GATE EC 2020 Set 1 — Question 21
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Control Systems → Stability Analysis → Nyquist Criterion
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Question
The pole-zero map of a rational function is shown below. When the closed contour is mapped into the -plane, then the mapping encircles
Correct answer
(B) the origin of the G(s) -plane once in the clockwise direction.
Solution
By the argument principle, as traverses a closed contour , the image encircles the origin times in the same sense as , where and are the zeros and poles of inside . (Encirclements of would concern , whose zeros are not shown, so options (C) and (D) cannot be decided from this map.)From the figure:
- Inside : three zeros (one on the negative real axis just inside the contour and a complex-conjugate pair) and two poles (on the real axis on either side of the origin).
- Outside : one zero on the negative real axis, a real pole on the positive axis and a complex pole pair.
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