GATE EC 2016 Set 2 — Question 30
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Control Systems → Frequency-Domain Analysis → Nyquist Criterion
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Question
The number and direction of encirclements around the point in the complex plane by the Nyquist plot of is
Correct answer
(A) zero.
Solution
The transfer function is .
1.Poles and Zeros: There is one open-loop pole at (LHP) and one zero at (RHP). Since there are no open-loop poles in the RHP, .
2.Frequency Response: .
- At , .
- At , .
- The imaginary part of is . For , the imaginary part is always negative, meaning the plot for positive frequencies lies in the 4th quadrant.
4.Encirclements: The point lies outside this circle (which only spans from to on the real axis). Therefore, the number of encirclements of the point is zero.
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