How can i tune Q and R parameters of a LQI controller?

Hi,

I benefit from the MATLAB's built-in function -lqi- to obtain a control input. In my design, i have only one input, however number of outputs is 2. I tried many of random number to tune my controller, unfortunately, i cannot find an optimal parameter set. Is there any way to determine Q and R weights of the LQI controller? I neglected N parameter for this design.

My state space representation is given below:

A = [-7.1167,-0.9680,0,0;... 
     3.3952,-11.2172,0,0;...
     0,1.0000,0,0;...
     13.5556,0,13.5556,0]; 

B = [3.5583; 44.2877; 0; 0];

C = [0,0,1,0;...
     0,0,0,1];

I am trying to follow step input. May you help me to solve this problem?

Thanks,

[Paul]

Hi Volcano,

To be clear, you want the integral control to act on an error signal from each output so that each output will track a step input?

[Volcano]

Yes. I integrate the errors between reference signals and system outputs. Each output should track the step input. Then, i will change the step input as a different reference signal.

[Sam Chak]

Hi @Volcano, are you intending to design a single feedback controller, u? This controller would be a function of the states, reference, and reference, denoted as . Moreover, and should independently track their respective reference signals.

Answer 1

[Paul]

This Answer thread may be of interest. Among other things, it shows how to use the Symmetric Root Locus (SRL) technique to design LQI controllers. The problem in this question is higher order and so the SRL method might be a bit more difficult to apply, but it might be a place to start. A Google search on Symmetric Root Locus will bring up a lot of information as well. It's just one method for desiging the Q and R matrices (actually only Q the matrix).