GATE EC 2017 Set 2 — Question 48
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Control Systems → Stability Analysis → Nyquist Criterion
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Question
A unity feedback control system is characterized by the open-loop transfer functionThe Nyquist path and the corresponding Nyquist plot of are shown in the figures below.
If , then the number of poles of the closed-loop transfer function that lie in the right-half of the -plane is
Correct answer
(C) 2
Solution
1.Determine open-loop poles in RHP ():
The characteristic equation of the open-loop system is . Using the Routh-Hurwitz criterion:- : 1, 0
- : 3, 10
- :
- : 10
2.Determine encirclements of ():
The Nyquist plot crosses the negative real axis at . For , the point lies to the left of . Looking at the provided Nyquist plot, the point is not encircled by the locus. Thus, .3.Calculate closed-loop poles in RHP ():
Using the Nyquist stability criterion (where is the number of clockwise encirclements):Therefore, there are 2 closed-loop poles in the right-half of the -plane.Continue learning with Success Tracker
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