GATE 2014 EC (EC1) – Question 30
A unity negative-feedback system has forward transfer $G(s)=K/((s+2)(s-1))$. Find K placing both closed-loop poles at the same location.
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Show answer and explanation
Correct answer: 2.24 to 2.26
Explanation
Unity negative feedback gives characteristic equation(s+2)(s−1)+K=0, or s²+s+(K−2)=0. Two poles coincide when the quadratic discriminant vanishes:1−4(K−2)=0. Hence **K=9/4=2.25**, placing both poles at−1/2.