State-Space Matrices
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Aysel Alimirzayeva
on 3 Nov 2022
Commented: Aysel Alimirzayeva
on 5 Nov 2022
Hello.Why do we write A-B*K1 in the example of LQR Control using State-Space Matrices in Matlab?Why is B negative?If anyone knows,can you please explain?
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Accepted Answer
Sam Chak
on 3 Nov 2022
The LQR function only computes .
Making a substitution
2 Comments
Sam Chak
on 5 Nov 2022
Edited: Sam Chak
on 5 Nov 2022
Just for a note, this "state-feedback"
sys1 = ss(A-B*K1, B, C, D)
only works if your reference state is 0.
If your system is tracking a non-zero reference state, then a pre-compensator N is required to be placed at the reference input. N is just a constant gain to rescale input so that the output converges to 1 in the step response
sys2 = ss(A-B*K1, N*B, C, D)
More Answers (1)
Sam Chak
on 5 Nov 2022
I added a simple example to show you. If you like this example, consider voting 👍 the Answer. Thanks!
Say, the reference state is 1.
A = [0 1; 2 3];
B = [0; 1];
K1 = lqr(A, B, eye(2), 1)
sys1 = ss(A-B*K1, B, [1 0], 0)
step(sys1, 20)
The step response shows that the output won't reach 1. Thus, a pre-compensator is needed:
N = 1/dcgain(sys1) % pre-compensator
sys2 = ss(A-B*K1, N*B, [1 0], 0)
step(sys2, 20)
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