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# Multiple choice question for engineering

## Set 1

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 [Reason:] complex conjugate (non-multiple): oscillatory (sustained oscillations) Complex conjugate (multiple): unstable (growing oscillations).

2. Consider a system with transfer function G(s) = s+6/Ks2+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 [Reason:] s+6/K[s2+s/K+6/K] Comparing with s2+2Gw+w2 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(t)= 1-e-t. What is the delay time Td?
a) 0.36
b) 0.18
c) 0.693
d) 0.289

Answer: c [Reason:] The output is given as a function of time. The final value of the output is limn->∞c(t)=1; . Hence Td (at 50% of the final value) 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 [Reason:] 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 [Reason:] C(s)/R(s) = 2/s+1 R(s) = 1/s (step input) C(s) = 2/s(s+1) c(t) = 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 [Reason:] C(s) = 1/s-1/s+5-5/(s+5)^2 C(s) = 25/s(s2+10s+25) R(s) = 1/s G(s) = 25/(s2+10s+25 ) w= √25 w = 5 rad/sec G = 1.

7. The loop transfer function of controller Gc(s) is :
a) 1+0.1s/s
b) -1+0.1s/s
c) –s/s+1
d) s/s+1

Answer: a [Reason:] The transfer function of the controller is 0.1s+1/s Gc(s) = 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 [Reason:] C(s)/R(s) = 1/s2+s+1 C(s)/R(s) = w/ws2+2Gws+w2 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(5%) 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 [Reason:] G = 1/√2 Gw = 5 s = -5+j5.

10. Which of the following quantities give a measure of the transient characteristics of a control system, when subjected to unit step excitation.
1. Maximum overshoot
2. Maximum undershoot
3. Overall gain
4. Delay time
5. Rise time
6. Fall time
a) 1,3 and 5
b) 2, 4 and 5
c) 2,4 and 6
d) 1,4 and 5

Answer: d [Reason:] Maximum overshoot, rise time and delay time are the major factor of the transient behaviour of the system and determines the transient characteristics.

## Set 2

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 [Reason:] 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(t) 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 [Reason:] 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 [Reason:] 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 [Reason:] 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 [Reason:] 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(s) = 100/(s+1) (s+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 [Reason:] 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(s2+ 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 [Reason:] 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 [Reason:] 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 [Reason:] 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.

10. Control system are normally designed to be:
a) Overdamped
b) Under damped
c) Un damped
d) Critically damped

Answer: b [Reason:] 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.

## Set 3

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 [Reason:] 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 (s)= 5/s(s2+3s+2), the initial value of f(t) is:
a) 5
b) 5/2
c) 5/3
d) 0

Answer: d [Reason:] 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 [Reason:] 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 (A): Many of the linear control system transfer function do not have poles or zeroes in the right half s-plane.
Reason (R): 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 [Reason:] 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:

6. The closed loop transfer function of a unity negative feedback system is 100/(s2+8s+100). Its open loop transfer function is:
a) 100/s+8
b) 1/s2+8s
c) 100/s2-8s
d) 100/s2+8s

Answer: d [Reason:] 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 (t) = e(-t)The transfer function of the system is equal to:
a) 1/s
b) 1/s(s+1)
c) 1/(s+1)
d) s/(s+1)

Answer: c [Reason:] 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 [Reason:] 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 [Reason:] 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.

10. The transfer function of any stable system which has no zeros or poles in the right half of the s-plane is said to be:
a) Minimum phase transfer function
b) Non-minimum phase transfer function
c) Minimum phase frequency response function
d) Minimum gain transfer function

Answer: a [Reason:] 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.

## Set 4

1. The systems with equation such as dx/dt =F (x) are called:
a) Stable systems
b) Control systems
c) Autonomous systems
d) Unstable control system

Answer: c [Reason:] 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 [Reason:] 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 [Reason:] 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 [Reason:] 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 [Reason:] 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 [Reason:] 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 [Reason:] 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 [Reason:] 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 [Reason:] 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.

10. If x (t) approaches near the origin as t tends to infinity then the system is :
a) Asymptotically stable
b) Asymptotically stable in the large
c) Stable
d) Unstable

Answer: a [Reason:] By definition, if x (t) approaches near the origin as t tend to the infinity then the system is asymptotically stable.

## Set 5

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 [Reason:] 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 [Reason:] 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 [Reason:] 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 [Reason:] 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 [Reason:] G(s) = Tp (1+Tds)/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 [Reason:] 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 [Reason:] 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 [Reason:] 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