the use of the linear quadratic requlator method in the state space controller and observer design

hi guys,I am new in matlab and simulink. can you help me find a degin method to find the values of the R and Q matrices that are used to find the optimal values of the state controller k that optimize the objective function. my problem how I can relate the required performance of nonovershoot and zero stedy state error for the output to the values of Q and R matrices.

Answer 1

[Arnaud Miege]

The matrices R and Q are essentially design parameters or weights that you have to choose as part of the control system design, there's no automated way of selecting those (as far as I know). However, you can use function like lqr to compute the optimal state feedback matrix K. Check out the other functions under LQR/LQG Design.

HTH,

Arnaud

[Mary]

Thank you Arnaud. my supervisor told me that I have to find a design method to calculate Q and R instead of using manual tunning. I have already used the function lqr to find the values of the matrix K that give the best response and the value of the Q matrix was adjusted manualy by changing the nonzero values of the matrix Q. so is there any method to achieve this and what is the relation with the Riccati equation

[Arnaud Miege]

The optimal state feedback matrix K is computed using the solution of the Ricatti equation. Have a look at this (in particular section 2.2) for more details:

http://www.ece.ucsb.edu/~roy/classnotes/147c/lqrlqgnotes.pdf