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Q#1 Frequency Domain Analysis GATE EE 2025 MCQ +1 mark -0.33 marks

The Nyquist plot of a strictly stable  having the numerator polynomial as  encircles the critical point -1 once in the anti-clockwise direction. Which one of the following statements on the closed-loop system shown in figure, is correct?

The system stability cannot be ascertained.

The system is marginally stable.

The system is stable.

The system is unstable.

Explanation:

Given that open loop system  is stable.

 No. of open -loop poles in RH of s-plane

Also, No. of encirclements about critical point  is once,

 

Assume Nyquist Contour is clockwise

N = 1

N = P-Z

P= Open Loop Poles in RHP = 0

Z = Closed Loop Poles in RHP

Hence Z = -1 which is invalid

Now assume Nyquist Contour is Anti-Clockwise

N = -1 = P – Z

Hence Z = 1, which means one closed loop pole

lies in RHP and hence closed loop system is unstable

Option (d) is correct.

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