GATE EC 2022 Set 1 — Question 21
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Control Systems → Stability Analysis → Nyquist Criterion
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Question
Consider a closed-loop control system with unity negative feedback and in the forward path, where the gain . The complete Nyquist plot of the transfer function is shown in the figure. Note that the Nyquist contour has been chosen to have the clockwise sense. Assume has no poles on the closed right-half of the complex plane. The number of poles of the closed-loop transfer function in the closed right-half of the complex plane is __________.
Correct answer
(C) 2
Solution
Critical point. With unity negative feedback and forward path , closed-loop poles satisfy , i.e. . For the critical point is on the real axis of the plane.Read the plot. The large circle crosses the negative real axis at ; the two small loops meet at . So lies
- inside the large circle, which is traversed clockwise, and
- inside the left small loop (between and ), which is also traversed clockwise.
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