Time Response of Second Order Systems – II

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 oscillations

Answer: c

Explanation: 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

Explanation: s+6/K[s2+s/K+6/K] Comparing with s2+2Gw+w2
w= √6/K
2*0.5*√6/K =1/K

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

Explanation: 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

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(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

Explanation: 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

Explanation: 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

Explanation: 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

Explanation: 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

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

Don't Miss Our Updates
Be the first to get exclusive content straight to your email.
We promise not to spam you. You can unsubscribe at any time.
Invalid email address

Leave a Comment