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

1. 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

View Answer

Explanation: For M =1 the constant M circle is a straight line at x=-1/2.

2. 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

View Answer

Explanation: Gain margin of a polar plot passing through the critical point is zero.

3. 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

View Answer

Explanation: Feedback increases the gain of the system in one frequency range but decreases in another and it can cause a system that is originally stable to become unstable.

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

View Answer

Explanation: Phase crossover frequency is calculated as by calculating the magnitude of the transfer function and equating it to 1 and the frequency calculated at this magnitude is phase cross over frequency.

5. 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

View Answer

Explanation: Gain margin is nothing but the inverse of the gain. Hence if the gain of the open loop system is doubled, then the gain margin will become half.

6. 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

View Answer

Explanation: The unit circle of the Nyquist plot transforms into 0dB line of the amplitude plot of the Bode diagram at any frequency.

7. 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

View Answer

Explanation: For unstable system the signs of gain margin and phase margin are always different or they can both be negative.

8. 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

View Answer

Explanation: The system is all pass system and the gain of the system at frequency of 1 rad/sec is 1.

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

View Answer

Explanation: Gain margin of the system is inverse of the intersect on the real axis and calculated in decibels.

G(s) = 1+s / s(1+0.5s).

10. The corner frequencies are

a) 0 and 1

b) 0 and 2

c) 0 and 1

d) 1 and 2

View Answer

Explanation: Corner frequency can be calculated by time constant form of the transfer function and here the corner frequencies are 1 and 2.

11. 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

View Answer

Explanation: Phase cross over frequency is calculated at the point where magnitude of the polar plot is 1.

12. 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

View Answer

Explanation: Gain margin of a system is calculated at the phase cross over frequency and expressed in decibels.

13. 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

View Answer

Explanation: Gain margin of a system is calculated at the phase cross over frequency and expressed in decibels.

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

View Answer

Explanation: All the circles pass through the points (0,0) and (-1,0).

**Sanfoundry Global Education & Learning Series – Control Systems.**

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