GATE EE 2020 Set 1 — Question 34
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Control Systems → Stability Analysis → Nyquist Criterion
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Question
Consider a negative unity feedback system with forward path transfer function , where are positive real numbers. For a Nyquist path enclosing the entire imaginary axis and right half of the -plane in the clockwise direction, the Nyquist plot of , encircles the origin of -plane once in the clockwise direction and never passes through this origin for a certain value of . Then, the number of poles of lying in the open right half of the -plane is ________.
Correct answer
2 to 2
Solution
The Nyquist stability criterion states , where:
.
Thus, the number of closed-loop poles in the RHP is 2.
- is the number of clockwise encirclements of the origin by the plot.
- is the number of open-loop poles of in the right half plane (RHP).
- is the number of closed-loop poles (zeros of ) in the RHP.
- (clockwise encirclement).
- . Since , the poles are at . Only is in the RHP, so .
.
Thus, the number of closed-loop poles in the RHP is 2.
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