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
For the Nyquist criterion with a clockwise Nyquist contour, , where is the number of clockwise encirclements of , is the number of zeros of (closed-loop poles) inside the contour and is the number of poles of inside the contour.
1.The open-loop poles of are at and .
2.The given contour (traversed clockwise) encloses the entire right half plane and detours around the origin through the left half plane, so the pole at lies inside it, while does not. Thus .
3.The closed-loop characteristic equation is , with roots . Both lie in the left half plane and neither is inside the contour (the small detour around the origin does not reach them). Thus .
4., i.e. the Nyquist plot encircles once in the counter-clockwise direction.
The number of encirclements is therefore (counter-clockwise), which is option (B).Continue learning with Success Tracker
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