GATE EC 2018 Set 1 — Question 15
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Control Systems → Stability Analysis → Nyquist Criterion
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Question
The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE:
Correct answer
(D) The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.
Solution
Let's evaluate the statements:
(A) True: Both Routh-Hurwitz and Nyquist criteria can be used to find the range of gain for which a system remains stable.
(B) True: For minimum-phase systems, there is a unique relationship between magnitude and phase. Thus, the Nyquist plot (polar plot) can be inferred from the Bode magnitude plot.
(C) True: The Routh criterion is designed for characteristic equations that are polynomials. Transport lag () makes the equation transcendental, which Routh cannot handle directly. Nyquist, being a frequency-domain graphical method, handles it easily.
(D) False: The closed-loop frequency response (magnitude and phase) can be obtained from the open-loop frequency response (Nyquist plot) using constant M-circles and constant N-circles.
Therefore, statement (D) is false.
(A) True: Both Routh-Hurwitz and Nyquist criteria can be used to find the range of gain for which a system remains stable.
(B) True: For minimum-phase systems, there is a unique relationship between magnitude and phase. Thus, the Nyquist plot (polar plot) can be inferred from the Bode magnitude plot.
(C) True: The Routh criterion is designed for characteristic equations that are polynomials. Transport lag () makes the equation transcendental, which Routh cannot handle directly. Nyquist, being a frequency-domain graphical method, handles it easily.
(D) False: The closed-loop frequency response (magnitude and phase) can be obtained from the open-loop frequency response (Nyquist plot) using constant M-circles and constant N-circles.
Therefore, statement (D) is false.
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