250+ TOP MCQs on Time Response of Second Order Systems – II and Answers

Control Systems Questions and Answers for Experienced people 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: Maximum overshoot, rise time and delay time are the major factor of the transient behaviour of the system and determines the transient characteristics.

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