The GATE Grind

GATE 2016 EC – Question 30

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

A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer function

  1. encircles the s-plane point $(-1 + j0)$ in the counterclockwise direction as many times as the number of right-half s-plane poles.
  2. encircles the s-plane point $(0 - j1)$ in the clockwise direction as many times as the number of right-half s-plane poles.
  3. encircles the s-plane point $(-1 + j0)$ in the counterclockwise direction as many times as the number of left-half s-plane poles.
  4. encircles the s-plane point $(-1 + j0)$ in the counterclockwise direction as many times as the number of right-half s-plane zeros.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) encircles the s-plane point $(-1 + j0)$ in the counterclockwise direction as many times as the number of right-half s-plane poles.

Explanation

By the Nyquist criterion, the number of closed-loop poles in the right half plane is $Z = N + P$, where $N$ is the number of clockwise encirclements of $-1 + j0$ and $P$ is the number of open-loop poles in the right half plane. For stability $Z = 0$, so the plot must encircle $-1 + j0$ counterclockwise exactly $P$ times.