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

2011 7 25
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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.

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Arnaud Miege
Arnaud Miege 2011-7-25

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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

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Mary
Mary 2011-7-25
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
Arnaud Miege 2011-7-25
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

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