GATE 2019 EC – Question 52
Consider a unity feedback system, as in the figure shown, with an integral compensator $\frac Ks$ and open-loop transfer function
$$G(s)=\frac{1}{s^2+3s+2}$$
where $K>0$. The positive value of $K$ for which there are exactly two poles of the unity feedback system on the $j\omega$ axis is equal to ________ (rounded off to two decimal places).
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Correct answer: 6
Explanation
The characteristic equation is $s(s^2+3s+2)+K=s^3+3s^2+2s+K=0$. From the Routh array, the $s^1$ row is $\frac{3\cdot2-K}{3}$, which vanishes at $K=6$, giving a pair of poles on the $j\omega$ axis.