GATE EC 2014 Set 1 — Question 31
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Control Systems → Frequency-Domain Analysis → Nyquist Criterion
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Question
Consider the feedback system shown in the figure. The Nyquist plot of is also shown. Which one of the following conclusions is correct?
Correct answer
(D) The closed-loop system is unstable for sufficiently large and positive k
Solution
The closed loop has open-loop transfer function ; its Nyquist plot is the plot of scaled by .From the figure, the Nyquist plot of is a closed circle-like contour that crosses the negative real axis at a point between and , and it does not shrink to the origin.
- (A) An all-pass filter has for all , i.e. a circle of radius 1 centred at the origin. The plot is not such a circle, so (A) is false.
- (B) A strictly proper has as , so its plot would end at the origin. The plot does not pass through the origin, so (B) is false.
- (C) Nothing in the plot establishes that is stable and minimum phase; this conclusion cannot be drawn.
- (D) Let the plot cut the negative real axis at with . The plot of cuts it at . For sufficiently large positive () the critical point gets encircled, so the closed-loop system becomes unstable.
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