# Linear Quadratic Regulator (Optimal Controller Design)

1. Apr 6, 2010

### preet

This is a general question. When using the optimal method to design a controller, specifically a linear quadratic regulator, you usually have a state-space representation of a system, and a cost function to minimize.

The cost function usually takes the (quadratic) form:

I don't understand how you choose the weight matrices Q and R to minimize or optimize your system. For example, say my single order state space system's input (u) is force, and the output (y) is speed. Further, I can make y=x, my state variable. So would a reasonable goal be to achieve minimal force and maximum speed? How do I choose Q and R to reflect this?

Also, I'm trying to tie all of this in with another method of controller design -- pole placement. I understand pole placement because I'm directly 'designing' the desired response characteristics of my system's behaviour. I don't really get optimal control in this sense. Is optimal control a 'final' step, after pole placement? Or do I use my original system and find Q and R to get desired behaviour?