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GATE 2019 EE – Question 23

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

The output response of a system is denoted as $y(t)$, and its Laplace transform is given by

$$Y(s)=\frac{10}{s\left(s^2+s+100\sqrt2\right)}.$$

The steady state value of $y(t)$ is

  1. $\dfrac{1}{10\sqrt2}$
  2. $10\sqrt2$
  3. $\dfrac{1}{100\sqrt2}$
  4. $100\sqrt2$

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Show answer and explanation

Correct answer: (A) $\dfrac{1}{10\sqrt2}$

Explanation

The poles of the quadratic factor are in the left half plane, so the final value theorem applies: $y(\infty)=\lim_{s\to0}sY(s)=\frac{10}{100\sqrt2}=\frac{1}{10\sqrt2}$.