I am trying to find out the inverse Laplace transform of the state transition matrix obtained using inv(S*I-A). Where I is the identity matrix, and A is a state-space matrix(24x24 matrix).
I have used syms S.
I have tried the same method to another matrix A=rand(24), and in both cases, the simulation is taking a long time.
Can anyone help me in resolving this issue?
Hello
My experience with the symbolic toolbox of MATLAB says that it is incapable of doing such inversion.
The first solution is to try to design a controller in state-space, instead of the Laplace domain.
Besides, since your system is large and as long as there exists no physical linear system, I think it is better to design nonlinear a control law for the original system.
Regards,
You may find this useful for you
https://www.mathworks.com/help/symbolic/ilaplace.html
What you are trying to do is following:
syms s;
A = rand(24);
STM = ilaplace(inv(s*eye(size(A))-A)); % This is state-transition matrix
This code will work, but will consume some amount of time. If you want to calculate STM, better way is to do it numerically rather than computing symbolically. My recommendation is to use the following property of STM:
d/dt(STM) = A*STM, with initialization as STM(t=0) = identity matrix of size of A.
You can easily solve this matrix differential equation using any ode solver, or may be in Simulink. This will give faster result than symbolic calculation.
- Badges
- Science topic
- Similar topics
- Mathematics
- Algebra
- Matrix