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GATE 2020 IN – Question 39

Control Systems · Stability and frequency response: Bode plot, phase and gain margins, Routh and Nyquist criteria, root loci · 2 marks · Multiple choice

A negative-feedback system has loop transfer function $G(s)H(s)=1/[s(s-2)]$. Its Nyquist plot

  1. Encircles −1 clockwise.
  2. Encircles −1 counterclockwise.
  3. Does not encircle −1.
  4. Encircles +1 counterclockwise.

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Show answer and explanation

Correct answer: (A) Encircles −1 clockwise.

Explanation

The open loop has one strictly right-half-plane pole at +2; the pole at zero is handled by the usual indented contour. The closed-loop characteristic equation is $s(s-2)+1=(s-1)^2=0$, giving two right-half-plane closed-loop poles. Using clockwise encirclements, $N=Z-P=2-1=1$. Thus the plot makes one clockwise encirclement of −1, A.

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