How to tune the matrices Q and R in LQR controller design

While controlling two variables using LQR controller, [I am] not able to properly tune Q and R. What is best way to tune them?

[hawi aboma]

hello, how to tuning lqr parameter (Q,R) ?please if any one have solution please send to me via email or comment

Answer 1

[Fanjie]

Bryson rule：

[杨]

which book this is ?

[Sam Chak]

Hi @杨

This information did not come from a book. Rather, it is from Prof. João Hespanha's lecture notes on LQR controller design.

https://web.ece.ucsb.edu/~hespanha/

Answer 2

[Raj]

Hi,

There is no fixed rule or formal method to estimate and tune the weight matrices Q and R. It is an iterative process wherein you will have to see your plant time response wiith respect to desired performance criteria and adjust the weights accordingly.

However a good way to start the process is by using Bryson's rule wherein weights of Q matrix determine the error permitted in each output state and weights of R matrix determine to control effort. Keep a track of the cost function for each selection of Q & R and keep it to minimum possible.

Example: You can take following matrices as initial estimate for a 8x8 system (i.e. 8 output states) with 4 control inputs when you want to control only the last four states;

Q = A* diag(0 0 0 0 1 1 1 1)

R = B* diag(1 1 1 1)

where A & B are scalar factors.