GATE 2021 CH – Question 62
A system has a transfer function $G(s)=\frac{3e^{-4s}}{12s+1}$. When a step change of magnitude M is given to the system input, the final value of the system output is measured to be 120. The value of M is _____.
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Correct answer: 40
Explanation
The steady-state gain is $G(0)=3$: the delay becomes $e^0=1$ and the first-order denominator becomes 1. With step input $U(s)=M/s$, the final-value theorem gives
$$y_\infty=\lim_{s\to0}sG(s)\frac{M}{s}=3M.$$
Since $y_\infty=120$, $M=120/3=\mathbf{40}$. The 4-unit delay and 12-unit time constant affect the timing, not the final gain.