**Polar Plots MCQ**

**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:** a

**Explanation:** If the gain of the open-loop system is doubled, the gain margin gets doubled.

**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

**Answer:** d

**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

**Answer:** d

**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

**Answer:** d

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

**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

**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).

**10. 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.

**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

**Answer:** b

**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

**Answer:** d

**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

**Answer:** b

**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

**Answer:** d

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