GATE EE 2016 Set 1 — Question 42
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Control Systems → Stability Analysis → Nyquist Criterion
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Question
Loop transfer function of a feedback system is . Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of encircles
Correct answer
(A) once in clockwise direction
Solution
The open-loop transfer function is .
The number of open-loop poles in the right-half plane (RHP) is .
Evaluating the plot shows that the point is encircled once in the clockwise direction. Therefore, the Nyquist plot encircles once in the clockwise direction.
1.Identify Open-Loop Poles:
The poles are at (double pole) and . The number of open-loop poles in the right-half plane (RHP) is .
2.Analyze the Nyquist Plot:
By mapping the Nyquist contour (which includes a small semi-circle around the origin to bypass the poles at ), we can determine the encirclements of the critical point .- For , the phase starts at and moves towards as increases.
- The large semi-circle at infinity maps to the origin.
- The small semi-circle around the origin poles maps to a large circular arc of in the clockwise direction.
Evaluating the plot shows that the point is encircled once in the clockwise direction. Therefore, the Nyquist plot encircles once in the clockwise direction.
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