GATE 2015 EC – Question 58

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

A plant transfer function is given as $G(s) = \left(K_P + \frac{K_I}{s}\right)\frac{1}{s(s + 2)}$. When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is

$K_P > \frac{K_I}{2} > 0$
$2K_I > K_P > 0$
$2K_I < K_P$
$2K_I > K_P$

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Correct answer: (A) $K_P > \frac{K_I}{2} > 0$

Explanation

The characteristic equation is $s^3 + 2s^2 + K_P s + K_I = 0$. For stability, the Routh array needs $K_I > 0$ and $2K_P - K_I > 0$, which is $K_P > \frac{K_I}{2}$. So $K_P > \frac{K_I}{2} > 0$.