GATE 2025 EE – Question 22

Control Systems · Transient and Steady-state analysis of linear time invariant systems · 1 mark · Multiple choice

Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of the system is

Time (sec)	0.6	1.6	2.6	10	∞
Output	0.78	1.65	2.18	2.98	3

1
2
3
4

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Correct answer: (B) 2

Explanation

The final value is 3, so $y(t)=3(1-e^{-t/\tau})$. At $t=0.6$: $0.78/3=0.26=1-e^{-0.6/\tau}$, so $e^{-0.6/\tau}=0.74$ and $\tau=0.6/0.301=1.99\approx2$ s. Check: at $t=10$, $3(1-e^{-5})=2.98$ ✓.