Optimal control with integral action for tracking a non-zero reference

Hello,

I have a discrete-time state-space realization:

x(k+1)=Ax(k)+Bu(k), y(k)=Cx(k)+Du(k)

I want to use LQ optimal control for tracking the output signal y with respect to a reference signal r different from 0. A classic way to do it is to add an integral action and to augment the original state-space system.

Is the MATLAB function lqi suitable for solving this problem? If it is, how can be done? If it is not, any hint?

From lqi help page http://www.mathworks.com/help/toolbox/control/ref/lqi.html, it seems it can only track zero reference signals:

The control law u = –Kz = –K[x;xi] minimizes the following cost functions (for r = 0)...

PS: Sorry for the possibly trivial question but I am not a control-theory expert.

Thank you very much!!

Answer 1

[Arkadiy Turevskiy]

Yes, lqi is exactly what you need. It works for non-zero reference signals.

Use that function to calculate gain K, the simulate your system either in MATLAB by using commands such as feedback, or just setup the system in Simulink.

Arkadiy

[Sergio Fresu]

First, thank you for answering and sorry for this late reply (I lost my hope to get an answer that I stopped to check for it).

What I don't understand, is how the reference signal r can be specified in the call to LQI function.

Didn't find it in the manual page.

Can you help me?