GATE EE 2022 Set 1 — Question 38
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Control Systems → Stability Analysis → Nyquist Criterion
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Question
The open loop transfer function of a unity gain negative feedback system is given as The Nyquist contour in the -plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point by the Nyquist plot of , corresponding to the Nyquist contour, is denoted as . Then equals to
Correct answer
(B) 1
Solution
The number of encirclements of the critical point is given by , where is the number of closed-loop poles in the RHP and is the number of open-loop poles enclosed by the Nyquist contour.
1.Open-loop poles of are at and .
2.The given Nyquist contour encloses the RHP and bypasses the origin to the left, meaning the pole at is inside the contour. Thus, .
3.The closed-loop characteristic equation is . The roots are , which are in the LHP. Thus, .
4..
The value indicates one counter-clockwise encirclement. The magnitude of encirclements is 1.Continue learning with Success Tracker
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