Seeking Help to Find Kalman Decomposition Matrices
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I need to find the matrix for a Kalman decomposition of the following problem. It would be even better if I could obtain the symbolic matrix as well.
Specifically, I am looking for the matrices At, Bt, and Ct.
Please help me as I'm having trouble finding the correct matrices, and my thesis is incomplete without solving this issue.
Thanks!!
2 Comments
Sam Chak
on 4 Oct 2023
@Edoardo Moroni, I'm not entirely clear on your approach to solving the problem and determining the Kalman Decomposition Matrices. Could you please provide a description of the system and explain why you introduce τ at ?
Answers (1)
Sam Chak
on 5 Oct 2023
% Parameters
m1 = 1;
m2 = 1;
m3 = 1;
k0 = 1;
% State-space system
A21 = [-k0/m1 k0/m1 0;
k0/m2 -2*k0/m2 k0/m2;
0 k0/m3 -k0/m3];
A = [zeros(3) eye(3);
A21 zeros(3)];
B = [1/m1 zeros(1,5)]';
C = [1 zeros(1,5)];
D = 0;
sys = ss(A, B, C, D)
% Kalman decomposition, where T is the transformation matrix
[sysr, T] = minreal(sys)
% Check by manually transforming the original matrices
At = T*A*T';
Bt = T*B;
Ct = C*T';
Dt = D;
Ksys = ss(At, Bt, Ct, Dt)
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