GATE EE 2021 Set 1 — Question 59
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Question
The state space representation of a first-order system is given aswhere, is the state variable, is the control input and is the controlled output. Let be the control law, where is the controller gain. To place a closed-loop pole at , the value of is ________.
Correct answer
1 to 1
Solution
The given state space equations are:The control law is . Substituting this into the state equation:The characteristic equation of the closed-loop system is obtained by taking the Laplace transform (assuming zero initial conditions):The closed-loop pole is at .
We want the closed-loop pole to be at , so:
We want the closed-loop pole to be at , so:
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