GATE 2015 EE (EE2) – Question 64

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

For unity feedback with $G(s)=K/[s(s+1)(s+2)]$, the real-axis breakaway point is

−0.42
−1.58
−0.42 and −1.58
none of the above

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Show answer and explanation

Correct answer: (A) −0.42

Explanation

The characteristic equation gives K=−s(s+1)(s+2). Stationary gain points satisfy 3s²+6s+2=0, giving s=−1±1/√3.

The point −0.42265 lies in the positive-gain locus segment (−1,0). The other point −1.57735 lies between −2 and −1, which is not on the positive-gain real-axis locus.

Therefore the actual breakaway is **−0.42, A**.

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