This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Assessment of Relative Stability Using Nyquist Criterion”.

1. The phase margin (in degrees) of a system having the loop transfer function G(s) H(s)=2√3/s(s+1) is:

a) 45°

b) -30°

c) 60°

d) 30°

View Answer

Explanation: Phase margin is calculated at gain cross over frequency where magnitude of the transfer function is 1.

2. The system with the open loop transfer function G(s) H(s) =1/s(s^{^}2+s+1) has the gain margin of :

a) -6 dB

b) 0 dB

c) 3.5 dB

d) 6 dB

View Answer

Explanation: Gain margin is calculated at phase cross over frequency where the phase is 180°.

3. The phase angle of the system, G(s) =s+5/s^{2}+4s+9, varies between :

a) 0° and 90°

b) 0° and -90°

c) 0° and -180°

d) -90° and -180°

View Answer

Explanation: As it is the type 0 system so the phase angle can be 0° and 90°.

4. The polar plot of the transfer function G(s) = 10(s+1)/s+10 will be in the :

a) First quadrant

b) Second quadrant

c) Third quadrant

d) Fourth quadrant

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Explanation: Polar plot of the given transfer function lies in the fourth quadrant.

5. As the polar plot moves toward the point (-1, 0) then the system becomes :

a) Stable

b) Marginally stable

c) Conditionally stable

d) Unstable

View Answer

Explanation: As the polar plot moves toward the point (-1, 0) then the system becomes unstable.

6. Polar plots moving toward the imaginary axis makes the system:

a) Stable

b) Marginally stable

c) Conditionally stable

d) Unstable

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Explanation: Polar plots moving toward the imaginary axis makes the system unstable.

7. The concepts used to measure relative stability are:

a) Phase margin

b) Gain margin

c) Phase and Gain margin

d) Stable

View Answer

Explanation: Relative stability is a measure of how fast the transient dies out in the system.The concepts used to measure relative stability are phase margin and gain margin.

8. Phase and gain margin are applicable to open and closed loop systems both.

a) True

b) False

View Answer

Explanation: Phase and gain margin are applicable only to open loop systems.

9. Gain margin is:

a) It is a factor by which the system gain can be increased to drive it to the verge of instability

b) It is calculated at gain cross over frequency

c) It is calculated at phase cross over frequency

d) Both a and c

View Answer

Explanation: Gain margin is a factor by which the system gain can be increased to drive it to the verge of instability and is calculated at phase cross over frequency.

10. Phase margin is:

a) It is amount of additional phase lag at the gain cross over frequency required to bring the system to the verge of instability

b) It is always positive for stable feedback systems

c) It is calculated at gain cross over frequency

d) All of the mentioned

View Answer

Explanation: Phase margin is the amount of additional phase lag at the gain cross over frequency required to bring the system to the verge of instability. It is always positive for stable feedback systems. It is calculated at gain cross over frequency.

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

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