GATE 2025 IN – Question 47
The shown closed-loop system has plant $G(s)=1/s^2$ and lead compensator $C(s)$. The desired dominant closed-loop poles are $-1.5\pm j\sqrt{27}/2$. The phase lead needed from the compensator is
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Correct answer: (B) 60°
Explanation
The upper desired pole −1.5+j√27/2 has angle 120° from the origin.
Plant 1/s² contributes −240°, equivalent to +120°.
The root-locus requirement is an odd multiple of 180°, so the compensator must add **60°, B** to obtain 180°.