Gain Margin and Phase Margin - Topic wise Questions in Control Systems (from 1987 onwards)

2003
1. The gain margin and the phase margin of a feedback system with G(s)H(s) = s/(s + 100)³ are
a) 0 dB, 0^o
b) ∞, ∞
c) ∞, 0^o
d) 88.5 dB, ∞

Answer:B

Solution : https://www.youtube.com/watch?v=n44i9T5koz4

2004
2. The gain margin for the system with open loop transfer function G(s)H(s) = 2(1 + s)/s², is
a) ∞
b) 0
c) 1
d) - ∞

Answer:B

Solution : https://www.youtube.com/watch?v=L2Y_rS_Zc9M

2005
Statement for Linked Answer Questions 3 & 4:
The open loop transfer function of a unity feedback is given by G(s) = 3e^–2s / [s(s + 2)].
3. The Gain and Phase cross over frequencies in rad/sec are, respectively
a) 0.932 and 1.26
b) 0.632 and 0.485
c) 0.485 and 0.632
d) 1.26 and 0.632

Answer:D

Solution : https://www.youtube.com/watch?v=eKZo_zPxjYI

4. based on the above results, the Gain and Phase Margins of the system will be
a) –7.09 dB and 87.5^o
b) 7.09 dB and 87.5^o
c) 7.09 dB and –87.5^o
d) –7.09 dB and –87.5^o

Answer:D

Solution : https://www.youtube.com/watch?v=aHVPuRMM0q8

2006
5. The open loop transfer function of a unity gain feedback control system is given by G(s) = K/[(s + 1)(s + 2)]. The gain margin of the system in dB is given by
a) 0
b) 1
c) 20
d) ∞

Answer:D

Solution : https://www.youtube.com/watch?v=_GEVQWlLBOs

Statement for Linked Answer questions: (6 and 7)
Consider a unity gain feedback control system whose open loop transfer function is G(s) = (as + 1)/s².
6. The value of "a" so that the system has a phase margin equal to π/4 is approximately equal to
a) 2.40
b) 1.40
c) 0.84
d) 0.74

Answer:C

7. With the value of "a" set for phase margin of π/4, the value of unit impulse response of the open loop system at t = 1 second is equal to
a) 3.40
b) 2.40
c) 1.84
d) 1.74

Answer:C

Solution (10 & 11) : https://www.youtube.com/watch?v=DlzZDVlirog

2011
Common Data Questions 8 & 9:
The input – output transfer function of a plant H(s) = 100/s(s+10)². The plant is placed in a unity negative feedback configuration as shown in figure below.

8. The signal flow graph that DOES NOT model the plant transfer function H(s) is

Answer:D

Solution : https://www.youtube.com/watch?v=gSg5jPv06fQ

9. The gain margin of the system under closed loop unity negative feedback is
a) 0 dB
b) 20 dB
c) 26 dB
d) 46 dB

Answer:C

Solution : https://www.youtube.com/watch?v=HreyReFPqag

2012
10. A system with transfer function is excited by sin(ωt).

The steady state output of the system is zero at
a) ω = 1 rad/sec
b) ω = 2 rad/sec
c) ω = 3 rad/sec
d) ω = 4 rad/sec

Answer:C

Solution : https://www.youtube.com/watch?v=UYEEuh71lxc

2014
11. The phase margin in degrees of

calculated using the asymptotic Bode plot is ____________

Answer:45

Solution : https://www.youtube.com/watch?v=ZwdvClI0_mU

2015
12. The phase margin (in degrees ) of the system G(s) = 10 /s(s+10) is _____________

Answer:83

Solution : https://www.youtube.com/watch?v=WXHKVhdLeOc