For the feedback control system shown, the steady-state error e ss= t[r(t)-y(t)] due to a unit-step reference r(t) is

GATE 2024 IN – Question 44

Control Systems · Time response and steady-state error · 2 marks · Multiple choice

For the feedback control system shown, the steady-state error $e_{ss}=\lim_{t\to\infty}[r(t)-y(t)]$ due to a unit-step reference $r(t)$ is

$(K-1)/K$
$1/2$
0
$(1-K)/K$

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Correct answer: (A) $(K-1)/K$

Explanation

The closed-loop transfer is $Y/R=G/(1+KG)$. As $s\to0$, $G=1/[s(s+1)]$ grows without bound, so the stable closed-loop DC gain is $1/K$. The external error is $r-y$, giving $e_{ss}=1-1/K=(K-1)/K$, **A**. The internal error $r-Ky$ is a different quantity.