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GATE 2016 EC (EC2) – Question 30

Control Systems · Routh-Hurwitz and Nyquist Stability Criteria · 1 mark · Multiple choice

The number and direction of encirclements of $-1+j0$ by the Nyquist plot of $G(s)=(1-s)/(4+2s)$ are

  1. zero
  2. one, anticlockwise
  3. one, clockwise
  4. two, clockwise

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Show answer and explanation

Correct answer: (A) zero

Explanation

The open-loop pole is at −2, so there are no right-half-plane poles. The closed-loop equation is $1+G(s)=(s+5)/(2s+4)=0$, whose root is −5; hence there are no unstable closed-loop roots either.

Nyquist therefore requires zero net encirclements of −1. The locus is also a circle with real-axis limits 1/4 and −1/2, leaving −1 outside. Thus **A**.

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