How to design LQR problem for tracking a reference output

Hi,

I am trying to design an optimal control for tracking a real time reference signal. As I know, the 'lqr/dlqr' command in MATLAB just works for regulator problem. Could anyone give me a help? or some reference readings.

Many thanks.

[Shashank Prasanna]

Could you elaborate on what you are looking for?

Answer 1

[M]

You can use the lqi function.

Answer 2

[Mohamed Abdullah]

you convert your problem to be in a regulator form. this is done by incorporating your desired states with the actual states in one vector and (that is the error vector) to be your new state vetor in this way, your controller is trying to bring the error between the desired and actual states or outputs to zero.

and the new cost function shall be

[Amirah Algethami]

Thanks@Mohamed Abdullah can you provide me with matlab example code.As you explination is what I need exactly.

[Sam Chak]

Hi @Amirah Algethami

The computed gains from the LQR approach, "K = lqr(A, B, Q, R)", do not affect the tracking capability from a theoretical perspective. Have you tested your code to regulate a process variable at a constant value and to track a sinusoidal reference signal?

If you're having trouble, please post a new question with a toy problem and a simple LQR code for a second-order system.