## Friday, April 29, 2016

### 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, 0o
b) ∞, ∞
c) ∞, 0o
d) 88.5 dB, ∞

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) - ∞

2005
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

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

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) ∞

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

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

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

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

2012
10. A system with transfer function is excited by sin(ωt).
The steady state output of the system is zero at

2014
11. The phase margin in degrees of

calculated using the asymptotic Bode plot is ____________

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