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
- A.0
- B.1
- C.4
- D.3
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Solution
Nyquist criterion. The number of closed-loop poles in the right-half plane iswhere is the net number of clockwise encirclements of by the complete Nyquist plot of , and is the number of open-loop poles in the right-half plane.What the data give.
- is not given. The stem says has one zero in the right-half plane, but open-loop zeros do not appear in . Only open-loop RHP poles do, and their number is not stated.
- from the figure. The large outer contour runs clockwise and encloses , contributing . The loop drawn around runs counter-clockwise, contributing . The left-hand loop and the small loop at the origin do not enclose . The net encirclement read from the figure as printed is therefore , so .
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