Question:
The state space representation of a first-order system is
\[
\dot{X} = -X + U, Y = X
\]
where \(X\) is the state variable, \(u\) is the control input and \(y\) is the controlled output. Let \(u = -KX\) be the control law. To place a closed-loop pole at \(-2\), the value of \(K\) is \(\underline{\hspace{1cm}}\).
The state space representation of a first-order system is
\[
\dot{X} = -X + U, Y = X
\]
where \(X\) is the state variable, \(u\) is the control input and \(y\) is the controlled output. Let \(u = -KX\) be the control law. To place a closed-loop pole at \(-2\), the value of \(K\) is \(\underline{\hspace{1cm}}\).
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For first-order systems, pole placement is done by matching the coefficient of the state variable in the closed-loop equation.
Updated On: Dec 29, 2025
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Correct Answer: 1
Solution and Explanation
Closed-loop system:
\[
\dot{X} = -X + u = -X - KX = -(1+K)X
\]
Desired closed-loop pole:
\[
-(1+K) = -2
\]
\[
1 + K = 2
\]
\[
K = 1
\]
This lies in the required range 1 to 1.
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