GATE EC 2016 Set 1 — Question 30
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Control Systems → Stability Analysis → Nyquist Criterion
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Question
A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer function
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.
Solution
The Nyquist stability criterion relates the number of open-loop poles in the right-half -plane (), the number of closed-loop poles in the right-half -plane (), and the number of counterclockwise encirclements () of the critical point by the Nyquist plot: .For a closed-loop system to be stable, it must have no poles in the right-half -plane, i.e., . This implies . Therefore, the Nyquist plot must encircle the point in the counterclockwise direction as many times as the number of right-half -plane poles of the open-loop transfer function.
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