GATE 2021 IN – Question 56
A system $G(s)=2/(s+1)$ receives a unit step $u(t)$ and produces $y(t)$. Define $e(t)=y(t)-u(t)$. Then $\lim_{t\to\infty}e(t)$ is ______.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 1 to 1
Explanation
For the unit step, y(t)=2(1−e^(−t)) and tends to the DC gain G(0)=2. The question defines e=y−u, so the limit is 2−1=**1**. Using the more common input-minus-output convention would reverse the sign.