GATE 2022 IN – Question 43

Control Systems · Stability and frequency response · 2 marks · Multiple choice

The Nyquist plot of stable open-loop $G(j\omega)$ for $0\le\omega<\infty$ intersects the unit circle at $P=-0.77-0.64j$. Points on the plot are $Q=14.40+0.00j$ and $R=-0.21+0.00j$. The phase margin PM and gain margin GM are ______.

Diagram for GATE 2022 IN question 43

PM = 39.7°, GM = 4.76
PM = 39.7°, GM = 0.07
PM = −39.7°, GM = 4.76
PM = −39.7°, GM = 0.07

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Correct answer: (A) PM = 39.7°, GM = 4.76

Explanation

At unit magnitude P, phase is −180°+atan(0.64/0.77)≈−140.3°, so PM≈39.7°. At negative-real crossing R=−0.21, GM=1/0.21=4.76.

Hence **A**; Q is not the negative-real crossing.