In MATLAB, I'm attempting to transform my model from continuous state space to discrete state space. The error occurred is "Matrix is Singular to working precision." Please, someone assist me.
A =[0 1.0000 0 0;
51.6923 0 0 0.0221;
0 0 0 1.0000;
-51.6923 0 0 -0.5361]
B =[0;
-0.3412;
0;
8.2597]
Q=[1 0 0 0;
0 1 0 0;
0 0 1 0;
0 0 0 1]
C=[1 0 0 0;
0 0 1 0]
D=[0;0]
R=1;
K=lqr(A,B, Q, R)
q1_int=0.01;
q1_dot_int=0;
q2_int=0;
q2_dot_int=0.01;
%converting our continuous state space model to discrete-time
fs=20;
T=1/fs;
Ad=expm(A*T)
Bd=(Ad-eye(4))/A*B
Hi,
First, you can use pseudo inverse instead your singular matrix inverse.
Second, if the matrix is real symmetric, one might approach such cases by orthogonal diagonalization.
Also, take a look at the links.
https://www.mathworks.com/matlabcentral/answers/246861-how-to-convert-model-from-continuous-state-space-with-disturbance-to-discrete
https://www.mathworks.com/matlabcentral/answers/322751-c2d-function-makes-ugly-system-model-matrix
Best regards
As mentioned, your A matrix has a rank deficiency, so you cannot take its inverse.
You may either use the following code to find the ss representation for your discrete system
sysc = ss(A,B,C,D);
sysd = c2d(sysc,T)
or use
Bd=pinv(A)*(Ad-eye(4))*B
Then you may also check the performance of the discretization using step(sysc,sysd), however you system is unstable to step input.
I hope this helps you.
Regards,
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