### Polar Plot and Nyquist Plot - Topic wise GATE previous questions on Control Systems (from 1987 onwards)

2003
1. Figure shows the Nyquist plot of the open loop transfer function G(s)H(s) of a system. If G(s)H(s) has one right hand pole, the closed loop system is
a) always stable
b) unstable with one closed loop right hand pole
c) unstable with two closed loop right hand poles
d) unstable with three closed loop right hand poles

2. 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
3. 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
4. Which one of the following polar diagrams corresponds to a lag network?

5. The polar diagram of a conditionally stable system for open loop gain K = 1 is shown in figure. The open loop transfer function of the system is known to be stable. The closed loop system is stable for

2006
6. The Nyquist plot of G(jω)H(jω) for a closed loop control system, passes through ( –1, j0) point on the GH – plane. The gain margin of the system in dB is equal to
a) infinite
b) greater than zero
c) less than zero
d) zero

2009
Common Data Questions: (7 & 8)
The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed loop system in the feedback configuration shown.
7. Which of the following statements is TRUE?
a) G(s) is an all pass filter
b) G(s) has a zero in the right half plane
c) G(s) is the impedance of a passive network
d) G(s) is marginally stable

8. The gain and phase margin of G(s) for closed loop stability are
a) 6 dB and 180o
b) 3 dB and 180o
c) 6 dB and 90o
d) 3 dB and 90o

2011
9. for the transfer function G(jω) = 5 + jω, the corresponding Nyquist plot for positive frequency has the form

2014
10. Consider the feedback system shown in the figure. The Nyquist plot of G(s) is also shown. Which of the following conclusions is correct?
a) G(s) is an all pass filter
b) G(s) is a strictly proper transfer function
c) G(s) is a stable and minimum phase transfer function
d) The closed loop system is unstable for sufficiently large and positive k

2015
11. The polar plot of the transfer function G(s) = 10(s+1)/(s+10) for 0 < ω < ∞ will be in the