Control System Questions and Answers - 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

Answer: a
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

Answer: a
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

Answer: c
Explanation:Feedback can cause the increase in gain and also can cause stable system 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

Answer: b
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

Answer: c
Explanation: If the gain of the open-loop system is doubled, the gain margin gets becomes half

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

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

7. 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

Answer: c
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).

8. The corner frequencies are
a) 0 and 1
b) 0 and 2
c) 0 and 1
d) 1 and 2

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

9. 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

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

10. 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

Answer: d
Explanation:Gain margin of a system is calculated at the phase cross over frequency and expressed in decibel