This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Polar Plots”.

1. The polar plot of a transfer function passes through the critical point (-1,0). Gain margin is

a) Zero

b) -1dB

c) 1dB

d) Infinity

2. 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

3. The constant M circle for M=1 is the

a) straight line x=-1/2

b) critical point (-1j0)

c) circle with r= 0.33

d) circle with r=0.67

4. The open loop transfer function of a system is G(s) H(s)= K / (1+s)(1+2s)(1+3s)

The phase cross over frequency ωc is

a) V2

b) 1

c) Zero

d) V3

5. 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

6. 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

7. 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

8. 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

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

10. For the transfer function

G(s) H(s) = 1 / s(s+1) (s+0.5), 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

11. The gain margin for the system with open loop transfer function

G(s) H(s) = G(s) =2(1+s) / s2 is

a) 8

b) 0

c) 1

d) -8

12. The corner frequencies are

a) 0 and 1

b) 0 and 2

c) 0 and 1

d) 1 and 2

13. The gain margin (in dB) of a system having the loop transfer function

G(s) H(s) = 2 / s(s+1) is

a) 0

b) 3

c) 6

d) 8

14. Statement 1: In constant M circles, as M increases from 1 to 8 radius of circle increases from 0 to 8 and Centre shifts from (-1,0) to (-8,0)

Statement 2: The circle intersects real axis at point (-1/2, 0)

a) Statement 1 is TRUE, 2 is FALSE

b) Statement 1 is FALSE, 2 is TRUE

c) Statement 1 & 2 TRUE

d) Statement 1 & 2 FALSE