Question
The state space representation of a first-order system is given as ẋ = -x + u y = x Where, x is the state variable, u is the control input and y is the controlled output. Let u = -K.x be the control law, where K is the controller gain. To place a closed-loop pole at -2, the value of K is ______
Answer :
1
Calculation:
Given state model,
ẋ = - x + u
u = - Kx
ẋ = - x - Kx
ẋ = - (K + 1)x = A x
A = - (K + 1)
Charactestic equation of a state model is given by
|sI - A| = 0
⇒ sI = s
s - [- (K + 1)] = 0
s + K + 1 = 0
s = - 1 - K
Given that a pole is located at -2
⇒ s = -2
-2 = - 1 - K
K = 1
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