GATE 2020 EC – Question 33
The loop transfer function of a negative feedback system is
$$G(s)H(s)=\frac{K(s+11)}{s(s+2)(s+8)}.$$
The value of $K$, for which the system is marginally stable, is ________.
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Correct answer: 160
Explanation
The characteristic equation is $s^3+10s^2+(16+K)s+11K=0$. In the Routh array the $s^1$ row vanishes when $\frac{10(16+K)-11K}{10}=0$, i.e. $160-K=0$, so $K=160$.