GATE 2016 EE (EE2) – Question 62

Control Systems · Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci · 2 marks · Multiple choice

The gain at the root-locus breakaway point for unity feedback and $G(s)=Ks/[(s-1)(s-4)]$ is

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Correct answer: (A) 1

Explanation

From 1+G=0, gain as a function of a real-axis root is $K=-(s-1)(s-4)/s=5-s-4/s$.

Stationary points satisfy dK/ds=−1+4/s²=0, giving s=±2. The breakaway between the open-loop poles 1 and 4 occurs at s=2, yielding K=5−2−2=**1, A**. The point s=−2 corresponds to K=9 and a different real-axis branch event.

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