GATE EC 2025 Set 1 — Question 16
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Control Systems → Frequency-Domain Analysis → Gain & Phase Margin
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Question
The Nyquist plot of a system is given in the figure below. Let , and be the positive frequencies at the points P, Q, R, and S, respectively.Which one of the following statements is TRUE?
Correct answer
(D) ω_S is the gain crossover frequency and ω_Q is the phase crossover frequency
Solution
The gain crossover frequency is the frequency at which the magnitude of the loop transfer function is unity, . In the Nyquist plot, this corresponds to the intersection with the unit circle. Point S lies on the unit circle, so . The phase crossover frequency is the frequency at which the phase of the loop transfer function is . In the Nyquist plot, this corresponds to the intersection with the negative real axis. Point Q lies on the negative real axis, so . Thus, statement (D) is true.
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