GATE 2020 EC – Question 65
Consider the following closed loop control system
where $G(s)=\dfrac{1}{s(s+1)}$ and $C(s)=K\dfrac{s+1}{s+3}$. If the steady state error for a unit ramp input is 0.1, then the value of $K$ is ________.
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Correct answer: 30
Explanation
The open loop is $C(s)G(s)=\frac{K(s+1)}{s(s+1)(s+3)}=\frac{K}{s(s+3)}$, a type 1 system with $K_v=\lim_{s\to0}s\,C(s)G(s)=\frac K3$. The ramp steady-state error is $\frac{1}{K_v}=\frac3K=0.1$, so $K=30$.