How do i use LQR control in state space form?
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I am trying to simulate the step response of the quarter car. for this i am using LQR controller. I have built the state space matrix in the form:
Xdot=AX+BU+GW;
Y = CX+DU;
Here, 'W' is the controller force and 'U' is the excitation displacement from the ground. I gave Matrices A, B, C and D matrices, where D is null matrix and C as unity. The problem is where do I put the matrix 'G' which is GAIN matrix from the controller. until now i have the following:
sys = ss(A,B,C,D);
[K,P] = lqr(A,B,Q,R,N); %where N=0
%we will obtain K and P values
sys = ss(A-B*K,B,C,D);
step(sys)
Theoretically, my G matrix is:
G = [U/m1 0; -U/m2 0];
Where must be the 'G' matrix be inputted?
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답변 (3개)
Azzi Abdelmalek
2016년 8월 23일
You have first to tell us what are the inputs and outputs of your system. Post the parameters representing your system, and post how did you use the lqr function.
Kwin
2016년 10월 12일
Both 'W' and 'U' are inputs to your system, however I assume that you will not be able to influence 'U', so it can be considered a disturbance. So 'G' is actually your 'B' matrix. LQR does not consider this disturbance, so you might want to use LQG instead.
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duc nguyentrong
2020년 1월 5일
I am researching about active suspension system using LQR in matlab-simulink software to simulate. I have the code of a quarter-car model but I have a problem running. Hope everyone can point out its faults. thanks
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