GATE 2022 EC – Question 60
The block diagram of a closed-loop control system is shown in the figure. $R(s)$, $Y(s)$, and $D(s)$ are the Laplace transforms of the time-domain signals $r(t)$, $y(t)$, and $d(t)$, respectively. Let the error signal be defined as $e(t)=r(t)-y(t)$. Assuming the reference input $r(t)=0$ for all $t$, the steady-state error $e(\infty)$, due to a unit step disturbance $d(t)$, is ________ (rounded off to two decimal places).

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Correct answer: -0.11 to -0.09
Explanation
With $r=0$ the output due to the disturbance is $\frac{Y}{D}=\frac{G}{1+10G}$ with $G=\frac{1}{s(s+10)}$, i.e. $\frac{Y}{D}=\frac{1}{s^2+10s+10}$, which is stable. For a unit step, $y(\infty)=\frac{1}{10}$, so $e(\infty)=r-y=-0.1$.