the system is unstable.

3. Determine the stability of closed loop control system whose characteristic equation is

s 5 +s 4 +2s 3 +2s 2 +11s+10=0.

a) Stable

b) Marginally stable

c) Unstable

d) None of the mentioned

Answer: b

Explanation: By Routh array s =0 and s =+j. It is having a pair of conjugate root lying on imaginary axis. System is marginally stable.

4. Determine the condition for the stability of unity feedback control system whose open loop transfer function is given by

G = 2e -st /s

a) T >1

b) T <0

c) T <1

d) T >0

Answer: c

Explanation: G =2/s

By Routh array analysis, for stable system, all the elements of first column need to be positive T<1.

5.Determine the value of K such that roots of characteristic equation given below lies to the left of the line s = -1. s 3 +10s 2 +18s+K.

a) K>16 and K<9

b) K<16

c) 9<K<16

d) K<9

Answer: c

Explanation: In Routh array analysis the first column must be positive and after solving K<16 and K>9.

6. Consider a negative feedback system where G =1/ and H =K/s. The closed loop system is stable for

a) K>6

b) 0<K<2

c) 8<K<14

d) 0<K<6

Answer: d

Explanation: Using Routh array, for stability k<6.

7. The characteristic equation of a feedback control system is s 3 +Ks 2 +9s+18. When the system is marginally stable, the frequency of the sustained oscillation:

a) 1

b) 1.414

c) 1.732

d) 3

Answer: d

Explanation: Solve using Routh array and for the system to be marginally stable, K = -2. Polynomial for sustained oscillation w = 3 rad/s.

8. Consider a characteristic equation, s 4 +3s 3 +5s 2 +6s+k+10=0. The condition for stability is

a) K>5

b) -10<K

c) K>-4

d) -10<K<-4

Answer: d

Explanation: Solve Roth array for the system stable, -10<K<4.

9. The polynomial s 4 +Ks 3 +s 2 +s+1=0 the range of K for stability is _____________

a) K>5

b) -10<K

c) K>-4

d) K-1>0

Answer: d

Explanation: Solving using Routh array we get K-1>0 and is always negative for K>1.

Answer: c

Explanation: There is missing coefficient so system is unstable.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “The Root Locus Concepts”.

1. Which one of the following statements is not correct?

a) Root loci can be used for analyzing stability and transient performance

b) Root loci provide insight into system stability and performance

c) Shape of the root locus gives idea of type of controller needed to meet design specification

d) Root locus can be used to handle more than one variable at a time

Answer: d

Explanation: For more than one variable state space is used.

2. Root locus of s+K =0 is a circle. What are the coordinates of the center of this circle?

a) -2,0

b) -3,0

c) -4,0

d) -5,0

Answer: c

Explanation: s+K =0

1+K/s =0.

GH =K/s

Centre = =.

3. The main objective of drawing root locus plot is :

a) To obtain a clear picture about the open loop poles and zeroes of the system

b) To obtain a clear picture about the transient response of feedback system for various values of open loop gain K

c) To determine sufficient condition for the value of ‘K’ that will make the feedback system unstable

d) Both b and c

Answer: d

Explanation: The main objective of drawing root locus plot is to obtain a clear picture about the transient response of feedback system for various values of open loop gain K and to determine sufficient condition for the value of ‘K’ that will make the feedback system unstable.

4. While increasing the value of gain K, the system becomes

a) Less stable

b) More stable

c) Unstable

d) Absolute stable

Answer: a

Explanation: Damping factor is inversely proportional to gain on increasing gain it reduces hence makes the system less stable.

5. The addition of open loop poles pulls the root locus towards:

a) The right and system becomes unstable

b) Imaginary axis and system becomes marginally stable

c) The left and system becomes unstable

d) The right and system becomes unstable

Answer: d

Explanation: The addition of open loop poles pulls the root locus towards the right and system becomes unstable.

6. Root locus is used to calculate:

a) Marginal stability

b) Absolute stability

c) Conditional stability

d) Relative stability

Answer: d

Explanation: Root locus is used to calculate relative stability.

7. Routh Hurwitz criterion is better than root locus.

a) True

b) False

Answer: b

Explanation: Root locus is better as it require less computation process.

8. Consider the following statements regarding root loci:

a) All root loci start from the respective poles of G H

b) All root loci end at the respective zeros of G H or go to infinity

c) The root loci are symmetrical about the imaginary axis of the s-plane

d) All root loci start and end from the respective poles of G H or go to infinity

Answer: b

Explanation: All the root locus start at respective poles and end at zeroes.

9. Number of roots of characteristic equation is equal to the number of ______________

a) Branches

b) Root

c) Stem

d) Poles

Answer: a

Explanation: Number of roots of characteristic equation is equal to the number of branches.

Answer: c

Explanation: Root locus and Complementary root locus are complementary to each other.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “The Root Locus”.

1. Consider the loop transfer function K/ In the root locus diagram the centroid will be located at:

a) -4

b) -1

c) -2

d) -3

Answer: c

Explanation: Centroid =Sum of real part of open loop pole-sum of real part of open loop zeros/P-Z.

2. Which one of the following applications software’s is used to obtain an accurate root locus for?

a) LISP

b) MATLAB

c) dBase

d) Oracle

Answer: b

Explanation: MATLAB stands for mathematics laboratory in which the input is in the form of the matrix and is the best software for drawing root locus.

3. Which one of the following is not the property of root loci?

a) The root locus is symmetrical about imaginary axis

b) They start from the open loop poles and terminate at the open loop zeroes

c) The breakaway points are determined from dK/ds = 0

d) Segments of the real axis are the part of the root locus if and only is the total number of real poles and zeroes to their right is odd.

Answer: a

Explanation: The root locus is the locus traced due to the gain of the system with changing frequency and need not be symmetrical about origin.

4. The breakaway point calculated mathematically must always lie on the root locus.

a) True

b) False

Answer: a

Explanation: The breakaway point of the two branches of the root locus is the point where the two branches either meet or they break and may or may not always lie on the root locus.

5. What is the number of the root locus segments which do not terminate on zeroes?

a) The number of poles

b) The number of zeroes

c) The difference between the number of poles and zeroes

d) The sum of the number of poles and the number of the zeroes

Answer: c

Explanation: The number of the root locus segments which do not lie on the root locus is the difference between the number of the poles and zeroes.

6. Which one of the following are correct?

The root locus is the path of the roots of the characteristic equation traced out in the s-plane?

a) As the input of the system is changed

b) As the output of the system is changed

c) As a system parameter is changed

d) As the sensitivity is changed

Answer: c

Explanation: The root locus is the locus of the change of the system parameters of the characteristic equation traced out in the s-plane.

7. If the gain of the system is reduced to a zero value, the roots of the system in the s-plane,

a) Coincide with zero

b) Move away from zero

c) Move away from poles

d) Coincide with the poles

Answer: d

Explanation: The roots of the system in s plane coincides with the poles if the gain of the system is reduced to a value zero.

8. The addition of open loop zero pulls the root loci towards:

a) The left and therefore system becomes more stable

b) The right and therefore system becomes unstable

c) Imaginary axis and therefore system becomes marginally stable

d) The left and therefore system becomes unstable

Answer: a

Explanation: The system can become stable by reducing the damping and also by adding zeroes in the s plane and moving left of the s plane system becomes more stable.

9. If root loci plots of a particular control system do not intersect the imaginary axis at any point, then the gain margin of the system will be:

a) 0

b) 0.707

c) 1

d) Infinite

Answer: d

Explanation: The gain margin is the inverse of the intersection of the root loci plot to the imaginary axis and if it does not intersect then the gain margin will be infinite.

Answer: c

Explanation: Branches of the root locus is equal to the number of poles or zeroes which ever is greater and tends toward infinity when poles or zeroes are unequal.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Construction of Root Loci”.

1. With reference to root locus, the complex conjugate roots of the characteristic equation of the O.L.T.F. given below GH =K/ 2 , lie on

a) Straight line

b) Parabola

c) Circle

d) Semi-circle

Answer: c

Explanation: Complex conjugate roots of the characteristic equation of the O.L.T.F.lie on circle.

2. Determine the centroid of the root locus for the system having GH = K/(s 2 +4s+5)

a) -2.1

b) -1.78

c) -1.66

d) -1.06

Answer: Roots of the open loop transfer function are -1,-2+j, -2-j then centroid =Σreal part of open loop pole-Σreal part of open loop zeroes/P-Z

Centroid =-0/3 =-5/3 =-1.66.

3. The loop transfer function of an LTI system is GH =K/s. For K>0, the point on the real axis that does not belong to the root locus of the system is

a) -0.5

b) -2.5

c) -3.5

d) -5.5

Answer: c

Explanation: The points present on the root locus are right to the odd number of poles and zeroes.

4. The angles of asymptotes of the root loci of the equation s 3 +5s 2 +s+K=0 are:

a) 0° and 270°

b) 0° and 180°

c) 90° and 270°

d) 90° and 180°

Answer: c

Explanation: P-Z =2

Angle of asymptote = 180°/P-Z

Angle are 90° and 270°.

5. The intersection of asymptotes of root loci of a system with open loop transfer function GH = K/s is

a) 1.44

b) 1.33

c) -1.44

d) -1.33

Answer: d

Explanation: The intersection of asymptotes of root loci of a system is same as the centroid which is centroid =Σreal part of open loop pole-Σreal part of open loop zeroes/P-Z.

Centroid = -4/3=-1.33.

6. If a feedback control system has its open loop transfer function GH = K/(s 2 +3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will be

a) -5

b) 10

c) 5

d) -10

Answer: b

Explanation: The intersection point on the imaginary axis at s =0 is obtained by Routh Hurwitz criteria making s^0 row zero and getting the value K = 10.

7. The open loop transfer function of the feedback control system is given by G =K/s 2 . The number of asymptotes and the centroid of asymptotes of the root loci of closed loop system is

a) 4 and 

b) 3 and 

c) -4 and 

d) -3 and 

Answer: a

Explanation: Number of Poles = 5

Zeroes =1

Asymptotes =P-Z =4

Centroid =Σreal part of open loop pole-Σreal part of open loop zeroes/P-Z

Centroid = -4-4-5-6+3/4 =-4.

8. The characteristic equation of a control system is given as 1+ K/s(s 2 +2s+2)=0. The real axis intercept for root locus asymptote is:

a) -2.25

b) -1

c) -1.67

d) 0

Answer: c

Explanation: Real axis intercept =centroid

Zero =-4 and Pole = -7, -1, -1, 0

Centroid =Σreal part of open loop pole-Σreal part of open loop zeroes/P-Z

Centroid = -7-1-1+4/3 = -1.67.

9. The OLTF of a unity feedback system is K/ the angle of arrival of the root loci as s =-2, and s =-4 respectively are:

a) 0°,180°

b) 180°,0°

c) 90°,180°

d) 180°, 90°

Answer: b

Explanation: As it is type zero system therefore the angle of arrival can be either 180°, 0°.

Answer: b

Explanation: Differentiating the equation of K with respect to s and equating it to zero.Breakaway points are -2, -2+1.414j,-2-j1.414. so 2 is complex breakaway point.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Frequency Response”.

1. Scientist Bode have contribution in :

a) Asymptotic plots

b) Polar plots

c) Root locus technique

d) Constant M and n circle

Answer: a

Explanation: Asymptotic plots are the bode plots that are drawn to find the relative stability of the system by finding the phase and gain margin and this was invented by Scientist Bode.

2. Scientist Evans have contribution in :

a) Asymptotic plots

b) Polar plots

c) Root locus technique

d) Constant M and n circle

Answer: c

Explanation: Root locus technique is used to find the transient and steady state response characteristics by finding the locus of the gain of the system and this was made Scientist Evans .

3. Scientist Nyquist have contribution in:

a) Asymptotic plots

b) Polar plots

c) Root locus technique

d) Constant M and n circle

Answer: b

Explanation: Nyquist plot is used to find the stability of the system by open loop poles and zeroes and the encirclements of the poles and zeroes and satisfying the equation N=P-Z and this is named under the name of scientist Nyquist.

4. For a stable closed loop system, the gain at phase crossover frequency should always be:

a) < 20 dB

b) < 6 dB

c) > 6 dB

d) > 0 dB

Answer: d

Explanation: Phase crossover frequency is the frequency at which the gain of the system must be 1 and for a stable system the gain is decibels must be 0 db.

5. Which one of the following methods can determine the closed loop system resonance frequency operation?

a) Root locus method

b) Nyquist method

c) Bode plot

d) M and N circle

Answer: d

Explanation: Closed loop system resonance frequency is the frequency at which maximum peak occurs and this frequency of operation can best be determined with the help of M and N circle.

6. If the gain of the open loop system is doubled, the gain of the system is :

a) Not affected

b) Doubled

c) Halved

d) One fourth of the original value

Answer: a

Explanation: Gain of the open loop system is doubled then the gain of the system is not affected as the gain of the system is not dependent on the overall gain of the system.

7. Which one of the following statements is correct?

Nichol’s chart is useful for the detailed study of:

a) Closed loop frequency response

b) Open loop frequency response

c) Close loop and open loop frequency responses

d) None of the mentioned

Answer: a

Explanation: Nichol’s chart has constant M and N circles that are used to find the stability of the system and the detailed study of their can be determined with the help of the closed loop frequency response.

8. Constant M- loci:

a) Constant gain and constant phase shift loci of the closed-loop system.

b) Plot of loop gain with the variation in frequency

c) Circles of constant gain for the closed loop transfer function

d) Circles of constant phase shift for the closed loop transfer function

Answer: d

Explanation: By definition, Constant M loci are Circles of constant phase shift for the closed loop transfer function.

9. Constant N-loci:

a) Constant gain and constant phase shift loci of the closed-loop system.

b) Plot of loop gain with the variation in frequency

c) Circles of constant gain for the closed loop transfer function

d) Circles of constant phase shift for the closed loop transfer function

Answer: c

Explanation: Constant N loci are the circles of constant gain for the closed loop transfer function and the intersection point of the M and N is always the point .

Answer: b

Explanation: Nichol’s chart are plot of loop gain with the variation in frequency and this is used to determine the stability of the system with the variation in the frequency.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Correlation between Time and Frequency Response”.

1. The forward path transfer function of a unity feedback system is given by G = 100/(s 2 +10s+100). The frequency response of this system will exhibit the resonance peak at:

a) 10 rad/sec

b) 8.66 rad/sec

c) 7.07 rad/sec

d) 5rad/sec

Answer: c

Explanation: G = 100/(s 2 +10s+100)

wn = 10rad/sec

G = 10/2wn =0.5

wr = 0.707 rad/s.

2. Assertion : All the systems which exhibit overshoot in transient response will also exhibit resonance peak in frequency response.

Reason : Large resonance peak in frequency response corresponds to a large overshoot in transient response.

a) Both A and R are true and R is the correct explanation of A

b) Both A and R are true and R is not the correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: a

Explanation: For G<1/√2 frequency parameters ex Mr resonant peak and time response parameters eg. Mp peak overshoot are well correlated. For G>1/√2 the resonant peak Mr does not exist and the correlation breaks down. This is not a serious problem as for this range of G, the step response oscillations are well-damped and Mp is hardly perceptible.

3. The transfer function of a system is given by Y/X = e −0.1 s/1+s. If x is 0.5sint, then the phase angle between the output and the input will be:

a) -39.27°

b) -45°

c) -50.73°

d) -90°

Answer: c

Explanation: Phase angle = -tan −1 -0.1*180°/π

w =1 rad/sec

Phase angle =-50.73°.

4. The critical value of gain for the system is 40. The system is operating at a gain of 20. The gain margin of the system is :

a) 2 dB

b) 3 dB

c) 6 dB

d) 4 dB

Answer: c

Explanation: G.M. =Kmarginal/Kdesire

Kmarginal =40

Kdesire = 20

G.M. =2

G.M.  = 6dB.

5. The phase angle of the system G =s+5/s 2 +4s+9;varies between

a) 0° and 90°

b) 0° and -90°

c) 0° and -180°

d) -90° and -180°

Answer: b

Explanation: Phase = tan −1 −11w−w 3 /45− 2 .

6. The open loop transfer function of a system is :

G H =K/   

The phase crossover frequency wpc is:

a) √2

b) 1

c) Zero

d) √3

Answer: b

Explanation: angle =-180°

3wpc/1-2wpc 2 =-3wpc

wpc = 1 rad/sec.

7. Which one of the following statements is correct for gain margin and phase margin of two closed-loop systems having loop functions G H and exp G H?

a) Both gain and phase margins of the two systems will be identical

b) Both gain and phase margins of G H will be more

c) Gain margins of the two systems are the same but phase margins of G H will be more

d) Phase margins of the two systems are the same but gain margin of G H will be less

Answer: c

Explanation: The factor exp  is the cause of the term transportation lag . The effect of e -st term is simply to rotate each point of the G H plot by an angle wT rad in the clockwise direction. So the phase margin of the system reduces as T increases. But since |e -s | =1, therefore the gain margins of both the systems are the same.

8. In a feedback control system, phase margin is

1. Directly proportional to G

2. Inversely proportional to G

3. Independent of G

4. Zero when G =0

Which of the above statements are correct?

a) 1 and 2

b) 2 and 3

c) 3 and 4

d) 1 and 4

Answer: d

Explanation: For small values of G, PM is directly proportional to G and at G =0. P.M. =0.

9. The gain margin in dBs of a unity feedback control system whose open loop transfer function, G H =1/s is

a) 0

b) 1

c) -1

d) ∞

Answer: d

Explanation: wpc = ∞

Magnitude of the transfer function =0

Gain Margin =∞ dB.

Answer: b

Explanation: – π/2-180/π*L*5 = -π

5L =π/2

L =π/10.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Polar Plots”.

1. The constant M circle for M=1 is the

a) straight line x=-1/2

b) critical point 

c) circle with r= 0.33

d) circle with r=0.67

Answer: a

Explanation: For M =1 the constant M circle is a straight line at x=-1/2.

2. The polar plot of a transfer function passes through the critical point . Gain margin is

a) Zero

b) -1dB

c) 1dB

d) Infinity

Answer: a

Explanation: Gain margin of a polar plot passing through the critical point is zero.

3. Consider the following statements:

1. The effect of feedback is to reduce the system error

2. Feedback increases the gain of the system in one frequency range but decreases in another

3. Feedback can cause a system that is originally stable to become unstable

Which of these statements are correct.

a) 1,2 and 3

b) 1 and 2

c) 2 and 3

d) 1 and 3

Answer: c

Explanation: Feedback can cause the increase in gain and also can cause stable system to become unstable.

4. The open loop transfer function of a system is G H= K / 

The phase cross over frequency ωc is

a) V2

b) 1

c) Zero

d) V3

Answer: b

Explanation: Phase crossover frequency is calculated as by calculating the magnitude of the transfer function and equating it to 1 and the frequency calculated at this magnitude is phase cross over frequency.

5. If the gain of the open-loop system is doubled, the gain margin

a) Is not affected

b) Gets doubled

c) Becomes half

d) Becomes one-fourth

Answer: a

Explanation: If the gain of the open-loop system is doubled, the gain margin gets doubled.

6. The unit circle of the Nyquist plot transforms into 0dB line of the amplitude plot of the Bode diagram at

a) 0 frequency

b) Low frequency

c) High frequency

d) Any frequency

Answer: d

Explanation: The unit circle of the Nyquist plot transforms into 0dB line of the amplitude plot of the Bode diagram at any frequency.

7. Consider the following statements:

The gain margin and phase margin of an unstable system may respectively be

1. Positive, positive

2. Positive, negative

3. Negative, positive

4. Negative, negative

Of these statements

a) 1 and 4 are correct

b) 1 and 2 are correct

c) 1, 2 and 3 are correct

d) 2,3 and 4 are correct

Answer: d

Explanation: For unstable system the signs of gain margin and phase margin are always different or they can both be negative.

8. If a system has an open loop transfer function

1-s / 1+s, then the gain of the system at frequency of 1 rad/s will be

a) 1

b) 1/2

c) Zero

d) -1

Answer: d

Explanation: The system is all pass system and the gain of the system at frequency of 1 rad/sec.

9. The polar plot of the open loop transfer function of a feedback control system intersects the real axis at -2. The gain margin of the system is

a) -5dB

b) 0dB

c) -6dB

d) 40dB

Answer: c

Explanation: Gain margin of the system is inverse of the intersect on the real axis and calculated in decibels.

G = 1+s / s.

10. The corner frequencies are

a) 0 and 1

b) 0 and 2

c) 0 and 1

d) 1 and 2

Answer: d

Explanation: Corner frequency can be calculated by time constant form of the transfer function and here the corner frequencies are 1 and 2.

11. For the transfer function

G H = 1 / s , the phase cross-over frequency is

a) 0.5 rad/sec

b) 0.707 rad/sec

c) 1.732 rad/sec

d) 2 rad/sec

Answer: b

Explanation: Phase cross over frequency is calculated at the point where magnitude of the polar plot is 1.

12. The gain margin  of a system having the loop transfer function

G H = 2 / s is

a) 0

b) 3

c) 6

d) 8

Answer: d

Explanation: Gain margin of a system is calculated at the phase cross over frequency and expressed in decibels.

13. The gain margin for the system with open loop transfer function

G H = G =2 / s2 is

a) 8

b) 0

c) 1

d) -8

Answer: 0

Explanation: Gain margin of a system is calculated at the phase cross over frequency and expressed in decibels.

Answer: d

Explanation: All the circles pass through the points  and .

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Bode Plots”.

1. Assertion : Relative stability of the system reduces due to the presence of transportation lag.

Reason : Transportation lag can be conveniently handled by Bode plot.

a) Both A and R are true but R is correct explanation of A

b) Both A and R are true but R is correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: b

Explanation: Transportation lag can be conveniently handled on Bode plot as well without the need to make any approximation.

2. Assertion : The phase angle plot in Bode diagram is not affected by the variation in the gain of the system.

Reason: The variation in the gain of the system has no effect on the phase margin of the system.

a) Both A and R are true but R is correct explanation of A

b) Both A and R are true but R is correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: c

Explanation: The variation in the gain of the system has effect on the phase margin but phase plot is not affected.

3. A system has poles at 0.01 Hz, 1 Hz and 80Hz, zeroes at 5Hz, 100Hz and 200Hz. The approximate phase of the system response at 20 Hz is :

a) -90°

b) 0°

c) 90°

d) -180°

Answer: a

Explanation: Pole at 0.01 Hz gives -180° phase. Zero at 5Hz gives 90° phase therefore at 20Hz -90° phase shift is provided.

4. The constant M-circle represented by the equation x ^ 2+2.25x+y ^ 2=-1.25 has the value of M equal to:

a) 1

b) 2

c) 3

d) 4

Answer: c

Explanation: Comparing with the M circle equation we have the value of M =3.

5. What is the value of M for the constant M circle represented by the equation 8x 2 +18x+8y 2 +9=0?

a) 0.5

b) 2

c) 3

d) 8

Answer: c

Explanation: Comparing with the M circle equation we have the value of M =3.

6. The constant N loci represented by the equation x ^ 2+x+y ^ 2=0 is for the value of phase angle equal to:

a) -45°

b) 0°

c) 45°

d) 90°

Answer: d

Explanation: Centre = 

Centre of N circle is 

N =tanα

α =90°.

7. All the constant N-circles in G planes cross the real axis at the fixed points. Which are these points?

a) -1 and origin

b) Origin and +1

c) -0.5 and 0.5

d) -1 and +1

Answer: a

Explanation: Centre of N circle is 

N =tanα

Constant –N circles always pass through  and .

8. Consider the following statements:

Nichol’s chart gives information about.

i. Closed loop frequency response.

ii. The value of the peak magnitude of the closed loop frequency response Mp.

iii. The frequency at which Mp occurs.

Which of the above statements are correct?

a) 2 and 3

b) 1 and 2

c) 1 and 3

d) 1,2 and 3

Answer: d

Explanation: Nichol’s chart gives information about closed loop frequency response, value of the peak magnitude of the closed loop frequency response Mp and the frequency at which Mp occurs.

9. Which one of the following statements is correct? Nichol’s chart is useful for the detailed study analysis of:

a) Closed loop frequency response

b) Open loop frequency response

c) Close loop and open loop frequency responses

d) None of the above

Answer: a

Explanation: Nichol’s chart is useful for the detailed study analysis of closed loop frequency response.

10. In a bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order all-pole system?

a) -80dB/decade

b) -40 dB/decade

c) 40 dB/decade

d) 80 dB/decade

Answer: a

Explanation: A 4th order all pole system means that the system must be having no zero or s-term in numerator and s 4 terms in denominator. One pole exhibits -20dB/decade slope, so 4 pole exhibits a slope of -80 dB /decade.

11. Frequency range of bode magnitude and phases are decided by :

a) The lowest and higher important frequencies of dominant factors of the OLTF

b) The lowest and highest important frequencies of all the factors of the open loop transfer function

c) Resonant frequencies of the second factors

d) None of the above

Answer: d

Explanation: T. F. = Kp 

There is only one zero which will give slope of +20dB/decade.

12. OLTF contains one zero in right half of s-plane then

a) Open loop system is unstable

b) Close loop system is unstable

c) Close loop system is unstable for higher gain

d) Close loop system is stable

Answer: c

Explanation: OLTF contains one zero in right half of s-plane then Close loop system is unstable for higher gain.

13. The critical value of gain for a system is 40 and gain margin is 6dB. The system is operating at a gain of:

a) 20

b) 40

c) 80

d) 120

Answer: a

Explanation: Gm  = 20log⁡GM

GM =2

As we know, GM =K /K 

K desired =40/2 =20.

14. Nichol’s chart is useful for the detailed study and analysis of:

a) Closed loop frequency response

b) Open loop frequency response

c) Close loop and open loop frequency responses

d) open loop and Close loop frequency responses

Answer: a

Explanation: Nichol’s chart is useful for the detailed study and analysis of closed loop frequency response.

Answer: b

Explanation: Real part represents the damping and imaginary part damped frequency.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “All-pass and Minimum-phase Systems”.

1. A minimum phase unity feedback system has a bode plot with a constant slope of -20dB/decade for all frequencies. What is the value of the maximum phase margins of the system?

a) 0°

b) 90°

c) -90°

d) 180°

Answer: b

Explanation: For given Bode plot, G H =K/jw

As H =1

PM  =90°.

2. The range of K for the stability of system is 0<K<100. For K =10, The gain Margin of the system

a) 10

b) 5

c) 0.1

d) 0.5

Answer: a

Explanation: Gain margin of the system is 10.

3. The frequency at which the Nyquist diagram cuts the unit circle is known as:

a) Gain crossover frequency

b) Phase crossover frequency

c) Damping frequency

d) Corner frequency

Answer: a

Explanation: The frequency at which the Nyquist diagram cuts the unit circle is known as gain cross over frequency.

4. The forward path transfer function of a unity feedback system is given by G = 1/ ^ 2.

What is the phase margin of the system?

a) –π rad

b) 0 rad

c) π/2 rad

d) π rad

Answer: d

Explanation: Magnitude at gain cross over frequency is 1 and PM is π rad.

5. Consider the following statements:

1. The delay time is the time required to reach 50% of the final value in the first time.

2. The rise time is the time required for the response to rise from 10% to 90% of its final value for underdamped systems.

3. The rise time is the time required for the response to rise from 0 to 100% for the underdamped systems.

Which of these statements are correct?

a) 1,2 and 3 only

b) 1 and 2 only

c) 1 and 3 only

d) 2 and 3 only negative real axis

Answer: c

Explanation: The rise time is the time required for the response to rise from 10% to 90% of its final value for overdamped systems.

6. For minimum phase systems:

a) Pole must lie on left plane

b) Zeroes must lie on left plane

c) Poles and zeroes must lie on left plane

d) Both must lie on right plane

Answer: c

Explanation: For minimum phase systems poles and zeroes must lie on the right s-plane.

7. For non-minimum phase systems:

a) Poles and zeroes must lie on the right s-plane

b) Zeroes must lie on right of s-plane

c) Both lie on left of s-plane

d) Poles must be on the left and zeroes can be on the right s –plane.

Answer: d

Explanation: For non-minimum phase systems poles must be on the left and zeroes can be on the right s –plane.

8. For all-pass systems:

a) Poles must lie on right of the s-plane

b) Zeroes must lie on the left of s-plane

c) Poles must lie on the left and zeroes on the mirror image of the pole can be on the right

d) None of the mentioned

Answer: c

Explanation: For all-pass systems poles must lie on the left and zeroes on the mirror image of the pole can be on the right.

9. All pass system and minimum phase system constitute_________________

a) Pole must lie on left plane

b) Minimum phase system

c) Non-minimum phase system

d) Both must lie on right plane

Answer: c

Explanation: All pass system and minimum phase system constitute non-minimum phase system.

Answer: a

Explanation: Minimum phase system has the least phase angle range for a given magnitude curve.

This set of Control Systems online quiz focuses on “Experimental Determination of Transfer Functions”.

1. The impulse response of a LTI system is a unit step function, then the corresponding transfer function is

a) 1/s

b) 1/s 2

c) 1

d) s

Answer: a

Explanation: The impulse response of a LTI system is the transfer function itself and hence for the unit step function . As input then the transfer function will be 1/s.

2. For a type one system, the steady – state error due to step input is equal to

a) Infinite

b) Zero

c) 0.25

d) 0.5

Answer: b

Explanation: The steady state error is defined as the error between the final value and the desired response and the difference in the value of both will be the steady state error due to step input for type one system is zero.

3. The equation 2s 4 +s 3 +3s 2 +5s+10=0 has roots in the left half of s–plane:

a) One

b) Two

c) Three

d) Four

Answer: b

Explanation: The roots of the equation can be calculated using Routh-Hurwitz criterion and hence there are 2 sign changes in the first column of the row and therefore the two roots lie on the right half of s-plane.

4. If the Nyquist plot of the loop transfer function G H  of a closed-loop system encloses the  point in the G H  plane, the gain margin of the system is

a) Zero

b) Greater than zero

c) Less than zero

d) Infinity

Answer: c

Explanation: Nyquist plot deals with the open loop poles and zero and equals the encirclements to the open loop poles of the system.

5. Consider the function F  =5/s (s 2 +s+2) , where F  is the Laplace transform f . Then the final value theorem is equal to

a) 5

b) 5/2

c) Zero

d) Infinity

Answer: b

Explanation: Final value theorem is given for the stable system only and this is a type 1 system and for step input the final value can be calculated as 5/2.

6. The transfer function of a phase-lead controller is given by

a) / , a>1 T>0

b) / , a<1 T>0

c) / , a>1 T>0

d) / , a<1 T>0

Answer: a

Explanation: For the phase lead controller in which the stability and speed of response is more for the system, the magnitude of the pole must be greater than the magnitude of the zero.

7. If the system matrix of a linear time invariant continuous system is given by

Its characteristic equation is given by:

a) s 2 +5s+3=0

b) s 2 -3s-5=0

c) s 2 +3s+5=0

d) s 2 +s+2=0

Answer: a

Explanation: The transfer function is calculated by the state variable analysis and hence the transfer function is calculated by state transition matrix and taking the inverse Laplace transform.

8. Given a unity feedback control system with G  = K/s, the value of K for which the damping ratio is 0.5.

a) 1

b) 16

c) 64

d) 32

Answer: b

Explanation: The value is found by using the Routh- Hurwitz criteria and equating one of the row of the Routh-Hurwitz criteria equal to zero and hence finding the value of K.

9. The LVDT is used in the measurement of:

a) Displacement

b) Acceleration

c) Velocity

d) Humidity

Answer:a

Explanation: The LVDT is the linear variable differential transformer and it is used to calculate the displacement with the inductor process.

Answer: c

Explanation: A system is relative stable not stable if the phase margin is close to zero then the stability is checked by gain margin.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Mathematical Preliminaries”.

1. Which of the following devices is used for conversion of co-ordinates?

a) Microsyn

b) Selsyn

c) Synchro-resolver

d) Synchro-transformer

Answer: c

Explanation: Synchro-Resolver is rotary transformer used for measuring degree of rotation and used for the conversion of the co-ordinates.

2. The effect of error damping is to

a) Provide larger settling lime

b) Delay the response

c) Reduce steady state error

d) All of the mentioned

Answer: c

Explanation: Error damping is to reduce steady state error as it is used to enhance the steady state response of the system and this can be done by increasing the damping of the system.

3. ______________technique gives quick transient and stability response

a) Root locus

b) Bode

c) Nyquist

d) Nichols

Answer: a

Explanation: Root locus is the right technique for the quick transient and stability response and gives the final response and quickly.

4. A phase lag lead network introduces in the output

a) Lag at all frequencies

b) Lag at high frequencies and lead at low frequencies

c) Lag at low frequencies and lead at high frequencies

d) None of the above mentioned

Answer: c

Explanation: A phase lag lead network is the combination of the lead and lag network and also it lags at low frequencies and lead at high frequencies.

5. Which of the following is the non-linearity caused by servomotor?

a) Static friction

b) Backlash

c) Saturation

d) None of the mentioned

Answer: c

Explanation: Linearity in the servo-motor is due to the saturation present and which is the important consideration for any type of the practical device.

6. ____________can be extended to systems which are time-varying?

a) Bode-Nyquist stability methods

b) Transfer functions

c) Root locus design

d) State model representatives

Answer: d

Explanation: State model representation is the best advantage for the systems over transfer function approach as it can be applied for the non-linear systems.

7. Laplace transform is used for the systems with:

a) Initial conditions infinite

b) Initial conditions zero

c) Initial conditions finite

d) Initial conditions equal to the initial input

Answer: b

Explanation: By definition of the transfer function by Laplace transform the initial conditions of the systems are considered to be zero.

8. Which of the following is an electromechanical device?

a) Induction relay

b) Thermocouple

c) LVDT

d) All of the mentioned

Answer: c

Explanation: LVDT is the electromechanical device which converts the displacement of the core to the electrical energy by the action of the transformer.

9. A differentiator is usually not a part of a control system because it

a) Reduces damping

b) Reduces the gain margin

c) Increases input noise

d) Increases error

Answer: c

Explanation: A differentiator is generally not the part of the control system as it increases the input noise due to reduced gain and increased bandwidth.

Answer: a

Explanation: On increasing the gain damping will automatically get reduced and hence the oscillations in the system increases.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Nyquist Stability Criterion”.

1. Which principle specifies the relationship between enclosure of poles & zeros by s-plane contour and the encirclement of origin by q plane contour?

a) Argument

b) Agreement

c) Assessment

d) Assortment

Answer: a

Explanation: Argument principle specifies the relationship between enclosure of poles & zeros by s-plane contour and the encirclement of origin by q plane contour.

2. If a Nyquist plot of G  H  for a closed loop system passes through  point in GH plane, what would be the value of gain margin of the system in dB?

a) 0 dB

b) 2.0201 dB

c) 4 dB

d) 6.0205 dB

Answer: d

Explanation: Gain Margin is calculated by taking inverse of the gain where the Nyquist plot cuts the real axis.

3. For Nyquist contour, the size of radius is _______

a) 25

b) 0

c) 1

d) ∞

Answer: d

Explanation: For Nyquist contour, the size of radius is ∞.

4. Consider a feedback system with gain margin of about 30. At what point does Nyquist plot crosses negative real axis?

a) -3

b) -0.3

c) -30

d) -0.03

Answer: b

Explanation: Gain Margin is always inverse of the point which cuts the Nyquist on the real axis.

5. According to Nyquist stability criterion, where should be the position of all zeros of q corresponding to s-plane?

a) On left half

b) At the center

c) On right half

d) Random

Answer: a

Explanation: According to Nyquist stability criterion zeroes must lie on the left half on the s plane.

6. If the system is represented by G H = k  / s  , what would be its magnitude at ω = ∞?

a) 0

b) ∞

c) 7/10

d) 21

Answer: a

Explanation: On calculating the magnitude of the system and putting the value of frequency one gets the magnitude as 0.

7. Consider the system represented by the equation given below. What would be the total phase value at ω = 0?

200/[s3   ].

a) -90°

b) -180°

c) -270°

d) -360°

Answer: c

Explanation: The phase can be calculated by the basic formula for calculating phase angle.

8. Due to an addition of pole at origin, the polar plot gets shifted by ___ at ω = 0 ?

a) -45°

b) -60°

c) -90°

d) -180°

Answer: c

Explanation: Addition of pole causes instability to the system.

9. In polar plots, if a pole is added at the origin, what would be the value of the magnitude at Ω = 0?

a) Zero

b) Infinity

c) Unity

d) Unpredictable

Answer: b

Explanation: Addition of pole causes instability to the system.

Answer: c

Explanation: Each and every point on the polar plot is the phasor where value of frequency varies.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Time Domain Analysis”.

1. The system with the open loop transfer function 1/s is:

a) Type 2 and order 1

b) Type 1 and order 1

c) Type 0 and order 0

d) Type 1 and order 2

Answer: d

Explanation: Type is defined as the number of poles at origin and order is defined as the total number of poles and this is calculated with the help of the transfer function from the above transfer function the type is 1 and order is 2.

2. The identical first order system have been cascaded non-interactively. The unit step response of the systems will be:

a) Overdamped

b) Underdamped

c) Undamped

d) Critically damped

Answer: d

Explanation: Since both the systems that is the first order systems are cascaded non-interactively, the overall unit step response will be critically damped.

3. A third order system is approximated to an equivalent second order system. The rise time of this approximated lower order system will be:

a) Same as the original system for any input

b) Smaller than the original system for any input

c) Larger than the original system for any input

d) Larger or smaller depending on the input

Answer: b

Explanation: As order of the system increases the system approaches more towards the ideal characteristics and if the third order system is approximated to an equivalent second order system then the rise time of this will be smaller than the original system for any input.

4. A system has a single pole at origin. Its impulse response will be:

a) Constant

b) Ramp

c) Decaying exponential

d) Oscillatory

Answer: a

Explanation: For a single pole at origin the system is of type 1 and impulse response of the system with single pole at the origin will be constant.

5. When the period of the observation is large, the type of the error will be:

a) Transient error

b) Steady state error

c) Half-power error

d) Position error constant

Answer: b

Explanation: The error will be the steady state error if the period of observation is large as the time if large then the final value theorem can be directly applied.

6. When the unit step response of a unity feedback control system having forward path transfer function G  =80/s?

a) Overdamped

b) Critically damped

c) Under damped

d) Un Damped oscillatory

Answer: a

Explanation: The open loop transfer function is first converted into the closed loop as unity feedback is used and then value of damping factor is calculated.

7. With negative feedback in a closed loop control system, the system sensitivity to parameter variation:

a) Increases

b) Decreases

c) Becomes zero

d) Becomes infinite

Answer: b

Explanation: Sensitivity is defined as the change in the output with respect to the change in the input and due to negative feedback reduces by a factor of 1/ .

8. An underdamped second order system with negative damping will have the roots :

a) On the negative real axis as roots

b) On the left hand side of complex plane as complex roots

c) On the right hand side of complex plane as complex conjugates

d) On the positive real axis as real roots

Answer: c

Explanation: An underdamped second order system is the system which has damping factor less than unity and with negative damping will have the roots on the right hand side of complex plane as complex conjugates.

9. Given a unity feedback system with G  =K/ s . What is the value of K for a damping ratio of 0.5?

a) 1

b) 16

c) 4

d) 2

Answer: b

Explanation: Comparing the equation with the standard characteristic equation gives the value of damping factor, natural frequency and value of gain K.

Answer: d

Explanation: Steady state error is the error as it is the difference between the final output and the desired output and by increasing the input the steady state error reduces as it depends upon both the states and input.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Assessment of Relative Stability Using Nyquist Criterion”.

1. The phase margin  of a system having the loop transfer function G H=2√3/s is:

a) 45°

b) -30°

c) 60°

d) 30°

Answer: d

Explanation: Phase margin is calculated at gain cross over frequency where magnitude of the transfer function is 1.

2. The system with the open loop transfer function G H =1/s(s ^ 2+s+1) has the gain margin of :

a) -6 dB

b) 0 dB

c) 3.5 dB

d) 6 dB

Answer: b

Explanation: Gain margin is calculated at phase cross over frequency where the phase is 180°.

3. The phase angle of the system, G =s+5/s 2 +4s+9, varies between :

a) 0° and 90°

b) 0° and -90°

c) 0° and -180°

d) -90° and -180°

Answer: a

Explanation: As it is the type 0 system so the phase angle can be 0° and 90°.

4. The polar plot of the transfer function G = 10/s+10 will be in the :

a) First quadrant

b) Second quadrant

c) Third quadrant

d) Fourth quadrant

Answer: d

Explanation: Polar plot of the given transfer function lies in the fourth quadrant.

5. As the polar plot moves toward the point  then the system becomes :

a) Stable

b) Marginally stable

c) Conditionally stable

d) Unstable

Answer: d

Explanation: As the polar plot moves toward the point  then the system becomes unstable.

6. Polar plots moving toward the imaginary axis makes the system:

a) Stable

b) Marginally stable

c) Conditionally stable

d) Unstable

Answer: d

Explanation: Polar plots moving toward the imaginary axis makes the system unstable.

7. The concepts used to measure relative stability are:

a) Phase margin

b) Gain margin

c) Phase and Gain margin

d) Stable

Answer: c

Explanation: The concepts used to measure relative stability are phase margin and gain margin.

8. Phase and gain margin are applicable to open and closed loop systems both.

a) True

b) False

Answer: b

Explanation: Phase and gain margin are applicable only to open loop systems.

9. Gain margin is:

a) It is a factor by which the system gain can be increased to drive it to the verge of instability

b) It is calculated at gain cross over frequency

c) It is calculated at phase cross over frequency

d) Both a and c

Answer: d

Explanation: Gain margin is a factor by which the system gain can be increased to drive it to the verge of instability and is calculated at phase cross over frequency.

Answer: d

Explanation: Phase margin is the measure of relative stability which is always positive for stable systems.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Closed-Loop Frequency Response”.

1. Closed loop frequency response is very useful as :

a) It approximately predicts the time response of the systems

b) Time response are converted into time domain specifications

c) After design time domain specification is converted into frequency domain

d) All of the mentioned

Answer: d

Explanation: Closed loop frequency response is very useful as it enables to use second order correlations between frequency and transient response.

2. Maximum peak overshoot in time domain corresponds to :

a) Resonance peak

b) Resonant frequency

c) Bandwidth

d) Cut-off rate

Answer: a

Explanation: Resonance peak in frequency domain correspond to maximum peak overshoot in time domain.

3. Frequency of oscillation in time domain correspond to :

a) Resonance peak

b) Resonant frequency

c) Bandwidth

d) Cut-off rate

Answer: b

Explanation: Resonant frequency in frequency domain correspond to frequency of oscillation in time domain.

4. Bandwidth is :

a) Range of frequencies for which the system gain is more than-3dB

b) This is considered good range for transmission of signals

c) For better communication bandwidth of signal must be less

d) All of the mentioned

Answer: d

Explanation: Bandwidth of a signal must be less but channel must be more foe better transmission or communication.

5. Cut-off rate is the ability of the system to distinguish the signal from _____________

a) Bandwidth

b) Noise

c) Resonance peak

d) Magnitude

Answer: b

Explanation: Cut-off rate is the ability of the system to distinguish the signal from noise.

6. The important figures of merit to the system in frequency domain are :

a) Maximum value of resonant peak

b) Value of resonance frequency

c) Maximum value of resonant peak and Value of resonance frequency

d) Minimum value of resonance frequency

Answer: c

Explanation: The important figures of merit to the system in frequency domain are maximum value of resonance peak and frequency at which it occurs.

7. In q plane Nyquist plot is symmetrical about the :

a) Imaginary axis

b) Real axis

c) Origin

d) None of the mentioned

Answer: b

Explanation: By definition, In q plane Nyquist plot is symmetrical about the real axis.

8. A polar plot intersects the unit circle at a point making -45° to the negative real axis then the phase margin of the system is :

a) -45°

b) 45°

c) 180°-45°

d) 180°+45°

Answer: b

Explanation: As the angle is with the negative real axis hence the Phase margin will be 45°.

9. The parameter which is constant along the constant N circle :

a) Frequency

b) Phase angle

c) Magnitude

d) Open loop gain

Answer: b

Explanation: Phase angle remains constant in constant N-circle.

Answer: c

Explanation: Gain margin is defined generally for systems with order greater than 3.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “The Design Problem”.

1. What should be the nature of bandwidth for a good control system?

a) Large

b) Small

c) Medium

d) All of the mentioned

Answer: a

Explanation: Bandwidth is defined as the difference in the highest frequency and lowest frequency and bandwidth must be large for the good control system and for higher bandwidth noise is also large.

2. Which system exhibits the initiation of corrective action only after the output gets affected?

a) Feed forward

b) Feedback

c) Both a and b

d) None of the mentioned

Answer: b

Explanation: Feedback is the process in which the output of the system is desired by comparing the output with the input and with the feedback system exhibits the initiation of corrective action only after the output gets affected.

3. A good control system should be sensitive to __________

a) Internal disturbances

b) Environmental parameters

c) Parametric variations

d) Input signals 

Answer: c

Explanation: A good control system is the system with high speed of response and steady state error must be less and bandwidth should be large and noise must be very low and must be sensitive to parametric variations.

4. What is the value of steady state error in closed loop control systems?

a) Zero

b) Unity

c) Infinity

d) Unpredictable

Answer: a

Explanation: Steady state error is the error which is the difference in the final output to the desired output and the value of steady state error for the good control system must be zero.

5. Into which energy signal does the position sensor convert the measured position of servomotor in servomechanisms?

a) Mechanical

b) Electrical

c) Thermal

d) Light

Answer: a

Explanation: In mechanical system the sensors are used in which the mechanical motion is converted into electrical energy and generally in mechanical system position sensor convert the measured position of servomotor in servomechanism.

6. Which among the following controls the speed of D.C. motor?

a) Galvanometer

b) Gauss meter

c) Potentiometer

d) Tachometer

Answer: d

Explanation: D.C. motor is the motor which operates with the direct current as in the construction of DC motors slip rings not commutators and tachometer control the speed of DC motor.

7. Which among the following represents an illustration of closed loop system?

a) Automatic washing machine

b) Automatic electric iron

c) Bread toaster

d) Electric hair drier

Answer: a

Explanation: Closed loop control system is the system with the positive or negative feedback and this is made so as to avoid the disadvantages of open loop control system and in the above options automatic washing machine represents closed loop system.

8. Which notation represents the feedback path in closed loop system representation?

a) b

b) c

c) e

d) r

Answer: c

Explanation: Feedback can be positive and negative and feedback is so used to reduce the error of the system by comparing the final output with the desired output and reducing the error and this error is denoted with the symbol as e.

9. Which among the following is not an advantage of an open loop system?

a) Simplicity in construction & design

b) Easy maintenance

c) Rare problems of stability

d) Requirements of system re-calibration from time to time

Answer: d

Explanation: Open loop system is the system with no feedback and the parameter variations in the open loop system are more as compared to the closed loop system and the system has to be re-calibrated as per the requirement as automatic calibration is not present in this system.

Answer: a

Explanation: For the output of the system, mainly the input and state of the system are required and the excitation or stimulus applied to the system from an external source for the generation of the output is called input signal.

This set of Control Systems Question Bank focuses on “Preliminary Considerations of Classical Design”.

1. The most important consideration for designing of control system are:

a) Transient response measures

b) Steady state error

c) Temporary response

d) Final response

Answer: c

Explanation: The important point to keep in mind for designing control system are the transient response and steady state response as for designing a control system both of the responses are used in detail. .

2. Steady state error is usually specified in terms of :

a) Error constants

b) Damping factor

c) Speed of response

d) Bandwidth

Answer: a

Explanation: Steady state error is the error that is specified as the time approaches infinite and value approaches the final value and specified mainly in terms of error constants that are mainly position, velocity and acceleration error constants.

3. Transient response measure is usually specified in terms of :

a) Error constants

b) Damping factor

c) Speed of response

d) Both b and c

Answer: d

Explanation: Transient response is the response taken at any particular time during analysis and that is mainly specified in terms of damping factor and speed of response that is mainly settling time and rise time.

4. In time domain the measure of relative stability is:

a) Damping factor

b) Maximum peak overshoot

c) Damping factor and Maximum peak overshoot

d) Speed of response

Answer: c

Explanation: Relative stability is the measure of stability of a particular control system with respect to some reference and is measured both in time and frequency domain as in time domain it is the measure of damping factor and maximum peak overshoot.

5. In frequency domain the measure of relative stability is:

a) Resonant peak

b) Phase margin

c) Resonant peak and phase margin

d) Maximum peak overshoot

Answer: c

Explanation: Relative stability is the measure of stability of a particular control system with respect to some reference and is measured both in time and frequency domain as in frequency domain it is the measure of both resonant peak and phase margin.

6. In time domain the speed of response is measured in terms of :

a) Rise time

b) Settling time

c) Natural frequency

d) All of the mentioned

Answer: d

Explanation: The value of rise time must be less so that the speed of response of control system must be large and it depends upon the rise time, settling time and natural frequency.

7. In frequency domain the speed of response is measured in terms of:

a) Resonant frequency

b) Bandwidth

c) Resonant peak and bandwidth

d) Maximum peak overshoot

Answer: c

Explanation: The speed of response is the time to get the final response and in frequency domain it depends upon the resonant frequency the frequency at which the resonant peak is obtained and bandwidth.

8. The compensator for the system can be:

a) Electrical

b) Mechanical

c) Hydraulic

d) All of the mentioned

Answer: d

Explanation: Compensator can be of any different type but mainly electric network serves as the compensator.

9. The compensator transfer function can be placed in:

a) Cascade or series compensation

b) Feedback or parallel compensation

c) Positive

d) Negative

Answer: c

Explanation: Compensator are the devices used in frequency domain so as to get the desired response and there are various methods to place the compensators in the system as cascade or series or feedback or parallel.

Answer: a

Explanation: Derivative compensation are also known as the lead compensators are these make the speed of response of the system more and also the bandwidth and hence make the system more stable.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Realization of Basic Compensators”.

1. Which of the following is not the correct reason to select feedback compensation over cascaded one?

a) No amplification is required as the energy transfer is from higher to lower level.

b) Suitable devices are not available for compensation

c) It is economical

d) Provides greater stiffness against load disturbances

Answer: c

Explanation: Feedback compensation is the compensation obtained due to feedback and cascade refers to the cascading of blocks in the forward path and feedback compensation is not preferred over cascading as it is ecenomical.

2. Operations performed by pneumatic controllers:

a) Flexible operations

b) High torque high speed operations

c) Fire and explosion proof operation

d) All of the mentioned

Answer: c

Explanation: Pneumatic controllers are the controllers that perform the control action to control the motion related to air and they always perform fire and explosion proof operation.

3. Operations performed by hydraulic controllers:

a) Flexible operations

b) High torque high speed operations

c) Fire and explosion proof operation

d) All of the mentioned

Answer: b

Explanation: Hydraulic controllers are the controllers that perform the control action in which the motion is due to the water and they have high torque and high speed operations.

4. Operations performed by electronic controllers:

a) Flexible operations

b) High torque high speed operations

c) Fire and explosion proof operation

d) All of the mentioned

Answer: a

Explanation: Electronic controllers are the most flexible controller and used over hydraulic and pneumatic controllers and they use the control action where the control is mainly handled by electronic components and can perform flexible operations as of high speed and high torque.

5. The compensator G =5/1+0.1s would provide a maximum phase shift of:

a) 20°

b) 30°

c) 45°

d) 60°

Answer: b

Explanation: The two corner frequencies are 1/0.3 and 1/0.1. The maximum phase lead occurs at mid frequency w =10/√ and maximum phase is 30°.

6. Consider the following systems:

System 1: G =1/  and System 2: G =1/ 

The true statement regarding the system is:

a) Bandwidth of the system 1 is greater than the bandwidth of the system 2

b) Bandwidth of the system 1 is lower than the bandwidth of the system 2

c) Bandwidth of both the systems are same

d) Bandwidth of both the systems are infinite

Answer: a

Explanation: For the system 1 B.W. is 0.5 and

For the system 2 B.W. is 0.2

Hence the system 1 is having more bandwidth compared to system 2.

7. With regard to the filtering capacity the lead compensator and lag compensator are respectively:

a) Low pass and high pass filter

b) High pass and low pass filter

c) Both high pass filter

d) Both low pass filters

Answer: b

Explanation: Lead compensator is similar to high pass filter which allows only the high frequencies to pass and rejects all the other and Lag compensator is similar to Low pass filter which allows only low frequencies to pass and rejects other.

8. What is the effect of phase lag compensation on the performance of a servo system?

a) For a given relative stability, the velocity constant is increased

b) For a given relative stability, the velocity constant is decreased

c) The bandwidth of the system is increased

d) The time response is made faster

Answer: a

Explanation: Phase lag compensation is an integrator. It reduces the steady state error.

Velocity constant =1/steady state error

So velocity constant is increased.

9. A composite R-C network yielded the following transfer function when calculated from its components:

T = 1+21s+20s 2 /1+11s+10s 2 . This network can be used as which one of the following?

a) Phase lead compensator

b) Phase lag compensator

c) Lag lead compensator

d) None of the mentioned

Answer: a

Explanation: T = 1+20s/1+10s.

Since zero is nearer to origin than pole, it is a phase lead compensator.

Answer: a

Explanation: G =1/

The lead compensator C should stabilize the plant as it is similar to the differentiator and the tendency of it is to stablize the system by increasing the damping hence remove the first term so only option  satisfies.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Cascade Compensation in Time Domain”.

1. A proportional controller leads to:

a) Zero steady state error for step input for type 1 system

b) Zero steady state error for step input for type 0 system

c) Infinite steady state error for step input for a type 1 system

d) Finite steady state error for step input for type 1 system

Answer: a

Explanation: A proportional controller is the controller block used in the system so as to follow the output and leads to zero steady state error for step input for type 1 system.

2. An all-pass network imparts only

a) Negative phase to the input

b) Positive phase to the input

c) 90 degree phase shift to the input

d) 180 degree phase shift to the input

Answer: d

Explanation: An all-pass network is the network that is the combination of the minimum and non-minimum phase systems and have the magnitude 1 for all frequencies and imparts only 180 degree phase shift.

3. Which of the following is an effect of lag compensation?

a) Decrease bandwidth

b) Improves transient response

c) Increases the effect of noise

d) Increases stability margin

Answer: a

Explanation: Lag compensation is the integral compensation that introduces the lag in the response by slowing the response and reducing the steady state error value by decreasing bandwidth.

4. PD controller:

a) Decreases steady state error and improves stability

b) Rise time decreases

c) Transient response becomes poorer

d) Increases steady state error

Answer: b

Explanation: In Proportional and Derivative controller the damping factor value is increases the oscillations are reduced and rise time decreases hence speed of response increases.

5. PID controller:

a) Decreases steady state error and improves stability

b) Rise time decreases

c) Transient response becomes poorer

d) Increases steady state error

Answer: a

Explanation: Proportional Integral and Derivative controller is the controller that is the combinational controller that increases the speed of response, decreases steady state error and improves stability.

6. PI controller:

a) Decreases steady state error and improves stability

b) Rise time decreases

c) Transient response becomes poorer

d) Increases steady state error

Answer: c

Explanation: In Proportional and Integral controller which is the extension of the integral controller which improves the steady state response but transient response becomes poorer.

7. Proportional controller

a) Decreases steady state error and improves stability

b) Rise time decreases

c) Transient response becomes poorer

d) Increases steady state error

Answer: d

Explanation: Proportional controller is the controller that is used in the system so that the output follows the input and increases steady state error.

8. PD controller is used to compensate a system, Compared to the uncompensated system, the compensated system has:

a) A higher type number

b) Reduced damping

c) Higher noise amplification

d) Large transient overshoot

Answer: c

Explanation: The compensated system of the proportional derivative controller has bandwidth increases and signal to noise ratio decreases.

9. Lead compensator increases bandwidth

a) True

b) False

Answer: a

Explanation: Lead compensator is similar to high pass filter and causes lead in the system and increases the speed of response of the system and hence increases Bandwidth.

Answer: b

Explanation: Lag compensator is the integral compensation that causes the lag in the response and reduces velocity constant.

This set of Control Systems Questions and Answers for Entrance exams focuses on “Cascade Compensation in Frequency Domain”.

1. A phase lead compensation leads to:

a) Increase in overshoot

b) Reduction in bandwidth of closed loop system

c) Reduction in rise time of closed loop system

d) Reduction in gain margin

Answer: c

Explanation: Phase lead compensation and this is similar to the high pass filter results in increase in bandwidth reduction in settling time and thus, speed of response is improved.

2. PD controller is used to compensate system. Compared to the uncompensated system, the compensated system has:

a) A higher type number

b) Reduced damping

c) Higher noise amplification

d) Large transient overshoot

Answer: c

Explanation: Proportional Derivative controller is used to increase the bandwidth and also increases the signal to noise ratio by reducing the noise and increasing the signal.

3. P+D controller:

a) Introduces offset

b) Increases bandwidth

c) Increases margin of stability

d) Reduces velocity constant

Answer: c

Explanation: Proportional Derivative controller is the controller increases margin of stability and also used to increase he bandwidth and also increases the signal to noise ratio.

4. Proportional controller:

a) Introduces offset

b) Increases bandwidth

c) Increases margin of stability

d) Reduces velocity constant

Answer: a

Explanation: Proportional controller is the controller that is block used to control the gain of the control system and introduces offset error and there is no effect on the damping factor.

5. The transfer function of a lead controller is 1+20s/1+5s. The high frequency magnitude of the lead controller to dB is ___________

a) 1

b) 2

c) 3

d) 4

Answer: d

Explanation: G = Tp /s^2

It is type-2 function.

The type-2 function has a finite steady state error for unit-parabolic input.

6. Controllers play the following role in control system:

a) They amplify the signals going to the actuator

b) They act on the error signal coming out of the summing junction and output a suitable to the actuator

c) They try to reduce steady state error optimizes overshoot.

d) All of the mentioned

Answer: a

Explanation: Controller amplify the signals going to the actuator and they are of many types as proportional, integral, derivative some combinational controller as combination of two controllers and combination of all the controllers.

7. The transfer function of the compensator is s+4/s+16. The maximum phase lead frequency and the corresponding phase is :

a) 6 rad/sec, 36.87°

b) 8 rad/sec, 36.87°

c) 6 rad/sec, -36.87°

d) 8 rad/sec, -36.87°

Answer: b

Explanation: Phase lead frequency is calculated when magnitude of transfer function is 1 and this is the phase cross over frequency and the phase is calculated by using the tanget formula with the transfer function.

8. Response to error is very fast for integral controller.

a) True

b) False

Answer: b

Explanation: Integral controller is used to reduce or eliminate the error of the control system and for derivative controller the damping factor is increased and speed of response also increases.

9. Consider the following statements:

1. Integral controller improves steady state response

2. By use of proportional controller, maximum peak overshoot decreases

3. Type and order of system reduces by one for derivative controller

4. Integral controller makes the system less stable in transient state due to oscillations

Select the correct answer using the codes given below:

a) 1,3 and 4

b) 1,2 and 3

c) 2.3 and 4

d) 1,2 and 4

Answer: a

Explanation: Integral controller improves steady state response and derivative controller improves the transient response, type and order of system reduces by one for derivative controller.

Answer: a

Explanation: Anticipatory controller mode is also known as the rate mode controller that is used to anticipate the future value with the use of the state.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Tuning of PID Controllers”.

1. The input of a controller is

a) Sensed signal

b) Error signal

c) Desired variable value

d) Signal of fixed amplitude not dependent on desired variable value

Answer: b

Explanation: Controller is the block in the control system that control the input and provides the output and this is the first block of the system having the input as the error signal.

2. Phase lag controller:

a) Improvement in transient response

b) Reduction in steady state error

c) Reduction is settling time

d) Increase in damping constant

Answer: b

Explanation: Phase lag controller is the integral controller that creates the phase lag and does not affect the value of the damping factor and that tries to reduce the steady state error.

3. Addition of zero at origin:

a) Improvement in transient response

b) Reduction in steady state error

c) Reduction is settling time

d) Increase in damping constant

Answer: a

Explanation: Stability of the system can be determined by various factors and for a good control system the stability of the system must be more and this can be increased by adding zero to the system and improves the transient response.

4. Derivative output compensation:

a) Improvement in transient response

b) Reduction in steady state error

c) Reduction is settling time

d) Increase in damping constant

Answer: c

Explanation: Derivative controller is the controller that is also like high pass filter and is also phase lead controller and it is used to increase the speed of response of the system by increasing the damping coefficient.

5. Derivative error compensation:

a) Improvement in transient response

b) Reduction in steady state error

c) Reduction is settling time

d) Increase in damping constant

Answer: d

Explanation: Damping constant reduces the gain, as it is inversely proportional to the gain and as increasing the damping gain reduces and hence the speed of response and bandwidth are both increased.

6. Lag compensation leads to:

a) Increases bandwidth

b) Attenuation

c) Increases damping factor

d) Second order

Answer: b

Explanation: Phase compensation can be lead, lag or lead lag compensation and integral compensation is also known as lag compensation and leads to attenuation which has least effect on the speed but the accuracy is increased.

7. Lead compensation leads to:

a) Increases bandwidth

b) Attenuation

c) Increases damping factor

d) Second order

Answer: a

Explanation: High pass filter is similar to the phase lead compensation and leads to increase in bandwidth and also increase in speed of response.

8. Lag-lead compensation is a:

a) Increases bandwidth

b) Attenuation

c) Increases damping factor

d) Second order

Answer: d

Explanation: Lag-Lead compensation is a second order control system which has lead and lag compensation both and thus has combined effect of both lead and lag compensation this is obtained by the differential equation.

9. Rate compensation :

a) Increases bandwidth

b) Attenuation

c) Increases damping factor

d) Second order

Answer: c

Explanation: Damping factor is increased for reducing the oscillations and increasing the stability and speed of response which are the essential requirements of the control system and damping factor is increased by the rate compensation.

Answer: a

Explanation: Transportation lag is the lag that is generally neglected in systems but for the accurate measurements the delay caused to transport the input from one end to the other is called the transportation lag in the system causes instability to the system.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Feedback Compensation”.

1. Which of the following are the not characteristics of the closed loop systems?

a) It does not compensate for disturbance

b) It reduces the sensitivity of plant-parameter variations

c) It does not involve output measurements

d) It does not has the ability to control the system transient response

Answer: d

Explanation: Feedback refers to the comparison of the final output to the desired output at respective input so as to get accurate and error free result and in the system improves the transient response of the system.

2. Which one of the following effect in the system is not caused by negative feedback?

a) Reduction in gain

b) Increased in bandwidth

c) Increase in distortion

d) Reduction in output impedance

Answer: c

Explanation: Distortion refers to the error in the open loop system and it has many oscillations in the output and is reduced in case of negative feedback.

3. Which of the statement is correct with regard to the bandwidth of the control loop system:

a) In systems where the low frequency magnitude in 0 dB on the bode diagram, the bandwidth is measured at the -3 dB frequency

b) The bandwidth is the measurement of the accuracy of the closed loop system

c) The stability is proportional to the bandwidth

d) The system with larger bandwidth provides slower step response and lower fidelity ramp response

Answer: a

Explanation: Bandwidth is the frequency measured at the gain of 3dB and for the good control system the value of the bandwidth must be large but the large value of the bandwidth increses the noise in the system.

4. Which of the statements are the advantages of closed loop systems over the open loop system:

a) The overall reliability of the open loop system is more than the closed loop system is more than closed loop system.

b) The transient response in closed loop system decays more quickly than in open loop system.

c) In open loop system closing the loop increases the gain of the system

d) In open loop system the effect of parameter variation is reduced

Answer: b

Explanation: Speed of response refers to the time taken to give the final output and it depends upon the rise and settling time of the transient response and speed of response of closed loop system is more than that of open loop system.

5. In control system excessive bandwidth is not employed because

a) Noise is proportional to bandwidth

b) It leads to low relative stability

c) It leads to slower time response

d) Noise is proportional to the square of the bandwidth

Answer: a

Explanation: In closed loop system the bandwidth of the system is more as compared to the open loop system and this is so required as higher the bandwidth means lower the selectivity and hence higher the noise.

6. Feedback control system is basically

a) High pass filter

b) Low pass filter

c) Band pass filter

d) Band stop filter

Answer: b

Explanation: Low pass filter is mainly as integral controller and it is used as the controller in the system so as to increase the accuracy by reducing or proper eliminating the steady state error of the control system.

7. Which of the following will not decrease as a result of introduction of negative feedback?

a) Instability

b) Bandwidth

c) Overall gain

d) Distortion

Answer: b

Explanation: Bandwidth always increases due to negative feedback as the speed of response is directly proportional to the bandwidth.

8. As compared to the closed loop system, an open loop system is

a) More stable but less accurate

b) Less stable as well as less accurate

c) More stable as well as more accurate

d) Less stable but more accurate

Answer: a

Explanation: Open loop system always follows the input but closed loop system always reduces the error irrespective of the input applied.

9. Insertion of negative feedback in control system affects:

a) The transient response to vanish uniformly

b) The transient response to decay very fast

c) No change in transient response

d) The transient response decays at slow rate

Answer: b

Explanation: Feedback can be positive or negative but practically positive feedback is not used as it causes oscillations in the system with more gain and hence negative feedback is use which causes speed of response to increase.

10. Open loop system is ___________ stable than closed loop system

a) More

b) Less

c) Inclined

d) Exponential

Answer: a

Explanation: Open loop system always follows the input but closed loop system always reduces the error irrespective of the input applied.

11. For the gain feedback system, does not affect the system output if KG is :

control-systems-questions-answers-feedback-compensation-q11

a) Small

b) Negative

c) One

d) Very large

Answer: d

Explanation: T=KG/

If KG>>1: then C=R/H.

12. Determine the sensitivity of the overall transfer function for the system shown in the figure below, at w=1 rad/sec with respect to the feedback path transfer function.

control-systems-questions-answers-feedback-compensation-q12

a) 1.11

b) -1.11

c) 2.22

d) -2.22

Answer: b

Explanation: S= -GH/1+GH-1.1.

Answer: a

Explanation: The major requirement of the feedback is to reduce of the system with parameter variations that may vary with age, with changing environment.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Spectrum Analysis of Sampling Process”.

1. Statement : Aliasing occurs when the sampling frequency is less than twice the maximum frequency in the signal.

Statement : Aliasing is a reversible process.

a) Both statement  and Statement  are individually true and Statement  is the correct explanation of Statement .

b) Both Statement  and Statement  are individually true but Statement  is not correct explanation of Statement 

c) Statement  is true but Statement  is false

d) Statement  is False but Statement  is true

Answer: c

Explanation: Aliasing is an irreversible process. Once aliasing has occurred then signal can-not be recovered back.

2. A band limited signal with a maximum frequency of 5 KHz to be sampled. According to the sampling theorem, the sampling frequency which is not valid is:

a) 5 KHz

b) 12 KHz

c) 15 KHz

d) 20 KHz

Answer: a

Explanation: fs  =2fm

fs  =2*5 =10 KHz

So, fs >=1o KHz.

3. Let x be a continuous-time, real valued signal band-limited to F Hz. The Nyquist sampling rate in Hz, For y =x +x-x is

a) F

b) 2F

c) 4F

d) 8F

Answer: c

Explanation: Expansion in time domain in compression in frequency domain and vice-versa. So, the maximum frequency component in given signal is 2F Hz. And according to sampling theorem.

Nyquist rate =2fm =4F Hz.

4. Increased pulse-width in the flat-top sampling leads to:

a) Attenuation of high frequencies in reproduction

b) Attenuation of low frequencies in reproduction

c) Greater aliasing errors in reproduction

d) No harmful effects in reproduction

Answer: a

Explanation: As pulse width is increased, the width of the first lobe of the spectrum is decreased. Hence, increased pulse-width in the flat-top sampling, leads to attenuation of high frequencies in reproduction.

5. A bandpass sampling extends from 4-6 kHz. What is the smallest sampling frequency required to retain all the information in the signal.

a) 1 kHz

b) 2 kHz

c) 3 kHz

d) 4 kHz

Answer: d

Explanation: fh =6 kHz

Bandwidth = 2 kHz

Fs =4 kHz.

6. A signal represented by x =5cos 400πt is sampled at a rate 300 samples/sec. The resulting samples are passed through an ideal low pass filter of cut-off frequency 150 Hz. Which of the following will be contained in the output of the LPF?

a) 100 Hz

b) 100 Hz, 150 Hz

c) 50 Hz, 100 Hz

d) 50 Hz, 100 Hz, 150 Hz

Answer: a

Explanation: x  =5cos400πt

fm =200 Hz

The output of the LPF will contain frequencies which are less than fc =150 Hz.

So, fs-fm =300-200 =100 Hz is the only component present in the output of LPF.

7. A signal m with bandwidth 500 Hz is first multiplied by a signal g. The resulting signal is passed through an ideal low pass filter with bandwidth 1 kHz. The output of the low pass filter would be :

a) Impulse

b) m

c) 0

d) mdel

Answer: c

Explanation: m  g ->M *G 

After low pass filtering with fc =1 kHz, hence the output is zero.

8. An LTI system having transfer function s 2 +1/s 2 +2s+1 and input x =sin is in steady state. The output is sampled at ws rad/s to obtain the final output {y }. Which of the following is true?

a) Y is zero for all sampling frequencies ws

b) Y is non zero for all sampling frequencies ws

c) Y is non zero for ws>2 but zero for ws<2

d) Y is zero for ws>2 but non zero for ws<2

Answer: a

Explanation: x  =sin 

w = 1 rad/s

X = e s /s 2 +1

Y = e s /s 2 +2s+1

Y  =0.

9. A digital measuring instrument employs a sampling rate of 100 samples/second. The sampled input x is averaged using the difference equation:

Y  =[x +x +x+x/4] For a step input, the maximum time taken for the output to reach the final value after the input transition is

a) 20 ms

b) 40 ms

c) 80 ms

d) ∞

Answer: b

Explanation: Since output y depends on input, such as no delay, delay by 1 unit, and delay by 2 unit, delay by 4 unit, so it will sum all the samples after 4 Ts , to get one sample of y[n].

T =40 msec.

Answer: b

Explanation: Output filter is the device that is used to filter some frequencies and make some frequencies in the response and in this case it contains 10π rad/sec.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Signal Reconstruction”.

1. Sampling can be done by:

a) Impulse train sampling

b) Natural sampling

c) Flat-top sampling

d) All of the mentioned

Answer: d

Explanation: Sampling is the process in which the continuous systems are sampled by the application of the zero order hold and can be done by all the three methods.

2. The first step required to convert analog signal to digital is :

a) Sampling

b) Holding

c) Reconstruction

d) Quantization

Answer: a

Explanation: Sampling is the process in which the continuous systems are sampled by the application of the zero order hold and is the first step in the conversion of analog to digital signals.

3. Sampling is necessary :

a) In complex control systems

b) Where high accuracy is required

c) Non automated control systems

d) Automated control system

Answer: b

Explanation: Sampling is the process where the continuous systems are converted into discrete time systems with the help of zero order hold of the signal and sampling is necessary where high accuracy is needed.

4. Sampled data technique is appropriate as:

a) For long distance data transmission

b) Pulses are transferred by little loss of accuracy

c) More than one channel of information is sequentially sampled and transmitted.

d) All of the mentioned

Answer: d

Explanation: Sampled data technique refers to the data which is sampled and is appropriate as for long distance communication, for accurate transmission and multi channel transmission.

5. Signal sampling reduces the power demand made on the signal.

a) True

b) False

Answer: a

Explanation: Signal sampling refers to the sampling of the signal and reduces the power demand that is the power required by the signal and is therefore helpful for signals of weak origin.

6. The use of sampled data control system are:

a) For using analog components as the part of the control loop

b) For time division of control components

c) Whenever a transmission channel forms a part of closed loop

d) None of the mentioned

Answer: c

Explanation: Sampled data control system is the system where the data used is sampled and is used whenever a transmission channel forms a part of closed loop system.

7. _______________ is a sampling pattern which is repeated periodically

a) Single order sampling

b) Multi order sampling

c) Zero order sampling

d) Unordered sampling

Answer: b

Explanation: Multi-order sampling is a sampling pattern in which the sampling is of different signals and which is repeated periodically.

8. For the successful reconstruction of signals :

a) Sampling frequency must be equal to the message signal

b) Sampling frequency must be greater to the message signal

c) Sampling frequency must be less to the message signal

d) Sampling frequency must be greater than or equal to the message signal

Answer: d

Explanation: Reconstruction of signals refers to the conversion of the discrete time signals into continuous tiem signals and for the succesful reconstruction of signals sampling frequency must be greater than or equal to the message signal but ideally it is always preferred to be greater.

9. The signal is reconstructed back with the help of

a) Zero order hold circuits

b) Extrapolations

c) Signal is reconstructed with zero order holds and extrapolations

d) Signal is not reconstructed

Answer: c

Explanation: The signal is reconstructed that is the process of converting the discrete time signals into the continuous time signals and this can be done with the help of hold circuits or extrapolations.

Answer: c

Explanation: Aliasing refers to the process when the discrete time signal is recontructed back then due to the error some part of the signal is lost and is caused when sampling frequency must be less than frequency of message signal.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Difference Equations”.

1. Difference equation model results in:

a) Sampled-data systems

b) Numerical analysis of continuous time systems

c) Continuous time feedback systems

d) Both a and b

Answer: d

Explanation: Equation in discrete time systems can be difference equation which are similar to the differentiation in the continuous time systems and difference equation results in sampled data system and numerical analysis of continuous system.

2. Difference equation is used in :

a) Discrete time analysis

b) Continuous time analysis

c) Digital analysis

d) None of the mentioned

Answer: a

Explanation: Difference equation are similar to the differentiation in the continuous systems and they have same function in discrete time systems and is used in discrete time analysis.

3. Difference equation in discrete systems is similar to the _____________ in continuous systems.

a) Difference equation

b) Differential equation

c) Quadratic equation

d) None of the mentioned

Answer: b

Explanation: Difference equation are the equations used in discrete time systems and difference equations are similar to the differential equation in continuous systems.

4. Difference equation solution yields at the sampling instants only:

a) True

b) False

Answer: a

Explanation: Difference equation are the equations used in discrete time systems and difference equations are similar to the differential equation in continuous systems solution yields at the sampling instants only.

5. Difference equation technique for higher order systems is used in:

a) Laplace transform

b) Fourier transform

c) Z-transform

d) None of the mentioned

Answer: c

Explanation: For higher order systems Z- transform which is transforming discrete time domain into z domain and is technique is convenient for analysis and design of linear sampled data systems.

6. Assertion : An LTI discrete system represented by the difference equation. y -5y+6y =x is unstable.

Reason : A system is unstable if the roots of the characteristic equation lie outside the unit circle.

a) Both A and R are true and R is the correct explanation of A

b) Both A and R are true but R is NOT the correct explanation of A

c) A is true but R is false

d) A is false but R is false

Answer: a

Explanation: Difference equation is y -5 y  + 6 y  =x .

Taking z-transform, H  =1/  .

The characteristic equation has roots z =2, 3. Since, the characteristic equation has roots outside the unit circle, hence the system is unstable.

7. The poles of a digital filter with linear phase response can lie

a) Only at z =0

b) Only on the unit circle

c) Only inside the unit circle but not at z =0

d) On the left side of Real  =0 line

Answer: b

Explanation: For stable systems the poles in z plane must lie inside or on the unit circle and Minimum number of delay elements = -.

8. If X =(z+z -3 )/(z+z -1 ), then x series has:

a) Alternate 0s

b) Alternate 1s

c) Alternate 2s

d) Alternate -1s

Answer: a

Explanation: Using the long division method divide from denominator. So, x series has alternate zeros n =1,3,5……

9. Assertion : The stability of the system is assured if the ROC includes the unit circle in z-plane.

Reason : For a causal stable system all the poles should be outside the unit circle in the z-plane.

a) Both A and R are true and R is the correct explanation of A

b) Both A and R are true bit R is NOT the correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: c

Explanation: A causal system LTI system is stable if and only if all of poles of H lie inside the unit circle.

Answer: b

Explanation: For the rational transfer function H  to be causal, stable and causally invertible, both the zeroes and the poles should lie within the unit circle in the z-plane. For a rational system, ROC is bounded by poles.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “The Z-Transform”.

1. The discrete-time signal x  =  n is periodic with fundamental period

a) 6

b) 4

c) 2

d) 0

Answer: c

Explanation: Period of the signal refers to the instant of time at which the signal repeats itself and for this Period =2 of the given discrete time signal.

2. The frequency of a continuous time signal x  changes on transformation from x  to x , α > 0 by a factor

a) α

b) 1/α

c) α 2

d) α

Answer: a

Explanation: x->x, α > 0

α > 1 compression in t, expansion in f by α.

α < 1 expansion in t, compression in f by α.

3. Two sequences x1  and x2  are related by x2  = x1 . In the z- domain, their ROC’s are

a) The same

b) Reciprocal of each other

c) Negative of each other

d) Complements of each other

Answer: b

Explanation: x1 is the signal in the discrete domain and X1 is the signal in the z domain, RoC Rx

z Reciprocals x2 = x1 X1, RoC 1/ Rx

4. The ROC of z-transform of the discrete time sequence x = control-systems-questions-answers-z-transform-q4 is:

a) 1/3>|z|<1/2

b) |z|>1/2

c) |z|<1/3

d) 2>|z|<3

Answer: a

Explanation: One part of the equation is the right sided signal and other part is the left sided signal hence the ROC of the system will be 1/3>|z|<1/2.

5. Which one of the following is the correct statement? The region of convergence of z-transform of x[n] consists of the values of z for which x[n] is:

a) Absolutely integrable

b) Absolutely summable

c) Unity

d) <1

Answer: b

Explanation: The region of convergence of z-transform of x[n] consists of the values of z for which x[n]r -n is absolutely summable.

6. The region of convergence of the z-transform of a unit step function is:

a) |z|>1

b) |z|<1

c) >0

d) <0

Answer: a

Explanation: h[n] =u[n] Hence, Region of Convergence is the region for which the values of the roots in z transform are lying in the function and is the range of values of z for which |z|>1.

7. If the region of convergence of x1[n]+x2[n] is 1/>|z|<2/3, the region of convergence of x1[n]-x2[n] includes:

a) 1/3>|z|<3

b) 2/3>|z|<3

c) 3/2>|z|<3

d) 1/3>|z|<2/3

Answer: d

Explanation: Region of Convergence is the region for which the values of the roots in z transform are lying in the function and ROC remains the same for addition and subtraction in z-domain.

8. A sequence x  with the z-transform X  = Z 4 + Z 2 – 2z + 2 – 3Z -4 is applied to an input to a linear time invariant system with the impulse response h  = 2δ . The output at n = 4 will be:

a) -6

b) Zero

c) 2

d) -4

Answer: b

Explanation: H  = 2z -3

Then taking the inverse Laplace transform of the equation of Y  at n=4 y =0.

9. H  is discrete rational transfer function. To ensure that both H and its inverse are stable:

a) Poles must be inside the unit circle and zeros must be outside the unit circle

b) Poles and zeroes must be inside the unit circle

c) Poles and zeroes must be outside the unit circle

d) Poles must be outside the unit circle and zeros must be inside the unit circle

Answer: b

Explanation: For H to be stable the poles must be inside the unit circle and for the inverse of H to be stable the poles of it must be inside the unit circle.

Answer: b

Explanation: z = e st

s =ln z/T.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “The Z-Transfer Function”.

1. Consider the following statements regarding a linear discrete-time system:

H  = z 2 +1/

1. The system is stable

2. The initial value of h of the impulse response is -4

3. The steady-state output is zero for a sinusoidal discrete time input of frequency equal to one-fourth the sampling frequency

Which of these statements are correct?

a) 1,2 and 3

b) 1 and 2

c) 1 and 3

d) 2 and 3

Answer: c

Explanation: Characteristic equation is   =0

Its root are z =0.5, -0.5

Since both roots are inside the unit circle, hence the system is stable.

2. The minimum number of delay elements required realizing a digital filter with transfer function

H  =

a) 2

b) 3

c) 4

d) 5

Answer: b

Explanation: H  =

Minimum number of delay elements= 

Minimum number of delay elements = 3.

3. A system can be represented in the form of state equations as:

S  =A S  +B x 

Y  = C S  +D x 

Where, A, B, C, D are the matrices , S is the state vector , x is the input and y is the output . The transfer function of the system.

H  =Y /X  is given by:

a) A -1 C + D

b) B -1 D + A

c) C -1 B + D

d) D -1 C + B

Answer: c

Explanation: Solving both the equations and substituting the value of the output equation into the state equation we get the value of the transfer function as obtained.

4. Assertion : The signals a n u and a n u have the same Z transform, z/

Reason : the region of convergence of a n u is |z|>|a|, whereas the ROC for a n u is |z| a) Both A and R are true and R is correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: d

Explanation: Both have the ROC as given in the reason is true but the z transform for the second is with a minus sign.

5. What is the number of roots of the polynomial F = 4z 3 -8z 2 -z+2, lying outside the unit circle?

a) 0

b) 1

c) 2

d) 3

Answer: b

Explanation: Factorizing F  and then the factors are the roots which here come out to be 3.

6. Assertion : The discrete time system described by y[n] =2x[n] +4x[n-1] is unstable

Reason : It has an impulse response with a finite number of non-zero samples

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: d

Explanation: For the system to be stable the value of the transfer function in the discrete time domain must be summable and H[n] calculated is summable hence the system is stable.

7. What is the z-transform of the signal x[n] = a n u?

a) X =1/z-1

b) X = 1/1-z

c) X = z/z-a

d) X = 1/z-a

Answer: c

Explanation: By definition this is the basic example of the z-transform and the Z-Transform of the equation is calculated is z/z-a.

8. Which one of the following rules determine the mapping of s-plane to z-plane?

a) Right side of the s-plane maps into outside of the unit circle in z-plane

b) Left half of s-plane maps into inside of the unit circle

c) Imaginary axis in s-plane maps into the circumference of the unit circle

d) All of the mentioned

Answer: d

Explanation: S- plane can be mapped into the z plane with certain rules than right side maps into the outside, left side maps into the inside and imaginary axis maps on the unit circle of the z plane.

9. Assertion : The z-transform of the output of the sampler is given by the series.

Reason : The relationship is the result of the application of z = e -sT , where T stands for the time gap between the samples.

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) A is true but R is false

d) A is false but R is true

Answer: c

Explanation: T is termed as the time of the sampling instant and z transform is always defined for the instant of the sampling event and this can be as desired by the user.

Answer: a

Explanation: Convolution of the two sequences is the combination of multiplication and addition of the two sequences at each instant and convolution in time domain is multiplication in the frequency domain.

This set of Control Systems Questions and Answers for Campus interviews focuses on “The inverse Z-transform and Response of Linear Discrete Systems”.

1. Unit step response of the system described by the equation y +y =x is:

a) z 2 /

b) z/

c) z+1/z-1

d) z/z+1

Answer: a

Explanation: Response of the system is calculated by taking the z-transform of the equation and input to the transfer function in the step input.

2. Inverse z-transform of the system can be calculated using:

a) Partial fraction method

b) Long division method

c) Basic formula of the z-transform

d) All of the mentioned

Answer: d

Explanation: Inverse z-transform is the opposite method of converting the transfer function in Z domain to the discrete time domain and this can be calculated using all the above formulas.

3. Assertion : The system function

H = z 3 -2z 2 +z/z 2 +1/4z+1/s is not causal

Reason : If the numerator of H  is of lower order than the denominator, the system may be causal.

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true and R is not correct Explanation of A

c) A is True and R is false

d) A is False and R is true

Answer: a

Explanation: The transfer function is not causal as for causality the numerator of H  is of lower order than the denominator, the system may be causal.

4. Assertion : Z-transform is used to analyze discrete time systems and it is also called pulsed transfer function approach.

Reason: The sampled signal is assumed to be a train of impulses whose strengths, or areas, are equal to the continuous time signal at the sampling instants.

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true and R is not correct Explanation of A

c) A is True and R is false

d) A is False and R is true

Answer: a

Explanation: Z-transform is used to convert the discrete time systems into the z domain and it is also called pulsed transfer function approach that is justified only at the sampling instants.

5. The z-transform corresponding to the Laplace transform G =10/s is

control-systems-questions-answers-campus-interviews-q5

Answer: b

Explanation: Laplace transform is the technique of relating continuous time to the frequency domain while the z transform is relating discrete time hence Laplace transform is first converted into time domain and then the z transform is calculated.

6. Homogeneous solution of: y -9/16y = x

a) C1 n +C2 -n

b) C1- n-1 +C2 n-1

c) C1 n

d) C1- n

Answer: a

Explanation: Taking the z-transform of the given difference equation and solving the homogeneous equation and finding the solution using complimentary function.

7. If the z transform of x is X =z/4z 2 -7z+3, then the final value theorem is :

a) 1

b) 2

c) ∞

d) 0

Answer: a

Explanation: Final value theorem is calculated for the transfer function by equating the value of z as 1 and this can be calculated only for stable systems.

8. Final value theorem is used for:

a) All type of systems

b) Stable systems

c) Unstable systems

d) Marginally stable systems

Answer: b

Explanation: Final value theorem is used to calculate the final value as for time infinite and for z = 1 the final value theorem can be calculated and final value theorem is for for stable systems.

9. If the z-transform of the system is given by

H  = a+z -1 /1+az -1

Where a is real valued:

a) A low pass filter

b) A high pass filter

c) An all pass filter

d) A bandpass filter

Answer: c

Explanation: The discrete time frequency response will be aperiodic and does not depend on the frequency and the transfer function will be representing the all pass filter.

Answer: a

Explanation: For the system to be stable in Z domain the pole in the this domain must lie inside the unit circle and for the causal stable region must be outside the circle and hence the locus will be a ring.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “The Z-transform Analysis of Sampled-Data Control Systems”.

1. The DFT of a signal x of length N is X. When X is given and x is computed from it, the length of x

a) Is increased to infinity

b) Remains N

c) Becomes 2N – 1

d) Becomes N2

Answer: a

Explanation: When X  is given and x  is computed from it, the length of x  is increased to infinity.

2. The system having input x  related to output y as y  = log |x | is:

a) Nonlinear, causal, stable

b) Linear, noncausal, stable

c) Nonlinear, causal, not stable

d) Linear, noncausal, not stable

Answer: a

Explanation: As y  is the function of x  hence it is nonlinear but it is bounded and also depends upon past and present values therefore it is stable and causal respectively.

3. Zero-order hold used in practical reconstruction of continuous-time signals is mathematically represented as a weighted-sum of rectangular pulses shifted by:

a) Any multiples of the sampling interval

b) Integer multiples of the sampling interval

c) One sampling interval

d) 1 second intervals

Answer: b

Explanation: Zero-order hold is used to reconstruct the continuous-time signal which is represented as a weighted sum of rectangular pulses shifted by integer multiples of the sampling interval.

4. When two honest coins are simultaneously tossed, the probability of two heads on any given trial is:

a) 1

b) 3/4

c) 1/2

d) ¼

Answer: d

Explanation: Total outcomes =4

Favorable outcomes =1

Hence probability =1/4.

5. A continuous-time periodic signal x, having a period T, is convolved with itself. The resulting signal is

a) Not periodic

b) Periodic having a period T

c) Periodic having a period 2T

d) Periodic having a period T/2

Answer: b

Explanation: Periodic having a period T Convolution of a periodic signal  with itself will give the same period T.

6. If the Fourier series coefficients of a signal are periodic then the signal must be

a) Continuous-time, periodic

b) Discrete-time, periodic

c) Continuous-time, non-periodic

d) Discrete-time, non-periodic

Answer: b

Explanation: Discrete-time, periodic these are the properties of the discrete-time periodic signal.

7. The region of convergence of a causal finite duration discrete-time signal is

a) The entire z-plane except z = 0

b) The entire z-plane except z = ∞

c) The entire z-plane

d) A strip in z-plane enclosing jω–axis

Answer: a

Explanation: For discrete time signal for any causal system the region of convergence is always entire z-plane but except z =0.

8. The probability cumulative distribution function must be monotone and

a) Increasing

b) Decreasing

c) Non-increasing

d) Non-decreasing

Answer: d

Explanation: The cumulative distribution function that is monotone and non-decreasing or can be increasing.

9. Convolution is used to find:

a) The impulse response of an LTI System

b) Frequency response of a System

c) The time response of a LTI system

d) The phase response of a LTI system

Answer: c

Explanation: Convolution is the combination of addition and multiplication of the signals and used to find the impulse response of the LTI system.

Answer: c

Explanation: The Fourier Transform of a rectangular pulse that is the sinc function.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “The Z- and S-Domain Relationship”.

1. The auto-correlation function of a rectangular pulse of duration T is

a) A rectangular pulse of duration T

b) A rectangular pulse of duration 2T

c) A triangular pulse of duration T

d) A triangular pulse of duration 2T

Answer: d

Explanation: The auto-correlation function is the method of correlating the various instants of the signal with itself and that of a rectangular pulse of duration T is a triangular pulse of duration 2T.

2. The FT of a rectangular pulse existing between t = − T 2/ to t = T / 2 is a

a) Sinc squared function

b) Sinc function

c) Sine squared function

d) Sine function

Answer: b

Explanation: By definition the Fourier transform is the transformation of time domain of signal to frequency domain and that of a rectangular pulse is a sinc function.

3. The system characterized by the equation y = ax + b is

a) Linear for any value of b

b) Linear if b > 0

c) Linear if b < 0

d) Non-linear

Answer: d

Explanation: The system is non-linear because x = 0 does not lead to y  = 0, which is a violation of the principle of homogeneity.

4. The continuous time system described by 2 y = x (t 2 ) is

a) Causal, linear and time varying

b) Causal, non-linear and time varying

c) Non causal, non-linear and time-invariant

d) Non causal, linear and time-invariant

Answer: d

Explanation: Y  depends upon the future value therefore the system is anticipative and hence is not causal. But as it follows the superposition theorem so it is linear.

5. If G represents the Fourier Transform of a signal g  which is real and odd symmetric in time, then G  is

a) Complex

b) Imaginary

c) Real

d) Real and non-negative

Answer: b

Explanation: For the real and odd symmetric signal in time domain on the Fourier transform the resulting signal is always imaginary.

6. If a periodic function f of period T satisfies f = −f  , then in its Fourier series expansion

a) The constant term will be zero

b) There will be no cosine terms

c) There will be no sine terms

d) There will be no even harmonics

Answer: b

Explanation: The fourier series will contain the cosine terms if the periodic function f  of period T satisfies f  = -f, and this can be proved by the basic definition of the fourier transform.

7. Given a unit step function u , its time-derivative is:

a) A unit impulse

b) Another step function

c) A unit ramp function

d) A sine function

Answer: a

Explanation: Unit step function is one of the test signals and for the basic standard signals they are interrelated as the function of differentiation and integration as unit step function is the integral of impulse function.

8. The order of a linear constant-coefficient differential equation representing a system refers to the number of

a) Active devices

b) Elements including sources

c) Passive devices

d) None of the mentioned

Answer: d

Explanation: The order of the differential equation is the power of the highest order of the differential term and which refers to the number of poles in the transfer function and practically it refers to the number of components that are energy storing elements .

9. Z-transform converts convolution of time-signals to

a) Addition

b) Subtraction

c) Multiplication

d) Division

Answer: c

Explanation: Convolution is the combination of addition and multiplication that is between the same signal or the different signals and convolution in time domain is always multiplication in z domain.

Answer: b

Explanation: Causal system refers to the system that is only defined for the positive time system and for positive values and therefore region of convergence of a causal LTI system is right half of s-plane.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Stability Analysis”.

1. First column elements of the Routh’s tabulation are 3, 5, -3/4, ½, 2. It means that there are:

a) Is one root in the left half of s-plane

b) Are two roots in the left half of s-plane

c) Are two roots in the right half of the s-plane

d) Is one root in the right half of s-plane

Answer: c

Explanation: Routh hurwitz criteria is used to find the stability of the system and this is determined by the number of roots in which the number of roots is equal to the number of sign changes.

2. Assertion : Feedback control system offer more accurate control over open-loop systems.

Reason : The feedback path establishes a link for input and output comparison and subsequent error correction.

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true and R is not correct Explanation of A

c) A is True and R is false

d) A is False and R is true

Answer: a

Explanation: Feedback control system offers more accuracy and also reduces the gain of the system and establishes the link for input and output comparison and subsequent error correction.

3. Consider the following statements:

a) The effect of feedback is to reduce the system error

b) Feedback increases the gain of the system in one frequency range but decreases in the other

c) Feedback can cause a system originally stable to become unstable

d) Both a and c

Answer: d

Explanation: Feedback reduces error and can cause stable system to become unstable and also can make unstable system stable.

4. The Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains any coefficients which is :

a) Negative real and exponential function

b) Negative real, both exponential and sinusoidal function of s

c) Both exponential and sinusoidal function of s

d) Complex, both exponential and sinusoidal function of s

Answer: b

Explanation: The Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains any coefficients which is negative real, both exponential and sinusoidal function of s.

5. The following characteristic equation results in stable operation of the feedback system s 3 +4s 2 +10s+11=0

a) True

b) False

Answer: a

Explanation: Stable operation can be checked using the Routh-Hurwitz criterion where the first row of the the table is checked and with that.

6. Consider the following statements:

Routh-Hurwitz criterion gives:

1. Absolute stability

2. The number of roots lying on the right half of the s-plane

3. The gain margin and the phase margin

a) 1,2 and3

b) 1 and 2

c) 2 and 3

d) 1 and 3

Answer: b

Explanation: Routh-Hurwitz criterion gives absolute stability and number of roots lying on the right half of the s-plane.

7. The given characteristic equation s 4 +s 3 +2s 2 +2s+3=0 has:

a) Zero root in the s-plane

b) One root in the RHS of s-plane

c) Two root in the RHS of s-plane

d) Three root in the RHS of s-plane

Answer: c

Explanation: The stability analysis is done using Routh-Hurwitz criterion and hence the number of roots on the right is calculated.

8. Which of the following techniques is utilized to determine at the actual point at which the root locus crosses the imaginary axis?

a) Nyquist technique

b) Routh-Hurwitz technique

c) Nichol’s technique

d) Bode technique

Answer: b

Explanation: Routh-Hurwitz technique is utilized to determine at the actual point at which the root locus crosses the imaginary axis.

9. The characteristic equation of a control system is given by s 6 +2s 5 +8s 4 +12s 3 +20s 2 +16s+16=0 . The number of the roots of the equation which lie on the imaginary axis of s-plane:

a) 0

b) 2

c) 4

d) 6

Answer: c

Explanation: The stability analysis is done using Routh-Hurwitz criterion and hence the number of roots on the right is calculated.

Answer: d

Explanation: A linear, negative feedback control system is not necessarily stable if its open loop configuration is stable.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Compensation Techniques”.

1. Assertion : The closed loop stability can be determined from the poles of an open loop system and the polar plot of the frequency response.

Reason : Unstable system has right half poles.

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true and R is not correct Explanation of A

c) A is True and R is false

d) A is False and R is true

Answer: b

Explanation: Closed loop system can be made stable if the poles of the closed loop system are all lying on the left half of the plane and this can be determined from the poles of an open loop system.

2. The open loop control transfer function of a unity feedback system is given by :

G =K/

Which is the value of K which causes sustained oscillations in the closed loop system?

a) 590

b) 790

c) 990

d) 1190

Answer: a

Explanation: The value of the sustained oscillations is calculated from the Rout-Hurwitz table by equation the quadratic equation=0.

3. The characteristic equation of the control system is s 5 +15s 4 +85s 3 +225s 2 +274s+120=0 . What are the number of roots of the equation which lie to the left of the line s+1 = 0?

a) 2

b) 3

c) 4

d) 5

Answer: c

Explanation: The solution is obtained with the help of the Routh-Hurwitz table and in this the solution is obtained by equating the value as s-1 in the given equation.

4. The characteristic equation of a system is 2s 5 +s 4 +4s 3 +2s 2 +2s+1=0 . Which one of the following is correct?

a) Stable

b) Marginally stable

c) Unstable

d) Oscillatory

Answer: c

Explanation: The solution is obtained by using the Routh-Hurwitz table in which with the conventional method the number of sign changes are seen in the first row of the table and number of sign changes is equal to the number of the roots on the right half of s plane.

5. The characteristic equation of a control system is given by s 5 +s 4 +2s 3 +2s 2 +4s+6=0. The number of the roots of the equation which lie on the right half of s-plane:

a) 0

b) 1

c) 2

d) 3

Answer: c

Explanation: The solution is obtained by using the Routh-Hurwitz table in which with the conventional method the number of sign changes are seen in the first row of the table and number of sign changes is equal to the number of the roots on the right half of s plane.

6. Which of the following may result in instability problem?

a) Large error

b) High selectivity

c) High gain

d) Noise

Answer: c

Explanation: High gain results in instability problem and this is due to the low damping factor and damping factor is inversely proportional to the gain of the system.

7. For what values of K does the polynomial s 4 +8s 3 +24s 2 +32s+K=0 have roots with zero real parts?

a) 10

b) 20

c) 40

d) 80

Answer: d

Explanation: The solution is obtained by using the Routh-Hurwitz table and in which with the conventional method the number of sign changes are seen in the first row of the table and number of sign changes is equal to the number of the roots on the right half of s plane.

8. How many roots with positive real parts do the equation s 3 +s 2 -s+1=0 have?

a) 0

b) 1

c) 2

d) 3

Answer: c

Explanation: The roots with positive real parts are calculated with the help of the routh-hurwitz table and since the sign changes two times in first column therefore have two roots have positive parts.

9. Phase margin is always positive for stable feedback system?

a) True

b) False

Answer: a

Explanation: Phase margin is calculated at the gain cross over frequency at which the gain is 1 and this is calculated for stability and is always positive for stable feedback system.

Answer: a

Explanation: The sensitivity of the control system is defined as the change in the output to the change in the input and senstivity of the gain of the overall system, M to the variation in G is 1/1+GH.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Concept of State, State Variables and State Models”.

1. The transfer function for the state representation of the continuous time LTI system:

dq/dt=Aq+Bx

Y=Cq+Dx

is given by:

a) C -1 B+D

b) B -1 B+D

c) C -1 B+A

d) D -1 B+C

Answer: a

Explanation: Transfer function which is ratio of Laplace output to the Laplace input when the initial conditions are zero and is calculated by using both the equations.

2. System transformation on function H for a discrete time LTI system expressed in state variable form with zero initial condition

a) C -1 B+D

b) C -1

c)  -1 z

d)  -1

Answer: a

Explanation: Transfer function which is ratio of Laplace output to the Laplace input when the initial conditions are zero in discrete is same as continuous but in the z-domain.

3. State space analysis is applicable for non-linear systems and for multiple input and output systems.

a) True

b) False

Answer: a

Explanation: State space analysis is the technique that used state variables and state model for the analysis and is applicable for non-linear systems and for multiple input and output systems.

4. Assertion : Transfer function approach has limitation that it reveals only the system output for a input and provides no information regarding the internal state of the system.

Reason : There may be situations where the output of a system is stable and yet some of the system elements may have a tendency to exceed their specified ratings.

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) A is true but R is False

d) A is False but R is True

Answer: a

Explanation: Transfer function approach has limitation over state variable analysis and for that it reveals only the system output for a input and provides no information regarding the internal state of the system.

5. When human being tries to approach an object, his brain acts as,

a) An error measuring device

b) A controller

c) An actuator

d) An amplifier

Answer: b

Explanation: Brain of human being acts as a controller in the human body system as human body is the control system and when human tries to approach an object the brain of the human acts as controller.

6. For two-phase AC servomotor, if the rotor’s resistance and reactance are respectively R and X, its length and diameter are respectively L and D then,

a) X/R and L/D are both small

b) X/R is large but L/D is small

c) X/R is small but L/D is large

d) X/R and L/D are both large

Answer: c

Explanation: Small X/R gives linear speed torque characteristic. Large L/D gives less inertia and good acceleration characteristic.

7. Consider the following statements relating to synchro’s:

1. The rotor of the control transformer is either disc shaped

2. The rotor of the transmitter is so constructed as to have a low magnetic reluctance

3. Transmitter and control transformer pair is used as an error detector

Which of these statements are correct?

a) 1,2 and3

b) 1 and 2

c) 2 and3

d) 1 and 3

Answer: c

Explanation: Rotor of control transformer is rotatory part of the transformer and is made cylindrical in shape so that air gap is practically uniform.

8. Error detector:

a) Armature controlled FHP DC motor

b) A pair of synchronous transmitter and control transformer

c) Tach generator

d) Amplidyne

Answer: a

Explanation: Error detector is the part in the armature controlled FHP DC motor where error detector is the first element that compares the final output with desired output and gives the accurate results.

9. Servomotor:

a) Armature controlled FHP DC motor

b) A pair of synchronous transmitter and control transformer

c) Tach generator

d) Amplidyne

Answer: b

Explanation: Servomotor is a rotary actuator or linear actuator that allows for precise control of angular or linear position, velocity and acceleration a pair of synchronous transmitter and control transformer.

Answer: d

Explanation: Amplifier is an amplidyne which is an amplidyne is an electromechanical amplifier invented during World War II by Ernst Alexanderson. It consists of an electric motor driving a DC generator.

This set of Control Systems Questions and Answers focuses on “State Models for Linear Continuous-Time Systems”.

1. Consider the following servomotors:

1. AC-two phase servomotor

2. DC servomotor

3. Hydraulic servomotor

4. Pneumatic servomotor

The correct sequence of these servomotor in increasing order of power handling capacity is:

a) 2,4,3,1

b) 4,2,3,1

c) 2,4,1,3

d) 4,2,1,3

Answer: c

Explanation: Power handling capacity is the capacity of the system where the system can handle very high power and among the given is maximum DC servomotor.

2. Open loop transfer function of a system having one zero with a positive real value is called.

a) Zero phase function

b) Negative phase function

c) Positive phase function

d) Non-minimum phase function

Answer: d

Explanation: Non-minimum phase system has zero lying on the right half but not pole and combination of the all pass and minimum phase system can be non-minimum phase system.

3. Assertion : The stator winding of a control transformer has higher impedance per phase

Reason : The rotor of control transformer is cylindrical in shape.

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true and R is not correct Explanation of A

c) A is True and R is false

d) A is False and R is true

Answer: b

Explanation: The control transformer has two parts as stator which is stationary having higher impedance and rotor which was rotatory was cylindrical in shape.

4. Assertion : In a shunt regulator, the control element is connected in shunt with the load to achieve constant output voltage.

Reason : The impedance of the control element varies to keep the total current flowing through the load and the control element constant.

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true and R is not correct Explanation of A

c) A is True and R is false

d) A is False and R is true

Answer: c

Explanation: Shunt regulator refers to the winding connected in shunt or parallel and to achieve constant output voltage.

5. Assertion : In the error detector configuration using a synchro transmitter and synchro control transformer, the latter is connected to the error amplifier.

Reason : Synchro control transformer has almost a uniform reluctance path between the rotor and the stator.

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true and R is not correct Explanation of A

c) A is True and R is false

d) A is False and R is true

Answer: c

Explanation: Synchro control transformer is amplifier that is used to amplify the error and synchro transmitter is used to detect error.

6. A tachometer is used as an inner loop in a position control servo-system. What is the effect of feedback on the gain of the sub-loop incorporating tachometer and in the effective time constant of the system?

a) Both are reduced

b) Gain is reduced but the time constant is increased

c) Gain is increased but the time constant is reduced

d) Both are increased

Answer: a

Explanation: Tachometer is the device that is used to control the speed of motor in the control system and Feedback and effective time constant of the system both are reduced on the gain of the sub-loop.

7. If the initial conditions are inherently zero, what does it physically mean?

a) The system is at rest but stores energy

b) The system is working but does not store energy

c) The system is at rests or no energy is stored in any of its parts

d) The system is working with zero reference input

Answer: c

Explanation: A system with zero initial condition is said to be at rest since there is no stored energy.

8. In case of DC servomotor the back-emf is equivalent to an “electric friction” which tends to :

a) Improve stability of the motor

b) Slowly decrease stability of the motor

c) Vary rapidly decrease stability of the motor

d) Have no effect on stability

Answer: a

Explanation: Back emf is the voltage that is generated in absence of the input and in case of DC servomotor tends to improve the stability of the motor.

9. Consider the following statements for the pneumatic and hydraulic systems:

1. The normal operating pressure of pneumatic control is very much higher than that of hydraulic control.

2. In, pneumatic control external leakage is permissible to a certain extent, but there should no leakage in a hydraulic control.

Which of the statements given above is/are correct?

a) 1 only

b) 2 only

c) Both 1 and 2

d) Neither 1 and 2

Answer: c

Explanation: Operating pressure of pneumatic as the control,action is mainly to control the flow of air is more and also no leakage is permitted in hydraulic systems.

Answer: a

Explanation: Steady state value is the final value and it is calculated from the final vale theorem and final value theorem is applicable for the stable systems only.

This set of Control Systems Assessment Questions and Answers focuses on “State Variables and Linear Discrete-Time Systems”.

1. Which of the following can be used as a tacho generator in control systems?

a) Microsyn

b) DC servomotor

c) AC servomotor

d) Magnetic Amplifier

Answer: c

Explanation: Tacho-generator in the control system is used to manage the speed and convert the speed into measurable terms and AC servomotor can be used as Tacho generator in control systems.

2. Consider the function F = 5/s(s 2 +3s+2), the initial value of f is:

a) 5

b) 5/2

c) 5/3

d) 0

Answer: d

Explanation: For initial value theorem in which time is at t =0 and for the frequency which is the inverse of time, the value of s is replaced with infinity and hence the value obtained is 0.

3. An electric motor is developing 10KW at a speed of 900rpm. The torque available at the shaft is:

a) 106 N-m

b) 66 N-m

c) 1600 N-m

d) 90 N-m

Answer: a

Explanation: The formula of the Torque =9.544*Power/speed in rpm and unit is N-m and by this the value of the torque can be calculated.

4. Assertion : Many of the linear control system transfer function do not have poles or zeroes in the right half s-plane.

Reason : These are called minimum phase transfer function.

a) Both A and R are true and R is correct explanation of A

b) Both A and R are true and R is not correct Explanation of A

c) A is True and R is false

d) A is False and R is true

Answer: a

Explanation: For minimum phase systems the poles and zeroes must be on the left side of the s-plane and for the systems which have zeroes on the right half of the s plane are called non-minimum phase systems.

5. The tacho meter has sensitivity of 5V/1000rpm. The gain constant of the tacho meter is:

a) 0.48V/rad/sec

b) 0.048V/rad/sec

c) 4.8V/rad/sec

d) 48V/rad/sec

Answer: b

Explanation: Gain constant = 5*60/2p*1000

0.048 V/rad/sec.

6. The closed loop transfer function of a unity negative feedback system is 100/(s 2 +8s+100). Its open loop transfer function is:

a) 100/s+8

b) 1/s 2 +8s

c) 100/s 2 -8s

d) 100/s 2 +8s

Answer: d

Explanation: For unity feedback system the closed loop transfer function is: G/1+GH and the open loop transfer function can be calculated by balancing the value of G.

7. The impulse response of a linear LTI system is given as g  = e  The transfer function of the system is equal to:

a) 1/s

b) 1/s

c) 1/

d) s/

Answer: c

Explanation: Impulse response is just the Laplace transform of the transfer function and the response is just the Laplace transform of the forward path block.

8. In a closed loop for which the output is the speed of the motor, the output rate control can be used to:

a) Limit the speed of the motor

b) Limit the torque output of the motor

c) Reduce the damping of the system

d) Limit the acceleration of the motor

Answer: a

Explanation: For motor to be the closed loop system the output of the system is the speed of the motor and output rate can be to limit the speed of the motor.

9. In servo-system, the device used for derivative feedback is known as:

a) Synchro

b) Servomotor

c) Potentiometer

d) Tacho generator

Answer: d

Explanation: Tacho generator provides the derivative feedback when used in a servo system and it controls the speed of the servo-system by providing the value of the speed as feedback.

Answer: a

Explanation: For a minimum phase system all the poles and zeroes of a transfer function must lie on the left of the imaginary axis and these type of the systems if causal are always stable.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Diagonalization”.

1. State models presented employed:

a) Physical variables

b) Phase variables

c) Canonical variables

d) All of the mentioned

Answer: d

Explanation: State models are used in the state model analysis and is employed in all the variables as physical, phase and canonical phase analysis.

2. State model is generally not suitable for measuring:

a) Investigation of system properties

b) Evaluation of time response

c) Real variables

d) Both a and b

Answer: d

Explanation: State models are used in the state model analysis and is employed in all the variables as physical, phase and canonical phase analysis and is generally not suitable for investigation of system properties and evaluation of time response.

3. ______________ are the techniques for converting general state models into canonical one.

a) Observable

b) Controllable

c) Diagoanlization

d) Cannonical

Answer: c

Explanation: Diagonalization is the form in which the roots are in the daigonal of the matrix and are the techniques for converting general state models into canonical one.

4. The values of the characteristic equation is given by:

a) Eigen values

b) State matrix

c) Eigen vector

d) None of the mentioned

Answer: a

Explanation: Eigen values are the values that are obtained by solving the characteristic equation these are the roots of the characteristic equation.

5. The matrix constructed by placing the Eigen vectors together is diagonalizing matrix.

a) True

b) False

Answer: a

Explanation: Eigen values are the values that are obtained by solving the characteristic equation these are the roots of the characteristic equation and the matrix constructed by placing the Eigen vectors together is diagonalizing matrix.

6. The diagonalizing matrix is also known as:

a) Eigen matrix

b) Modal matrix

c) Constant matrix

d) State matrix

Answer: b

Explanation: The modal matrix is the matrix formed formed by placing the eigen values that is the roots of the characteristic equation and this is also known as the diagonalizing matrix.

7. In an open loop control system

a) Output is independent of control input

b) Output is dependent on control input

c) Only system parameters have effect on the control output

d) None of the mentioned

Answer: a

Explanation: In an open loop control system the system in which there is no feedback present and in which the output is independent of control input.

8. Which of the following is exhibited by Root locus diagrams?

a) The poles of the transfer function for a set of parameter values

b) The bandwidth of the system

c) The response of a system to a step input

d) The frequency response of a system

Answer: a

Explanation: Root locus diagram is the diagram that is constructed in which the locus is traced with the gain with increasing frequency has the poles of the transfer function for a set of parameter values.

9. The first order control system, which is well designed, has a

a) Small bandwidth

b) Negative time constant

c) Large negative transfer function pole

d) None of the mentioned

Answer: c

Explanation: The first order control system is the control system which has atleast the one pole at the origin or at max one pole, which is well designed has a large negative transfer function pole.

Answer: c

Explanation: A.C. servomotor is a rotary actuator or linear actuator that allows for precise control of angular or linear position, velocity and acceleration is basically a two phase induction motor.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Solution of State Equations”.

1. Which of the following is an electromechanical device ?

a) Induction relay

b) Thermocouple

c) LVDT

d) Any of the mentioned

Answer: c

Explanation: LVDT is linear variable differential transformer which is an inductive transducer and converts the displacement of the core to the electrical energy and also is electromechanical device.

2. A differentiator is usually not a part of a control system because it

a) Reduces damping

b) Reduces the gain margin

c) Increases input noise

d) Increases error

Answer: c

Explanation: A differentiator is the phase lead compensator which increases the speed of response and bandwidth and manages the transient response of the system.

3. If the gain of the critical damped system is increased it will behave as

a) Oscillatory

b) Critically damped

c) Overdamped

d) Underdamped

Answer: d

Explanation: Gain of the critical system is inversely proportional to the root of the damping factor and hence on increasing the gain the damping reduces and system becomes the underdamped.

4. In a control system integral error compensation _______ steady state error

a) Increases

b) Minimizes

c) Does not have any effect on

d) All of the mentioned

Answer: b

Explanation: Integral error compensation is the phase lag compensation and reduces the steady state error and eliminates the error.

5. With feedback _____ reduces.

a) System stability

b) System gain

c) System stability and gain

d) None of the mentioned

Answer: b

Explanation: Feedback reduces the gain as it causes the stability to the closed loop system and for the good control system the stability of the system should be high and also the speed of response.

6. An amplidyne can give which of the following characteristics?

a) Constant current

b) Constant voltage

c) Constant current as well as constant voltage

d) Constant current, constant voltage and constant power

Answer: d

Explanation: An amplidyne has constant current, voltage and power.

7. Which of the following can be measured by LVDT?

a) Displacement

b) Velocity

c) Acceleration

d) All of the mentioned

Answer: d

Explanation: LVDT can measure displacement, velocity and acceleration which is a linear variable differential transformer and inductive transducer.

8. ____________directly converts temperature into voltage.

a) Thermocouple

b) Potentiometer

c) Gear train

d) LVDT

Answer: a

Explanation: Thermocouple is a device that converts the change in the temperature into voltage in which the change in temperature of the different metals results in change in voltage.

9. The transfer function technique is considered as inadequate under which of the following conditions?

a) Systems having complexities and non-linearity’s

b) Systems having stability problems

c) Systems having multiple input disturbances

d) All of the mentioned

Answer: d

Explanation: Transfer function is the ratio of laplace output to the laplace input with the zero initial conditions and is considered inadequate due to complexity, stability problems and multiple input disturbances.

Answer: d

Explanation: Thermocouple is the device that is used to convert the change in temperature gives output in DC form.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Controllability and Observability”.

1. A system is said to be_____________ if it is possible to transfer the system state from any initial state to any desired state in finite interval of time.

a) Controllable

b) Observable

c) Cannot be determined

d) Controllable and observable

Answer: a

Explanation: By definition a system is said to be controllable, if it is possible to transfer the system state from any initial state to any desired state in finite interval of time.

2. A system is said to be_________________ if every state can be completely identified by measurements of the outputs at the finite time interval.

a) Controllable

b) Observable

c) Cannot be determined

d) Controllable and observable

Answer: b

Explanation: By definition, a system is said to be observable, if every state can be completely identified by measurements of the outputs at the finite time interval.

3. Kalman’s test is for :

a) Observability

b) Controllability

c) Optimality

d) Observability and controllability

Answer: d

Explanation: Kalman’s test is the test that is done for the controllability and observability by solving the matrix by kalman’s matrix individually for both tests.

4. Consider a system if represented by state space equation and x1  =x2 , then the system is:

a) Controllable

b) Uncontrollable

c) Observable

d) Unstable

Answer: b

Explanation: After calculating the matrix which for controllable system and finding the determinant and should not be zero but in this case comes to be zero.

5. For the system control-systems-questions-answers-controlability-observability-q5 , which of the following statements is true?

a) The system is controllable but unstable

b) The system is uncontrollable and unstable

c) The system is controllable and stable

d) The system is uncontrollable and stable

Answer: By Kalman’s stability test the system is uncontrollable and root of the characteristic equation lies on the right side of the s-plane.

6. A transfer function of the system does not have pole-zero cancellation? Which of the following statements is true?

a) System is neither controllable nor observable

b) System is completely controllable and observable

c) System is observable but uncontrollable

d) System is controllable and unobservable

Answer: b

Explanation: If the transfer function of the system does not have pole-zero cancellation then it is completely controllable and observable.

7. Complex conjugate pair:

a) Center

b) Focus point

c) Saddle point

d) Stable node

Answer: b

Explanation: Complex conjugate pair is the complex pair of the roots of the equation and has a focus point.

8. Pure imaginary pair:

a) Centre

b) Focus point

c) Saddle point

d) Stable node

Answer: a

Explanation: Pure imaginary pair is the nature of the root of the equation that has no real part only has the nature of center for linearized autonomous second order system.

9. Real and equal but with opposite sign.

a) Center

b) Focus point

c) Saddle point

d) Stable node

Answer: c

Explanation: Saddle point are real and equal with opposite sign and these points are called the saddle point as the points are different with real and equal with opposite sign.

Answer: d

Explanation: Stable node is real distinct and negative and this node is stable as the points or roots are real and neative lying on the left side of the plane.

This set of Basic Control Systems Questions and Answers focuses on “Pole Placement by State Feedback”.

1. ______________ is not a final control element.

a) Control valve

b) Potentiometer

c) Electro-pneumatic converter

d) Servomotor

Answer: b

Explanation: Control element refers to the various blocks in the whole control process and the various control elements can ce controller as control valve, potentiometer, servomotors and tachometers but potentiometer is not the final control element.

2. Which of the following is the definition of proportional band of a controller?

a) The range of air output as measured variable varies from maximum to minimum

b) The range of measured variables from set value

c) The range of measured variables through which the air output changes from maximum to minimum

d) All of the mentioned

Answer: c

Explanation: Proportional band of controller is the range of measured variables through which the air output changes from maximum to minimum.

3. In pneumatic control systems the control valve used as final control element converts

a) Pressure signal to electric signal

b) Pressure signal to position change

c) Electric signal to pressure signal

d) Position change to pressure signal

Answer: b

Explanation: In pneumatic control system the control force is the air and and can be used as final control element converts the pressure signal to position change.

4. Pressure error can be measured by which of the following?

a) Differential bellows and strain gauge

b) Selsyn

c) Strain gauge

d) Strain gauge and potentiometer

Answer: a

Explanation: Pressure error is the error that is caused due to change in the pressure and the error can be measured by differential bellows and strain gauge which is by the change of dimensions.

5. Which of the following devices is used for conversion of co-ordinates?

a) Microsyn

b) Selsyn

c) Synchro-resolver

d) Synchro-transformer

Answer: c

Explanation: Dimensions of the container can be changed by conversion of the coordinates and this can ne done with the help of the synchro-resolver.

6. The effect of error damping is to

a) Provide larger settling lime

b) Delay the response

c) Reduce steady state error

d) None of the mentioned

Answer: c

Explanation: Error damping refers to the error that is caused by the damping in the system and the effect of this error damping is that it reduces the steady state error and gain of the system reduces.

7. Technique gives quick transient and stability response

a) Root locus

b) Bode

c) Nyquist

d) Nichols

Answer: a

Explanation: Root locus is the locus of the system that is drawn by the change in the gain with respect to the frequency and this technique gives the quick transient and stability response of the system.

8. A phase lag lead network introduces in the output

a) Lag at all frequencies

b) Lag at high frequencies and lead at low frequencies

c) Lag at low frequencies and lead at high frequencies

d) None of the mentioned

Answer: c

Explanation: A phase lag lead network is the network that is similar to the differentiator and it is used to increase the speed response and increases the stability of the system and this introduces lag at low frequencies and lead at high frequencies.

9. Which of the following is the non-linearity caused by servomotor?

a) Static friction

b) Backlash

c) Saturation

d) None of the mentioned

Answer: c

Explanation: Non-linearity is the irregular variation in the two parameters of the servomotor and this is caused by the saturation in the servomotor.

Answer: a

Explanation: Zero initial condition refers to the condition in which the stored energy is zero and hence the system implies that the system is at rest without any energy stored in it .

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Observer Systems”.

1. A control system in which the control action is somehow dependent on the output is known as

a) Closed loop system

b) Semi closed loop system

c) Open system

d) Non feedback control system

Answer: a

Explanation: Closed system is a control system in which the feedback is present that can be positive or negative and in which the control action is somewhat dependent on the output.

2. In closed loop control system, with positive value of feedback gain the overall gain of the system will

a) Decrease

b) Increase

c) Be unaffected

d) Exponentially increase

Answer: b

Explanation: Closed loop control system, can be both positive and negative and with positive value of feedback gain where the overall gain of the system will increase and also the oscillations.

3. Which of the following is an open loop control system?

a) Field controlled D.C. motor

b) Ward Leonard control

c) Metadyne

d) Stroboscope

Answer: a

Explanation: Open loop control systems are the systems which have no feedback and cannot be used to obtain the desired response and field controlled system is an open loop control system.

4. Which of the following statements is not necessarily correct for open control system?

a) Input command is the sole factor responsible for providing the control action

b) Presence of non-linearities causes malfunctioning

c) Less expensive

d) Generally free from problems of non-linearities

Answer: b

Explanation: Open loop control system are the systems which have no feedback and cannot be used to obtain the desired response and non-linearities does not cause malfunctioning.

5. In open loop system

a) The control action depends on the size of the system

b) The control action depends on system variables

c) The control action depends on the input signal

d) The control action is independent of the output

Answer: d

Explanation: In open loop system the output cannot be used to obtain the desired response and the control action is independent of the output.

6. ___________has tendency to oscillate.

a) Open loop system

b) Closed loop system

c) Open and closed loop systems have tendency to oscillate

d) No Systems have tendency to oscillate

Answer: a

Explanation: Open loop control systems are the systems where the output cannot be the desired output and no feedback is used and gain of the system is very high due to this damping is very less and hence system has tendency to oscillate.

7. A good control system has all the following features except

a) Good stability

b) Slow response

c) Good accuracy

d) Sufficient power handling capacity

Answer: b

Explanation: A good control system is mainly negative feedback closed loop control system where the gain of system is not very high and damping is present and no oscillations are present and has fast output response.

8. A car is running at a constant speed of 50 km/h, which of the following is the feedback element for the driver?

a) Clutch

b) Eyes

c) Needle of the speedometer

d) Steering wheel

Answer: c

Explanation: For car as control system steering wheel is the feedback element for the driver as for driver to maintain constant speed or desired speed steering wheel is the important element and error detector.

9. The initial response when the output is not equal to input is called

a) Transient response

b) Error response

c) Dynamic response

d) All of the mentioned

Answer: a

Explanation: Transient response in the response at any time instant other than final response and this response is at any instant which is mainly dependent on the maximum peak overshoot and settling time.

Answer: c

Explanation: A control system is the system which is having feedback and can be both positive and negative and working under unknown random actions is called stochastic control system.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Liapunov’s Stability Criterion – I”.

1. If the system is asymptotically stable irrespective that how close or far it is from the origin then the system is:

a) Asymptotically stable

b) Asymptotically stable in the large

c) Stable

d) Unstable

Answer: b

Explanation: For the good control system system must be stable and if the system is asymptotically stable irrespective that how close or far it is from the origin then the system is asymptotically stable in large.

2. A system is said to be locally stable if:

a) The region S  is small

b) There exist a real number >0 such that || x  || <=r

c) Every initial state x  results in x  tends to zero as t tends to infinity

d) They are unstable

Answer: a

Explanation: By the definition of Liapunov’s stability criteria a system is locally stable if the region of system is very small.

3. The system is asymptotically stable at the origin if :

a) It is stable

b) There exist a real number >0 such that || x  || <=r

c) Every initial state x  results in x  tends to zero as t tends to infinity

d) It is unstable

Answer: d

Explanation: By the definition of Liapunov’s stability criteria the system is asymptotically stable at the origin if there exist a real number >0 such that || x  || <=r and every initial state x  results in x  tends to zero as t tends to infinity .

4. The system is asymptotically stable in the large at the origin if :

a) It is stable

b) There exist a real number >0 such that || x  || <=r

c) Every initial state x  results in x  tends to zero as t tends to infinity

d) Both a and c

Answer: d

Explanation: By the definition of Liapunov’s stability criteria the system is asymptotically stable in the large at the origin if there exist a real number >0 such that || x  || <=r and every initial state x  results in x  tends to zero as t tends to infinity.

5. The stability of non-linear systems:

a) Disturbed steady state coming back to its equilibrium state

b) Non-linear systems to be in closed trajectory

c) In limit cycles that is oscillations of the systems

d) All of the mentioned

Answer: d

Explanation: For the stability of non-linear systems as they differ from the linear systems as they have disturbed state coming back to its equilibrium and in closed trajectory and in limit cycles that is oscillations in the system.

6. The direct method of Liapunov is :

a) Concept of energy

b) Relation of stored energy

c) Using the equation of the autonomous systems

d) All of the mentioned

Answer: d

Explanation: Liapunov has two methods as direct and indirect and the direct method of Liapunov is using concept of energy, relation of stored energy and using the equation of the autonomous systems.

7. The results for the energy :

a) Energy of the system is non-negative

b) Energy of the system decreases as t increases

c) Energy is non-negative and decreases as t increases

d) Energy is negative

Answer: c

Explanation: Energy is defined as the work done or force which produces certain displacement and the results for the energy are that energy of the system in non-negative and it decreases as t increases.

8. The visual analogy of the Liapunov energy description is:

a) Ellipse

b) Circle

c) Square

d) Rectangle

Answer: a

Explanation: For the results of the Liapunov energy the loci is traced by the Liapunov energy description and is a ellipse.

9. The idea that the non-negative scalar functions of a system state can also answer the question of stability was given in Liapunov function:

a) True

b) False

Answer: a

Explanation: The stability of the liapunov function can be determined with the help of the scalar functions of a system state.

Answer: a

Explanation: Liapunov’s stability is the major factor of the autonomous functions and it can be determined with the help of the direct method.

This set of Control Systems Questions and Answers for Aptitude test focuses on “Liapunov’s Stability Criterion – II”.

1. The systems with equation such as dx/dt =F  are called:

a) Stable systems

b) Control systems

c) Autonomous systems

d) Unstable control system

Answer: c

Explanation: Autonomous systems are represented by the differential equations as stated above and these systems are tested by liapunov’s stability criteria.

2. The points at which derivatives of all the state variables are zero are:

a) Singular points

b) Nonsingular points

c) Poles

d) Zeros

Answer: a

Explanation: Singular points are the points that are calculated by equating the denominator equal to zero and at which the derivatives of all the state variables are zero.

3. The system if kept in the singular points will continue to lie on these points undisturbed.

a) True

b) False

Answer: a

Explanation: The derivative of all the phase variables being zero, the system shall remain unchanged and the system if lying on these points will continue to lie on these points undisturbed.

4. A system is stable with zero input if:

a) The resulting trajectory tends towards the equilibrium state.

b) If for the bounded input output is also bounded

c) It is a free system

d) It is forced system

Answer: a

Explanation: A system with zero input is the system in which the input is zero and initial states are taken as the input and a free system but it is stable only if the resulting trajectory tends toward the equilibrium state.

5. A Forced system is stable if:

a) The resulting trajectory tends towards the equilibrium state.

b) If for the bounded input output is also bounded

c) It is a free system

d) It is forced system

Answer: b

Explanation: For forced system input is given externally and response has two terms due to the initial states and input given and it is stable if output is bounded for bounded input.

6. In non-linear systems forced and free responses are:

a) Related

b) Not related

c) Contemporary

d) None of the mentioned

Answer: a

Explanation: Forced response is due to the external input and free response is due to the initial state and total response is sum of both the responses and in non-linear systems both are related.

7. The linear autonomous systems:

a) Have one equilibrium state

b) Their behavior determines the qualitative behavior of the s-plane

c) System behavior for small deviations about the equilibrium point may be different from the large deviation

d) Both a and b

Answer: d

Explanation: The linear autonomous systems having the differential terms with the linear relationship and have one equilibrium state and their behavior determines the qualitative behavior of the s-plane.

8. The non-linear system

a) Have one equilibrium state

b) Their behavior determines the qualitative behavior of the s-plane

c) System behavior for small deviations about the equilibrium point may be different from the large deviation

d) Both a and b

Answer: c

Explanation: For the non-linear system where the input parameters or external input is having non-linear relationship with the output and behavior for small deviations about the equilibrium point may be different from the large deviation.

9. The system is stable at origin if for every initial state which is sufficiently close to the origin remains near the origin for all t then the system is :

a) Asymptotically stable

b) Asymptotically stable in the large

c) Stable

d) Unstable

Answer: c

Explanation: By definition, the system is stable at origin if for every initial state which is sufficiently close to the origin remains near the origin for all t then the system is stable.

Answer: a

Explanation: By definition, if x  approaches near the origin as t tend to the infinity then the system is asymptotically stable.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “The Direct Method and Constructing of Liapunov for the Linear and Non-Linear System”.

1. If the Liapunov’s function cannot be found then the system is:

a) Stable

b) Unstable

c) Conditionally stable

d) Marginally stable

Answer: b

Explanation: It is very difficult to find the Liapunov’s function and several techniques are devised for the same and if the Liapunov’s function is not available then the system is unstable.

2. Liapunov’s stability analysis is for the :

a) LTI system

b) Time variant system

c) Non-linear system

d) Linear system

Answer: c

Explanation: Liapunov’s stability criterion is for the non-linear system.

3. The system is unstable for:

a) W >0; x not equal to zero

b) W  =0

c) W  has continuous partial derivative with respect to all components of x

d) All of the mentioned

Answer: d

Explanation: It requires much ingenuity of devise a suitable W function to devise a Liapunov function V. In stability analysis of nonlinear systems, it is valuable to establish conditions for which the system is unstable.

4. Liapunov’s stability for non-linear system is same as the Routh Hurwitz criteria for the linear system.

a) True

b) False

Answer: a

Explanation: Liapunov stability is similar in function as the Routh Hurwitz criteria and Silvester’s theorem can be used to prove it.

5. Conditions of ___________ are necessary and sufficient condition for the asymptotic stability of the system.

a) Linear system

b) Krasovskii’s method

c) positive definiteness

d) Variable gradient method

Answer: c

Explanation: For the system to be asymptotic stable which is desired for the Liapunov stability positive definiteness of the system must be fulfilled.

6. It is difficult to form Liapunov’s function for:

a) Linear system

b) Non-linear

c) Time variant systems

d) Time –invariant systems

Answer: b

Explanation: For non-linear system it is difficult to form the Liapunov’s function

And we use various method to do this.

7. If the V is positive definite, for the system to be asymptotically stable, Q should be negative definite.

a) Krasovskii’s method

b) Variable gradient method

c) Constant method

d) Non-variable gradient method

Answer: a

Explanation: If the V is positive definite, for the system to be asymptotically stable, Q should be negative definite. For Krasovskii’s method and in addition V should tend to infinity and the system is asymptotically stable in-the large.

8. The method which provides considerable flexibility in finding the Liapunov’s function is:

a) Krasovskii’s method

b) Variable gradient method

c) Constant method

d) Non-variable gradient method

Answer: b

Explanation: Variable gradient method provides considerable flexibility in finding the Liapunov’s function as the quadratic form approach is too restrictive.

9. Liapunov stability analysis is different from the classical theories approach of stability.

a) True

b) False

Answer: a

Explanation: Liapunov’s stability theorem is applied for the non-linear systems but other stability theorems are applied for the linear systems.

Answer: b

Explanation: For non-linear systems the equation for damping factor as in linear system is called Vander pol’s equation which depends upon x and damping factor has large positive values for this.

This set of Control Systems Problems focuses on “Parameter Optimization: Servomechanims”.

1. Any externally introduced signal affecting the controlled output is called a

a) Feedback

b) Stimulus

c) Signal

d) Gain control

Answer: b

Explanation: Externally introduced signal is called stimulus that is affecting the controlled output and is a factor also affecting steady state error.

2. A closed loop system is distinguished from open loop system by which of the following?

a) Servomechanism

b) Feedback

c) Output pattern

d) Input pattern

Answer: b

Explanation: An open loop system does not has feedback while the closed loop system has feedback.

3. ______________ is a part of the human temperature control system.

a) Digestive system

b) Perspiration system

c) Ear

d) Leg movement

Answer: b

Explanation: Perspiration system is a system that is controlling the body temperature of the human body.

4. By which of the following the control action is determined when a man walks along a path?

a) Brain

b) Hands

c) Legs

d) Eyes

Answer: d

Explanation: Control action is the action which is the generated by the system performance and determined by eyes when man walks along the path.

5. _______________ is a closed loop system.

a) Auto-pilot for an aircraft

b) Direct current generator

c) Car starter

d) Electric switch

Answer: a

Explanation: Auto-pilot for an aircraft is an example of the closed loop system as the output is the desired destination without the use of any pilot.

6. Which of the following devices are commonly used as error detectors in instruments?

a) Vern stats

b) Microsyn

c) Resolvers

d) All of the mentioned

Answer: d

Explanation: All of the mentioned can be used as an error detectors as they can give the difference between the current output and desired output.

7. Which of the following should be done to make an unstable system stable?

a) The gain of the system should be decreased

b) The gain of the system should be increased

c) The number of poles to the loop transfer function should be increased

d) The number of zeros to the loop transfer function should be increased

Answer: b

Explanation: The gain of the system should be increased to make an unstable system stable and for positive feedback of the system the gain is more and for the negative feedback the gain is reduced for which the stable system can become unstable.

8. __________increases the steady state accuracy.

a) Integrator

b) Differentiator

c) Phase lead

d) Phase lag

Answer: a

Explanation: Integrator that is also the low pass filter reduces or eliminates the steady state error but is causes the slow and sluggish response but tries to eliminate the error.

9. A.C. servomotor resembles

a) Two phase induction motor

b) Three phase induction motor

c) Direct current series motor

d) Universal motor

Answer: a

Explanation: AC servomotor is a type of the two phase induction motor.

Answer: b

Explanation: Overall gain reduces due to negative feedback and due to this reduction in gain the stable system can become unstable but excess increase in the gain causes oscillations to increase.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Optimal Control Problems”.

1. The output of the system is considered near :

a) 1

b) 2

c) 3

d) 0

Answer: d

Explanation: Our main objective in the optimal control problem is to reduce the performance index of the system as minimize the output and make it near equal to zero.

2. A performance index written in terms of :

a) 1 variable

b) 2 variable

c) 3 variable

d) 5 variable

Answer: Generally the performance index be of any variables but in standard form we consider the performance index to be in 2 variable only.

3. Matrix Q is :

a) Positive semi definite symmetric matrix

b) Positive definite non-symmetric matrix

c) Negative definite symmetric matrix

d) Negative definite non-symmetric matrix

Answer: a

Explanation: Matrix Q defines positive definite or non-definite symmetric matrix which is used in the performance index so as to give equal weightage to each element.

4. Matrix R is :

a) Positive semi definite symmetric matrix

b) Positive definite non-symmetric matrix

c) Negative definite symmetric matrix

d) Negative definite non-symmetric matrix

Answer: a

Explanation: Matrix R defines positive definite or non-definite symmetric matrix which is used in the performance index so as to give equal weightage to each element.

5. The major requirement of making the output of the system small in output regulator problem is :

a) The system must be controllable

b) The system must be stable

c) The system must be observable

d) The system must be LTI

Answer: c

Explanation: We are concerned with making the output of the output regulator problem small this is achieved when the system is observable.

6. Minimum principle was given by:

a) Pontryagin

b) Hamiltonian

c) Bellman

d) Jacobi

Answer: a

Explanation: The minimum principle to minimize the performance index is given by Pontryagin.

7. Dynamic programming is developed by:

a) Pontryagin

b) Hamiltonian

c) Bellman

d) Jacobi

Answer: c

Explanation: Dynamic programming for minimizing the performance index is given by Bellman.

8. The performance index is reduced by:

a) State variable constraint

b) Input constraint

c) Control function minimization

d) Control function constraint

Answer: c

Explanation: Once the performance index is calculated the next task is to find the control function which is used to minimize the performance index.

9. Minimum principle is based on :

a) Concepts of calculus of variations

b) Principle of calculus

c) Principle of invariant imbedding

d) Principle of optimality

Answer: a

Explanation: Minimum principle of Pontryagin is based on the concept of calculus of variations.

Answer: d

Explanation: Dynamic programming is based on principle of calculus, invariant imbedding and optimality and these are the basic laws of the nature and does not need complex mathematical development to explain its validity.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Optimal Control Problems-2”.

1. The main step for solving the optimal control problem:

a) Transfer function of system which is optimal with respect to the given performance criterion

b) Compensators for the system

c) Minimizing the quadratic function

d) All of the mentioned

Answer: d

Explanation: For solving the problem using optimal control problem various steps are required as first is to form the transfer function and then to compute the compensators and the major requirement is to minimize the quadratic function.

2. For minimizing the transfer function the condition is :

a) Second differentiation of the function must be zero

b) Second differentiation of the function must be positive

c) Second differentiation of the function must be negative

d) Second differentiation of the function must be complex

Answer: c

Explanation: In optimal control problems the main objective is to reduce the performance criterion which is used only when the second differentiation of the function must be negative.

3. For the stability in optimal control poles of the transfer function must be :

a) Located on the right half of s plane

b) Left half of s plane

c) On the s plane

d) None of the mentioned

Answer: b

Explanation: For the stability point of view the basic definition continues that the poles must be located on the left half of s plane.

4. The method of choosing compensator is the configuration must be:

a) Forward path

b) Cascade and feedback compensation

c) Feed forward configuration

d) All of the mentioned

Answer: d

Explanation: The above mentioned are the various configurations of choosing a compensator.

5. When some of the states are inaccessible, then we may set the feedback coefficients equal to zero.

a) True

b) False

Answer: a

Explanation: This is done to adjust coefficients to realize the transfer function and if it is not possible then reconstruction of signals can be done.

6. Z-transform is used in:

a) Continuous optimal control problem

b) Discrete optimal problem

c) Control systems

d) None of the mentioned

Answer: b

Explanation: Z-transform by definition can is used in discrete case only both in optimal and normal control functions.

7. For the stable system in discrete optimal control systems:

a) Poles must lie outside the unit circle

b) Poles must lie within the unit circle

c) Poles must be on the unit circle

d) Pole must be in infinity

Answer: b

Explanation: Poles in discrete system must be inside the unit circle and for causal system it must be outside the circle but no including the infinity.

8. The special case of the tracking problem with input equal to zero:

a) Free response

b) Regulator problem

c) Forced response

d) Output regulator problem

Answer: d

Explanation: For zero input output is zero if all the initial conditions are zero the response are due to non-initial conditions which are caused due to disturbances.

9. The primary objective of the output regulator problem is to damp out:

a) Initial conditions quickly

b) Reducing the effect of excessive oscillations

c) Reducing the effect of excessive overshoot

d) All of the mentioned

Answer: d

Explanation: The primary objective of the output regulator problem is to damp out the initial conditions quickly and also reduce the effect of excessive oscillations and overshoot.

Answer: a

Explanation: The limitation of transfer function approach is that is it useful only for quadratic performance index and multi input and multi output systems are obvious and also it is ineffective for time varying and non-linear systems.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “The Infinite Time Regulator Problem”.

1. In infinite time regulator for the final time is:

a) t1

b) t0

c) Infinite

d) Zero

Answer: c

Explanation: In infinite time regulator is the extended version of the state regulator and the final time for the infinite time regulator is infinite in this case.

2. When time and the state variables tend to infinity then the system becomes:

a) Unstable

b) Stable

c) Marginally stable

d) Conditionally stable

Answer: b

Explanation: The terminal penalty term has no significance and it does not appear in the performance index and terminal time if tends to infinity then the system becomes stable.

3. In finite time regulator:

a) There is no restriction on the controllability of the plant

b) Performance index is infinite

c) Instability imposes problem in finite-interval control

d) No restriction on controllability and performance index

Answer: a

Explanation: In finite time regulator there is no restriction on the controllability of the plant. This is because is always finite and instability does not impose any problems in finite-time control.

4. Performance index can become infinite if:

a) One or more state are uncontrollable

b) The uncontrollable states are uncontrollable

c) The unstable states are reflected in system performance index

d) All of the mentioned

Answer: d

Explanation: Performance index can become infinite if one or more states are uncontrollable and unstable states are reflected in system performance index.

5. In Infinite regulator the optimal control cannot be differentiated from other controls.

a) True

b) False

Answer: a

Explanation: In infinite regulator the optimal control may have same output for all the controls as the same solution for the infinite regulators will exist.

6. The differential term in the riccati equation in infinite regulator is:

a) Finite

b) Positive

c) Infinite

d) Zero

Answer: d

Explanation: As the final time is not defined hence the differential term of the riccati equation becomes zero and the equation we get is the modified riccati equation.

7. The solution of the modified riccati equation may be:

a) Independent

b) Dependent

c) Unique

d) Non-unique

Answer: d

Explanation: The solution of the modified Riccati equation may not be unique as the solution depends upon the requirement that P must be positive and definite.

8. If Q is positive semi- definite:

a) The optimal closed loop system is asymptotically stable

b) The asymptotic stability is not guaranteed

c) The system is stable

d) The system is unstable

Answer: b

Explanation: If the plant is controllable and bounded and in infinite state regulators the asymptotic stability is not guaranteed even if the Q is positive and semi-definite.

9. Tracking problem can be in:

a) Infinite state regulators

b) Finite state regulator

c) Sub-optimal state regulators

d) Non-linear regulators

Answer: c

Explanation: The application of the optimal regulators is that the minimum time, energy, fuel and tracking problems are designed.

Answer: d

Explanation: In infinite state regulators stability is not guaranteed and hence the nonlinear stability is converted into to the linear stability.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Output Regulator and Tracking Problem”.

1. For output regulator problem in performance index the parameter which is set to zero:

a) Input vector

b) Output vector

c) Control vector

d) State vector

Answer: b

Explanation: As the problem is to minimize the performance index involving output vector then the output vector must be close to zero.

2. In tracking problem the parameter reduced is :

a) Error

b) Output

c) Input

d) State

Answer: a

Explanation: In tracking problem the main objective is to reduce error and this is the main concern so as to reduce error.

3. Riccati equation is formed by using:

a) Output regulator problem

b) Finite state regulator problem

c) Infinite state regulator problem

d) Tracking problem

Answer: d

Explanation: Riccati equation can be formed using the results of the tracking problem as it is mainly applied in the cases where the errors are reduced to the minimum.

4. The value of K must further follow the following constraint that the closed loop system must be:

a) Asymptotically stable

b) Stable

c) Marginally stable

d) Conditionally stable

Answer: a

Explanation: The value of Ki must further follow the following constraint that the closed loop system must be asymptotically stable and this is due to the fact that the value of k matrix can be varied.

5. For suboptimal control the value of R is assumed to be:

a) Positive definite

b) Non-positive definite

c) Negative

d) Complex

Answer: b

Explanation: For suboptimal control the value of R is not assumed to be positive definite but it can also be assumed to be zero.

6. Which one of the following compensation is required for improving the transient response of the system?

a) Phase lead compensation

b) Phase lag compensation

c) Gain compensation

d) Both phase lag compensation and gain compensation

Answer: a

Explanation: For increasing or improving the transient response derivative controller is used and which is the phase lead compensation.

7. Pneumatic controller

a) Flexible operation

b) High torque high speed operation

c) Fire and explosion proof operation

d) No leakage

Answer: c

Explanation: Pneumatic controllers are fire and explosion proof operation as they require air and gas fuel for its operation.

8. Hydraulic controller:

a) Flexible operation

b) High torque high speed operation

c) Fire and explosion proof operation

d) No leakage

Answer: b

Explanation: Hydraulic controller must have no leakage and also it requires high torque and high speed operation due to high density of the controller.

9. Electronic Controller:

a) Flexible operation

b) High torque high speed operation

c) Fire and explosion proof operation

d) No leakage

Answer: a

Explanation: Flexible in all sense as it does not require heavy components or extra torque or high speed operations.

Answer: c

Explanation: The introduction of a time delay element decreases both the phase and gain margin.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Parameter Optimization”.

1. A conditionally stable system exhibits poor stability at :

a) Low frequencies

b) Reduced values of open loop gain

c) Increased values of open loop gain

d) High frequencies

Answer: b

Explanation: A conditionally stable system is the system which is stable only for certain values of K and exhibits poor stability at the reduced values of open loop gain.

2. The type 0 system has ______ at the origin.

a) No pole

b) Net pole

c) Simple pole

d) Two poles

Answer: a

Explanation: The type of the system is defined as the property of the system which has pole at the origin.

3. The type 1 system has ______ at the origin.

a) No pole

b) Net pole

c) Simple pole

d) Two poles

Answer: c

Explanation: The type of the system is defined as the pole at the zero and type 1 is defined as the 1 pole at the origin.

4. The type 2 system has at the origin.

a) No net pole

b) Net pole

c) Simple pole

d) Two poles

Answer: d

Explanation: Type of the system is defined as the number of pole at origin and type 2 is the 2 poles at the origin.

5. The position and velocity errors of a type-2 system are :

a) Constant, constant

b) Constant, infinity

c) Zero, constant

d) Zero, zero

Answer: c

Explanation: The position and velocity error of the type 2 system is zero and a constant value as for type 2 system velocity error is finite while acceleration error is infinite.

6. Velocity error constant of a system is measured when the input to the system is unit _______ function.

a) Parabolic

b) Ramp

c) Impulse

d) Step

Answer: b

Explanation: Velocity error constant of a system is measured when the input to the system is unit ramp function then only velocity error is finite but error due to other inputs are not defined.

7. In case of type-1 system steady state acceleration is :

a) Unity

b) Infinity

c) Zero

d) 10

Answer: b

Explanation: In case of type-1 system steady state acceleration is infinity as for the type less than 3 acceleration is not defined it is infinity.

8. If a step function is applied to the input of a system and the output remains below a certain level for all the time, the system is :

a) Not necessarily stable

b) Stable

c) Unstable

d) Always unstable

Answer: a

Explanation: If the input is bounded and output is also bounded then the system is always stable and step input is bounded and the output is always under certain li its then the system is stable.

9. Which of the following is the best method for determining the stability and transient response?

a) Root locus

b) Bode plot

c) Nyquist plot

d) None of the mentioned

Answer: a

Explanation: Root locus is the best method for determining stability of the transient response as it gives the exact pole zero location and also their effect on the response.

Answer: b:

Explanation: Phase margin of the system can be used for determining the absolute stability of the system.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Common Physical Nonlinearities”.

1. The term backlash is associated with:

a) Servomotors

b) Induction relays

c) Gear trains

d) Tacho generator.

Answer: c

Explanation: The term backlash is associated with Gear trains.

2. With feedback _____ increases.

a) System stability

b) Sensitivity

c) Gain

d) Effects of disturbing signals

Answer: a

Explanation: Feedback can increase system stability as well as can reduce the stability of the stable system.

3. By which of the following the system response can be tested better?

a) Ramp input signal

b) Sinusoidal input signal

c) Unit impulse input signal

d) Exponentially decaying signal

Answer: c

Explanation: System response can be best treated with the impulse response as when the input is impulse input then the output is itself the response of the transfer function.

4. In a system zero initial condition means that :

a) The system is at rest and no energy is stored in any of its components

b) The system is working with zero stored energy

c) The system is working with zero reference signal

d) Laplace transform is not possible

Answer: a

Explanation: In system zero initial condition means the system is at rest and no energy is stored in the system previously.

5. In a system low friction co-efficient facilitates:

a) Reduced velocity lag error

b) Increased velocity lag error

c) Increased speed of response

d) Reduced time constant of the system

Answer: a

Explanation: In a system low friction facilitates reduced velocity error as the friction error is equal to the velocity error.

6. Hydraulic torque transmission system is analog of :

a) Amplidyne set

b) Resistance-capacitance parallel circuit

c) Motor-generator set

d) Any of the mentioned

Answer: c

Explanation: Hydraulic torque transmission system is analog of Motor-generator set.

7. Spring constant in force-voltage analogy is analogous to?

a) Capacitance

b) Reciprocal of capacitance

c) Current

d) Resistance

Answer: b

Explanation: Spring constant in force-voltage analogy is analogous to reciprocal of the resistance which is also series analogy.

8. The frequency and time domain are related through which of the following?

a) Laplace Transform and Fourier Integral

b) Laplace Transform

c) Fourier Integral

d) Either b or c

Answer: a

Explanation: The frequency and time domain mainly continuous time domain are related by the Laplace and Fourier transform and discrete time and frequency are related by the discrete time Fourier transform and z transform.

9. An increase in gain, in most systems, leads to:

a) Smaller damping ratio

b) Larger damping ratio

c) Constant damping ratio

d) Zero damping ratio

Answer: a

Explanation: Damping factor is inversely proportional to the gain and if the gain increases the damping factor and hence the value reduces.

Answer: d

Explanation: Static error coefficients are used as a measure of the effectiveness of closed loop system for specified acceleration, velocity and position of input signal.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Stability of Nonlinear System”.

1. Stability of a system implies that :

a) Small changes in the system input does not result in large change in system output

b) Small changes in the system parameters does not result in large change in system output

c) Small changes in the initial conditions does not result in large change in system output

d) Small changes in the initial conditions result in large change in system output

Answer: a

Explanation: Stability of the system implies that small changes in the system input, initial conditions, and system parameters does not result in large change in system output.

2. A linear time invariant system is stable if :

a) System in excited by the bounded input, the output is also bounded

b) In the absence of input output tends zero

c) Both a and b

d) None of the mentioned

Answer: c

Explanation: A system is stable only if it is BIBO stable and asymptotic stable.

3. Asymptotic stability is concerned with :

a) A system under influence of input

b) A system not under influence of input

c) A system under influence of output

d) A system not under influence of output

Answer: b

Explanation: Asymptotic stability concerns a free system relative to its transient behavior.

4. Bounded input and Bounded output stability notion concerns with :

a) A system under influence of input

b) A system not under influence of input

c) A system under influence of output

d) A system not under influence of output

Answer: a

Explanation: BIBO stability concerns with the system that has input present.

5. If a system is given unbounded input then the system is:

a) Stable

b) Unstable

c) Not defined

d) Linear

Answer: c

Explanation: If the system is given with the unbounded input then nothing can be clarified for the stability of the system.

6. Linear mathematical model applies to :

a) Linear systems

b) Stable systems

c) Unstable systems

d) All of the mentioned

Answer: b

Explanation: As the output exceeds certain magnitude then the linear mathematical model no longer applies.

7. For non-linear systems stability cannot be determined due to:

a) Possible existence of multiple equilibrium states

b) No correspondence between bounded input and bounded output stability and asymptotic stability

c) Output may be bounded for the particular bounded input but may not be bounded for the bounded inputs

d) All of the mentioned

Answer: d

Explanation: For non-linear systems stability cannot be determined as asymptotic stability and BIBO stability concepts cannot be applied, existence of multiple states and unbounded output for many bounded inputs.

8. If the impulse response in absolutely integrable then the system is :

a) Absolutely stable

b) Unstable

c) Linear

d) None of the mentioned

Answer: a

Explanation: The impulse response must be absolutely integrable for the system to absolutely stable.

9. The roots of the transfer function do not have any effect on the stability of the system.

a) True

b) False

Answer: b

Explanation: The roots of transfer function also determine the stability of system as they may be real, complex and may have multiplicity of various order.

Answer: b

Explanation: Repetitive roots on the imaginary axis makes the system unstable.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Stability of NonLinear System-II”.

1. In a control system integral error compensation _______steady state error

a) Increases

b) Minimizes

c) Does not have any effect on steady state error

d) All of the mentioned

Answer: b

Explanation: Integral compensation is the phase lag compensation as it reduces or minimizes the steady state error by not affecting the damping factor but reducing the natural frequency.

2. With feedback _____ reduces.

a) System stability

b) System gain

c) System stability and gain

d) Damping

Answer: b

Explanation: With feedback damping increases and system gain reduces as they are inversely proportional to each other and for the good control system the speed of response must be high with low gain and oscillations.

3. An amplidyne can give which of the following characteristics?

a) Constant current

b) Constant voltage

c) Constant current as well as constant voltage

d) Constant current, constant voltage and constant power

Answer: d

Explanation: An amplidyne is the device so constructed so as can give constant current, voltage and power and it is the important device as single device can achieve all these features.

4. Which of the following cannot be measured by LVDT?

a) Displacement

b) Velocity

c) Acceleration

d) Pressure

Answer: d

Explanation: LVDT is the linear variable differential transformer and it is an inductive transformer and can measure displacement, velocity and acceleration but pressure cannot be measured by using LVDT.

5. __________directly converts temperature into voltage.

a) Thermocouple

b) Potentiometer

c) Gear train

d) LVDT

Answer: a

Explanation: Among all the instruments Thermocouple is the instrument that has two different metals with different temperatures and the difference in temperature is converted into the potential difference.

6. The transfer function technique is considered as inadequate under which of the following conditions?

a) Systems having complexities and nonlinearities

b) Systems having stability problems

c) Systems having multiple input disturbances

d) All of the mentioned

Answer: d

Explanation: State variable analysis is used as Transfer function approach cannot be practically used in the systems having complexities, nonlinearities, stability problems and multiple input.

7. Which of the following is the output of a thermocouple?

a) Alternating current

b) Direct current

c) A.C. voltage

d) D.C. voltage

Answer: d

Explanation: Thermocouple is the instrument that has two different metals with different temperatures and the difference in temperature is converted into the potential difference and gives output in D.C. Voltage.

8. A.C. servomotor is basically a

a) Universal motor

b) Single phase induction motor

c) Two phase induction motor

d) Three phase induction motor

Answer: c

Explanation: A.C. Servomotor is the servomotor in which the input is mainly the alternating current and is basically two phase induction motor.

9. The first order control system, which is well designed, has a

a) Small bandwidth

b) Negative time constant

c) Large negative transfer function pole

d) None of the mentioned

Answer: c

Explanation: The first order control system which is the system with maximum one root which can be at origin and has well designed large negative transfer function pole.

Answer: a

Explanation: Root locus diagrams is constructed by the locus traced by the gain of the system with the varying frequency and have the poles of the transfer function for a set of parameter values.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Construction of Phase-trajectories”.

1. Electrical time-constant of an armature-controlled dc servomotor is :

a) Equal to mechanical time-constant

b) Smaller than mechanical time-constant

c) Larger than mechanical time-constant

d) Not related to mechanical time-constant

Answer: b

Explanation: Electrical time constant is smaller than the mechanical time constant and hence the delay in the mechanical systems is more than the electrical systems.

2. The open-loop transfer function of a unity feedback system is K/(s ^ 2 )The system is unstable for

a) K>5

b) K<5

c) K>0

d) All of the mentioned

Answer: d

Explanation: The open loop transfer function of a unity feedback system is used to calculate the conditional stability by using the Routh Hurwitz criteria or the Root locus technique.

3. Peak overshoot of step-input response of an underdamped second-order system is explicitly indicative of

a) Settling time

b) Rise time

c) Natural frequency

d) Damping ratio

Answer: d

Explanation: Peak overshoot refers to the damping of the system as if the damping id less than the peak will be more.

4. A unity feedback system with open-loop transfer function G  = 4/[s] is critically damped. The value of the parameter p is

a) 4

b) 3

c) 2

d) 1

Answer: a

Explanation: The value of the p can be calculated by comparing the equation with the standard characteristic equation.

5. Polar plot of G  = 1/jw is

a) Crosses the negative real axis

b) Crosses the negative imaginary axis

c) Crosses the positive imaginary axis

d) None of the mentioned

Answer: d

Explanation: Polar plot can be made of the following function by following appropriate steps and thus the plot neither crosses the real axis nor imaginary axis.

6. In optimum time switching curve the system takes :

a) Minimum time in reaching desired location

b) Maximum time in reaching desired location

c) Never reaches

d) No desired location is present

Answer: a

Explanation: If switching is made to occur the crossing of the starting trajectory with the thick line trajectory the system follows the trajectory and reaches the desired output at the minimum time.

7. System with logic switching are :

a) Hang on

b) Bang on

c) Bang-bang

d) Hang out

Answer: c

Explanation: Suitable logic circuitry has to be added to the controller structure for the kind of the switching and such systems are known as the bang-bang control system.

8. Zeroes are defined as:

a) Roots of the denominator of the closed loop transfer function

b) Roots of the numerator of the closed loop transfer function

c) Both of the mentioned

d) None of the mentioned

Answer: b

Explanation: Zeroes are defined as the roots of the numerator of the closed loop system.

9. As zero moves sufficiently left from the origin the effect of zero becomes less pronounced.

a) True

b) False

Answer: a

Explanation: The effect of zero on transient response will be negligible if the zero moves left from the origin due to dominant pole mechanism.

Answer: b

Explanation: The zeroes on the real axis near the origin are generally avoided in design as they cause system instability.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Constructing Phase-trajectories”.

1. In liquid level and electrical system analogy, voltage is considered analogous to :

a) Head

b) Liquid flow

c) Liquid flow rate

d) Air flow rate

Answer: a

Explanation: In liquid level and electrical system analogy, voltage is considered analogous to the head which can be pressure head that is the potential energy.

2. The viscous friction co-efficient, in force-voltage analogy, is analogous to:

a) Charge

b) Resistance

c) Reciprocal of inductance

d) Reciprocal of conductance

Answer: b

Explanation: The viscous friction co-efficient in force-voltage analogy, is analogous to resistance of the electrical circuit that can be found out mathematically.

3. In force-voltage analogy, velocity is analogous to:

a) Current

b) Charge

c) Inductance

d) Capacitance

Answer: a

Explanation: In force-voltage analogy, velocity is analogous to the current in force-voltage that is also called series circuit.

4. In thermal-electrical analogy charge is considered analogous to:

a) Heat flow

b) Reciprocal of heat flow

c) Reciprocal of temperature

d) Temperature

Answer: d

Explanation: In thermal-electrical analogy in which heat transfer in the wire or conductor can be related to the temperature.

5. Mass, in force-voltage analogy, is analogous to:

a) Charge

b) Current

c) Inductance

d) Resistance

Answer: c

Explanation: Mass, is analogous to the inductance in the force-voltage analogy in the series form as all the elements of the circuit are connected in the parallel.

6. The transient response of a system is mainly due to:

a) Inertia forces

b) Internal forces

c) Stored energy

d) Friction

Answer: c

Explanation: The transient response of the system is mainly due to stored energy as it is due to the initial conditions which is nothing but the stored energy.

7. ___________ signal will become zero when the feedback signal and reference signs are equal.

a) Input

b) Actuating

c) Feedback

d) Reference

Answer: b

Explanation: Actuating signal is the difference between the feedback signal and the reference signal and when both of the signals are equal then the signal is zero.

8. A signal other than the reference input that tends to affect the value of controlled variable is known as

a) Disturbance

b) Command

c) Control element

d) Reference input

Answer: a

Explanation: Disturbance signal is also the reference signal only there can be multiple inputs in a control system or the other input is called the disturbance signal.

9. The transfer function is applicable to which of the following?

a) Linear and time-in variant systems

b) Linear and time-variant systems

c) Linear systems

d) Non-linear systems

Answer: a

Explanation: The transfer function is different from the state space approach as the transfer function approach is similar to the LTI systems only while the state variable analysis is applicable to the non-linear time variant systems also.

Answer: a

Explanation: The transfer function can be obtained by using signal flow graphs from among these given methods.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Stability Analysis of the Describing Functions”.

1. The characteristic equation of a feedback control system is given bys 3 +5s 2 +s+K=0. In the root loci diagram, the asymptotes of the root loci for large K meet at a point in the s plane whose coordinates are:

a) 

b) 

c) 

d) 

Answer: c

Explanation: The point is calculated by using Routh Hurwitz table and then equating the S 0 term equal to zero.

2. The root locus diagram has loop transfer function GH = K/ s(s 2 +4s+5) has

a) No breakaway points

b) Three real breakaway points

c) Only one breakaway points

d) One real and two complex breakaway points

Answer: b

Explanation: The breakaway points are the points where the root locus branches break and it is not necessary that this point must lie on the root locus calculated by differentiating the value of K with respect to s and equating it with zero.

3. For asymptotes passing from breakaway point then this point is also centroid

a) True

b) False

Answer: True

Explanation: Asymptotes are the lines of infinite length and these are tangents to the root locus that meet at infinity and for these, passing from breakaway point then this point is also centroid.

4. Transportation lag is seen in systems:

a) Amount to be transferred in large

b) Time take to transfer is large

c) Inefficiency of the process

d) Errors

Answer: b

Explanation: Transportation lag is the delay that is seen in the systems where the output is not following the input and is seen in systems where the time taken to transfer is very large.

5. Mediums responsible for transportation lag are:

a) Lines

b) Pipes

c) Belt conveyors

d) All of the mentioned

Answer: d

Explanation: Transportation lag is the delay that is seen in the systems where the output is not following the input and is mainly seen in the practical mediums where the time of transfer is very large.

6. Linear lumped parameter models are not valid under situations as:

a) Transmission pipe between the hydraulic pump and the motor causes a time lag in transportation of oil from pump to motor

b) Transmission of heat by conduction or convection produces serious transportation lag

c) Transmission pipe causes the time lag and loss of heat by conduction and convection

d) Transmission of pipe causes neither any time lag nor any heat loss

Answer: c

Explanation: Linear lumped parameter models are the models that simplifies the description of the behaviour of spatially distributed physical systems into a topology consisting of discrete systems and not valid when the pure time lags are negligible compared to other lags in the system.

7. Practically all the systems have transportation lag :

a) True

b) False

Answer: b

Explanation: Not all systems have transportation lag but whose transmission time is more.

8. Transportation lag causes :

a) Instability in system

b) Stability in system

c) System remains unaffected

d) Bandwidth increases

Answer: a

Explanation: Transportation lag is the delay that is seen in the systems where the output is not following the input and causes instability in the system.

9. The polar plot of a transfer function passes through the critical point .Gain margin is

a) zero

b) -1dB

c) 1dB

d) Infinity

Answer: a

Explanation: Gain margin is the point where the at phase cross over frequency gain of the system i 1 dB and of a polar plot passing through the critical point is zero.

Answer: c

Explanation: Feedback can be of two types as positive and negative and cause the increase in gain and also can cause stable system to become unstable.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Adaptive Control”.

1. Which of the following programs is not a popular desktop publishing program?

a) Adobe PageMaker

b) Microsoft Publisher

c) Lotus AmiPro

d) QuarkXPress

Answer: c

Explanation: Lotus AmiPro is a word processing package.

2. Programs used to create or modify bitmap images are called __________

a) Illustration programs

b) Paint programs

c) Graphical modifiers

d) Bit publishing packages

Answer: b

Explanation: Image editors  are programs for creating and editing bitmap images.

3. Paint programs and image editors are used for creating and editing __________

a) Bitmap images

b) Vector images

c) Text

d) HTML codes

Answer: a

Explanation: Paint programs and image editors are programs for creating and editing bitmap images.

4. Raster images are also known as :

a) Bitmap images

b) Vector images

c) Clip art images

d) Multimedia images

Answer: a

Explanation: Raster images are also known as bitmap images.

5. Images made up of thousands of pixels are called ___________

a) Bitmap

b) Vector

c) Story boards

d) Graphics

Answer: a

Explanation: Bitmap images use thousands of dots or pixels to represent images.

6. Which of the following programs is not a popular professional image editor program?

a) Adobe PageMaker

b) Microsoft Paint

c) Adobe Photoshop

d) Corel Photo Paint

Answer: a

Explanation: Adobe PageMaker is a desktop publishing package.

7. Vector images are __________

a) Composed of pixels

b) Composed of thousands of dots

c) Slightly more difficult to manipulate than other images

d) Composed of objects such as lines, rectangles, and ovals

Answer: d

Explanation: Vector images use geometric shapes or objects.

8. Programs used to create or modify vector images are called __________

a) Illustration programs

b) Image editors

c) Graphical modifiers

d) Bit publishing packages

Answer: a

Explanation: Illustration programs  are used to create and to edit vector images.

9. CorelDraw is an example of a __________

a) Groupware application

b) Bit publishing package

c) Paint program

d) Graphics suite

Answer: d

Explanation: CorelDraw is an example of a graphics suite program.

Answer: c

Explanation: A graphics suite is a combination or bundle of separate graphics packaged in groups.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Fuzzy Logic Control”.

1. Fuzzy logic is :

a) Used to respond to questions in a humanlike way

b) A new programming language used to program animation

c) The result of fuzzy thinking

d) A term that indicates logical values greater than one

Answer: a

Explanation: Fuzzy logic allows users to respond to questions in a very humanlike way with proper thinking and analyzing capabilities.

2. A robot is a __________

a) Computer-controlled machine that mimics the motor activities of living things

b) Machine that thinks like a human

c) Machine that replaces a human by performing complex mental processing tasks

d) Type of virtual reality device that takes the place of humans in adventures

Answer: a

Explanation: Robots are computer-controlled machines that mimic the motor activities of living things.

3. Perception system robots are :

a) Act as a transportation system, like a “mail mobile”

b) Imitate some human senses

c) Perform manufacturing tasks like painting cars

d) Are another name for virtual reality

Answer: b

Explanation: Perception system robots imitate some of the human senses.

4. A mobile robot :

a) Acts as a transportation system, like a “mail mobile”

b) Imitates some human senses

c) Performs manufacturing tasks like painting cars

d) Is another name for virtual reality

Answer: a

Explanation: Mobile robots act as transports and are widely used for a variety of different tasks.

5. Computer-controlled machines that mimic the motor activities of living things are :

a) Virtual reality

b) Robotics

c) Knowledge-based systems

d) Machines that think like a human

Answer: b

Explanation: Robots are computer-controlled machines that mimic the motor activities of living things.

6. Robots used in automobile plants would be classified as :

a) Perception systems

b) Industrial robots

c) Mobile robots

d) Knowledge robots

Answer: b

Explanation: Industrial robots are used in automobile plants.

7. One difference between desktop publishing and word processing is that with desktop publishing you can mix text and graphics.

a) True

b) False

Answer: a

Explanation: Desktop publishing allows you to mix text and graphics to create publications of professional quality.

8. Software that allows the user to create professional-quality layout and type styles is __________

a) Perception systems

b) desktop publishing

c) desktop editing

d) Knowledge robots

Answer: b

Explanation: Desktop publishing allows you to create publications of professional quality.

9. Graphic programs widely used in the graphic arts profession include __________

a) Desktop publishing programs, image editors and illustration programs

b) Artificial intelligence, virtual reality, and illustration programs

c) Mega media programs, image editors, and desktop publishing programs

d) Virtual reality, desktop publishing programs, and illustration programs

Answer: a

Explanation: The graphic arts profession would use desktop publishing, image editors and illustrator programs in their work.

Answer: a

Explanation: Desktop publishing allows you to mix text and graphics to create publications of professional quality.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Neural Networks”.

1. An essential ingredient for effective multimedia presentations incorporates user participation or __________

a) Links

b) Buttons

c) Interactivity

d) Integration

Answer: c

Explanation: Interactivity allows the user to choose the information to view, to control the pace and flow of information, and to respond to items and receive feedback.

2. The term that describes a user’s participation with a multimedia presentation is __________

a) Hyperactivity

b) Interactivity

c) Inactivity

d) Reactivity

Answer: b

Explanation: Interactivity allows the user to choose the information to view, to control the pace and flow of information, and to respond to items and receive feedback.

3. Multimedia can contain

a) Graphics, animation, video, music, and voice

b) Only numeric type data

c) Numeric, text, and picture data

d) Databases that turn contain other databases creative massive data collection

Answer: a

Explanation: Multimedia includes video, music, voice, graphics, and text and is the main source of entertainment in day to day life.

4. Primary uses of business interactive multimedia include all of the following except

a) Product demonstrations

b) Web page development

c) Entertainment

d) High-quality presentations

Answer: c

Explanation: Entertainment interactive multimedia is primarily used in the home and multimedia includes video, music. voice, graphics and text.

5. The connection between a multimedia presentation and a file containing a song to be played is called a _________

a) Link

b) Chain

c) Pointer

d) Tie

Answer: a

Explanation: Each page presents information and provides links or connections to related information and the connection between a multimedia presentation and file containing a song to be played is called link.

6. Clicking on special areas called __________ activates the various features of a multimedia presentation.

a) Activators

b) Starters

c) Pages

d) Buttons

Answer: d

Explanation: By clicking on special areas called buttons on a page, you can make appropriate links and navigate through a presentation to locate and discover information.

7. When determining the overall objective of the project, the resources required and the persons or team who will work on the project, you are in the __________ step of developing a multimedia presentation.

a) Planning

b) Designing

c) Creating

d) Supporting

Answer: a

Explanation: The planning process would be the part of developing a multimedia presentation when determining the overall objective of the project the resources required and the persons or team who will work on the project.

8. The creation of a storyboard is essential to the development of the project. This is the __________ step of development.

a) Planning

b) Designing

c) Creating

d) Supporting

Answer: b

Explanation: The storyboard is part of the design process in the development of a project which the primary part of in building of the project and describes the whole working of the project and functionalities.

9. Errors are identified and the presentation is evaluated in terms of effectiveness in the __________ step.

a) Planning

b) Designing

c) Creating

d) Supporting

Answer: d

Explanation: Evaluate effectiveness, identify errors, and revise as needed is done in the support stage and this is the stage in which necessary measures are taken to complete the project as a whole.

Answer: d

Explanation: A storyboard is a design tool used to record the intended overall logic, flow, and structure of a multimedia presentation.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Steady State Error”.

1. The steady state error for a unity feedback system for the input r to the system G = K/s(s 3 +7s 2 +12s) is 6R/K. The input r  is _______

a) Rt2/2

b) Rt3/2

c) Rt5/2

d) Rt7/2

Answer: a

Explanation: Ka = 2K/12 = K/6. Ess = 6R/K. So, as we take Rt 2/2 we get 6R/K as the error. The other options can’t be true because the input is exceeding the desired input. It is inversely proportional to the gain.

2. The ramp input is applied to a unity feedback system with type number 1 and zero frequency 20. What is the percentage of steady state error?

a) 1%

b) 2%

c) 5%

d) 9%

Answer: c

Explanation: Steady state error is the error calculated between the final output and desired output and the error must be less and this steady state error is inversely proportional to gain. Here unity feedback system is given with zero frequency 20 so we take 1/20 th part and the answer comes as 5%.

3. A unit integrator is applied to a modified system along with a ramp input. The modified value of the steady state error is 0.25. What was the initial value?

a) 0.05

b) 0.1

c) 0.15

d) 0.2

Answer: d

Explanation: The integrator is similar to the phase lag systems and it is used to reduce or eliminate the steady state error and when it is cascaded with the ramp input. We know that when unit integrator is applied with a ramp input the steady state error will automatically increase but here we wanted the initial value which will be obviously less than the modified steady state error and by the same proportion.

4. Systems of type higher than 1 are not employed in practice.

a) True

b) False

Answer: b

Explanation: Systems of type higher than 2 are not employed in practice as they’re difficult to stabilize and dynamic error increases. Systems of type 2 or lower are already stable and has less dynamic error.

5. The initial response when output is not equal to input is ______

a) Error response

b) Transient response

c) Dynamic response

d) Static response

Answer: b

Explanation: The response is not long last lasting and real, so it is a transient response. It can’t be a static or dynamic response as the output doesn’t match the input and also there’s no chance of error response.

6. The steady state error for a unit step input is ________

a) 1/kp

b) 1/

c) 1/2kp

d) 1/

Answer: d

Explanation: R =1/s for unit step and for the transfer function whose limit tends to zero, it is 1/1+kp. We use Laplace and Inverse Laplace Transform to calculate the same.

7. For a unity feedback system, the open loop transfer function is G = K/s 2 (s 2 +7s+12). What is the type of system?

a) One

b) Two

c) Three

d) Four

Answer: b

Explanation: As in the numerator it is mentioned K so we got two poles in the open loop transfer function at the origin. For a given transfer function we calculate poles and zeros and the number of poles determine the type of the system.

8. The For a unity feedback system the open loop transfer function is G = K/s 2 (s 2 +7s+12). What is the value of Ka?

a) 12/k

b) k/12

c) k/6

d) 6/k

Answer: c

Explanation: As limit s tends to zero : s 2 G = K/ (s 2 +7s+12) = k/6. Ka is the acceleration error constant which is calculated by the above method.

9. For a system whose transfer function is G =10/s , what are the dynamic error coefficients k2 & k3 respectively as k1 is infinity?

a) 11, 10.1

b) 10.1, 11

c) 10, 11.1

d) 9, 10.1

Answer: c

Explanation: We should compare it with E/R = 1/k1+1/k2s+1/k3s 2 . G = 10/s is compared with the above equation which is the parent equation for calculating dynamic error constants where k1 comes as infinity and K2, K3 takes the value of 10 & 11.1 respectively.

10. The Laplace transform of a parabolic signal is _______

a) 1

b) A/s 3

c) A/s 2

d) A/s

Answer: a

Explanation: As u is a unity step function r=0;t<0 and r=1; t=0. The parabolic signal is a signal which has varying amplitudes and when we take Laplace Transform of that we get 1 as the answer.

This set of Control Systems Multiple Choice Questions & Answers  focuses on “Integral Square Error & its Minimization”.

1. A unity feedback system has an open loop transfer function G =25/s. What is the percentage of it’s peak overshoot?

a) 0.13%

b) 1.13%

c) 1.26%

d) 1.52%

Answer: d

Explanation: Damping ratio is calculated from the characteristic equation and placing that value in the formula for peak overshoot Mp = e 3.14DR (1- DR 2 ) we get the answer. Peak overshoot arises especially in the step response of the systems such as low pass filters which are band limited.

2. What is the analogous electrical element of Frictional coefficient  in Force-Current Analogy for mechanical translational system?

a) Resistance

b) Conductance

c) Flux

d) Voltage

Answer: b

Explanation: As Resistance is the analogous element of B in F-V analogy so here it is the reciprocal of resistance, conductance is the answer. Force voltage analogy means both the equations will have differential equation of the same form.

3. What is the response of the feedback function with open loop transfer function G = 4/s and input is input step?

a) 1-1/3(4e -t – e -4t )

b) 1-1/2(6e -t – e -4t )

c) 1-1/3(6e -t – e -4t )

d) 1-1/2(4e -t – e 4t )

Answer: a

Explanation: We should first get the response in s domain which is C/R = G/1+G = R 4/ and as the input is unit step which R=1/s the equation becomes 4/s. Then we apply partial fraction to the equation and we get values of A, B, C as 1, -4/3, 1/3 and then inverse Laplace transform is applied to C and we get response as 1-1/3(4e -t – e -4t ).

4. The response of a servomechanism is 1+0.2e -60t -1.2e -10t when subjected to a unit step input. What is the damping ratio?

a) 1.21

b) 1.43

c) 1.59

d) 1.74

Answer: b

Explanation: First we apply Laplace Transform to the system and as R = 1/s we get closed loop transfer function as C/R = 600/s 2 +70s+600. Then we compare it with the standard equation for second order transfer function we got damping ratio = 70/2w n = 1.43.

5. The open loop transfer function for a unit feedback system is G = K/s. By what factor the amplitude gain K should be reduced so that the peak overshoot becomes 25% from 75%?

a) 75

b) 25

c) 20

d) 10

Answer: c

Explanation: The peak overshoot is decreased by increasing the damping ratio. The damping ratio is increased by reducing the gain K by same proportion and for decreasing the peak overshoot from 75% to 25% the factor of amplitude becomes 19.6% which is approximately 20%.

6. A performance index must offer selectivity.

a) True

b) False

Answer: a

Explanation: It must offer selectivity, that is, an optimal adjustment of parameters must clearly distinguish non optimal adjustment of parameters. If there was no selectivity we would not have been able to distinguish between parameters.

7. For a unity feedback control system, the open loop transfer function G = 10/s 2 . What is the acceleration error constant?

a) Infinity

b) 5

c) 10

d) 20

Answer: d

Explanation: As limit s tends to zero s 2 G H = s 2 G = 10*2/1 = 20. Therefore we get the value of Ka as 20 and both kv and ks are infinity.

8. Actuator is the basic component of an automatic control system.

a) False

b) True

Answer: b

Explanation: There are 5 basic components of an automatic control system. They are error detector, amplifier, actuator, plant, and sensor. So, Actuator is a basic component of automatic control system.

9. What is the need for a controller?

a) Receive control signals

b) Transmit control signals

c) Modify control signals

d) Create control signals

Answer: c

Explanation: Controller is needed to modify control signals for better control action. Some control signals are raw signals which can’t function properly so we use controllers for modifying them.

10. How many types of controllers and compensators are there respectively?

a) 4, 3

b) 3, 4

c) 4, 5

d) 5, 4

Answer: a

Explanation: There are 4 types of controllers namely PID, PI, PD. There are 3 types of compensators namely Lag, Lead & Lag-Lead compensators.