GATE 2015 EC – Question 30
A unity negative feedback system has the open-loop transfer function $G(s) = \frac{K}{s(s + 1)(s + 3)}$. The value of the gain $K$ ($> 0$) at which the root locus crosses the imaginary axis is ________.
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Correct answer: 12
Explanation
The characteristic equation is $s^3 + 4s^2 + 3s + K = 0$. In the Routh array the $s^1$ row begins with $\frac{4 \times 3 - K}{4}$, and the locus crosses the imaginary axis when this is zero, so $K = 12$.