# Week 12: Linear Quadratic Regulators

#### 13 January 2003

 Overview Reading FAQ Homework CDS 110b

### Overview

The linear quadratic regulator (LQR) problem provides a design method for building state space controllers. We start with a review of the optimal control problem and basic LQR results (details and proofs are left to the reading). The results are illustrated using the ducted fan example and exploring how different choices of weights affect the performance. We then explore how to incorporate reference inputs and integral action into the LQR formalism. Finally, some notions of robustness are explored and a comparison with frequency domain techniques is given.

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### Homework

The homework covers the basic design of LQR controllers through a set of four different problems. In addition, one problem covers the design of feedforward controllers for nonzero desired states and integral action in LQR compensators.

Homework #10