GATE 2025 IN – Question 59
The shown feedback control system has disturbance input $d(t)$ and output $y(t)$. The maximum allowable integer $n$ such that any step disturbance produces zero steady-state output is ______.
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Correct answer: MTA
Explanation
The diagram uses positive feedback.
Its closed-loop characteristic equation is $1-1/[s^2(s+1)]=0$, or $s^3+s^2-1=0$.
This polynomial is negative at $s=0$ and positive at $s=1$, so it has a positive real root.
The loop is unstable, independently of $n$.
A stable steady-state limit therefore cannot be established as requested.
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