GATE 2021 EE – Question 59

Control Systems · State space model, Solution of state equations of LTI systems · 2 marks · Numerical answer

The state space representation of a first-order system is given as

$\dot x=-x+u$

$y=x$

where, $x$ is the state variable, $u$ is the control input and $y$ is the controlled output. Let $u=-Kx$ be the control law, where $K$ is the controller gain. To place a closed-loop pole at $-2$, the value of K is ________.

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Correct answer: 1

Explanation

With $u=-Kx$ the closed-loop equation is $\dot x=-(1+K)x$, whose pole is at $-(1+K)$. For the pole to be at $-2$, $K=1$.