GATE EC 2021 Set 1 — Question 24
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Control Systems → Stability Analysis → Nyquist Criterion
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Question
The complete Nyquist plot of the open-loop transfer function of a feedback control system is shown in the figure.
If has one zero in the right-half of the -plane, the number of poles that the closed-loop system will have in the right-half of the -plane is
Correct answer
(D) 3
Solution
The Nyquist stability criterion relates the number of clockwise encirclements () of the critical point to the number of open-loop poles () and closed-loop poles () in the right-half of the -plane (RHP) using the formula:
1.Determine from the plot: By observing the provided Nyquist plot, the critical point is encircled 3 times in the clockwise direction. Thus, .
2.Determine : The question states that has one zero in the RHP, but it does not explicitly state the number of open-loop poles in the RHP. In the absence of such information, we typically assume the open-loop system is stable, meaning .
3.Calculate :
Thus, the number of closed-loop poles in the right-half of the -plane is 3. The correct option is (D).Continue learning with Success Tracker
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