GATE 2016 EC (EC2) – Question 29

The response of $G(s)=(s-2)/[(s+1)(s+3)]$ to unit step $u(t)$ is $y(t)$. The value of $dy/dt$ at $t=0^+$ is ________.

Show answer and explanation

Correct answer: 0.96 to 1.04

Explanation

For a zero-state step response, $Y(s)=G(s)/s$. The output starts at zero because the transfer function is strictly proper.

The initial value theorem applied to its derivative gives $y\prime(0^+)=\lim_{s\to\infty}s[sY(s)-y(0^-)]=\lim_{s\to\infty}sG(s)$.

This limit is the ratio of the leading coefficients of $s(s-2)$ and $(s+1)(s+3)$, equal to **1**.

GATE 2016 EC (EC2) Q55 – The feedback system shown has G(s)=1/(s2+2s). Its closed-loop step response should have…
GATE 2016 EC (EC3) Q30 – A unity-negative-feedback system has open-loop G(s)=2/[s(s+1)], as shown. Its steady-state…
GATE 2024 EC Q13 – In the feedback control system shown in the figure below, G(s)=6s(s+1)(s+2). R(s), Y(s),…
GATE 2023 EC Q41 – A closed loop system is shown in the figure where k>0 and >0. The steady state error due…
GATE 2022 EC Q50 – Two linear time-invariant systems with transfer functions G 1(s)=10s2+s+1and G…
GATE 2022 EC Q60 – The block diagram of a closed-loop control system is shown in the figure. R(s), Y(s), and…