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QUESTION: 1

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

Solution:

Answer: c

Explanation: complex conjugate (non-multiple): oscillatory (sustained oscillations)

Complex conjugate (multiple): unstable (growing oscillations).

QUESTION: 2

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

Solution:

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.

QUESTION: 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?

Solution:

Answer: c

Explanation: The output is given as a function of time. The final value of the output is lim_{n->∞}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.

QUESTION: 4

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

Solution:

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.

QUESTION: 5

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

Solution:

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.

QUESTION: 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?

Solution:

Answer: d

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

C(s) = 25/s(s^{2}+10s+25)

R(s) = 1/s

G(s) = 25/(s^{2}+10s+25 )

w= √25

w = 5 rad/sec

G = 1.

QUESTION: 7

The loop transfer function of controller Gc(s) is :

Solution:

Answer: a

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

Gc(s) = 0.1s+1/s.

QUESTION: 8

The peak percentage overshoot of the closed loop system is :

Solution:

Answer: c

Explanation: C(s)/R(s) = 1/s^{2}+s+1

C(s)/R(s) = w/ws^{2}+2Gws+w^{2}

Compare both the equations,

w = 1 rad/sec

2Gw = 1

Mp = 16.3 %

QUESTION: 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?

Solution:

Answer: b

Explanation: G = 1/√2

Gw = 5

s = -5+j5.

QUESTION: 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

Solution:

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.

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