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GATE 2017 EC (EC2) – Question 58

Control Systems · Routh-Hurwitz and Nyquist Stability Criteria · 2 marks · Multiple choice

A unity-feedback control system has $G(s)=10K(s+2)/(s^3+3s^2+10)$. Its Nyquist path and Nyquist plot are shown. For $0<K<1$, the number of closed-loop poles in the right half of the s-plane is

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Correct answer: (C) 2

Explanation

The closed-loop characteristic polynomial is $s^3+3s^2+10Ks+(10+20K)$.

Its Routh first column is $1$, $3$, $(10K-10)/3$, and $10+20K$. For $0<K<1$, the signs are positive, positive, negative, positive.

There are two sign changes, so there are **2 right-half-plane closed-loop poles, C**. This also agrees with the supplied Nyquist construction; the open-loop unstable poles must be included when using its encirclement count.

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