# Difference between revisions of "CDS 101/110 - State Feedback"

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'''Wednesday:''' State Feedback Design ({{cds101 mp3 placeholder|cds101-2007-10-31.mp3|MP3}}) | '''Wednesday:''' State Feedback Design ({{cds101 mp3 placeholder|cds101-2007-10-31.mp3|MP3}}) | ||

− | This lecture will present more advanced analysis on control using state feedback. | + | This lecture will present more advanced analysis on reachability and on control using state feedback. |

<!-- This lecture will describe how to design state feedback controllers via eigenvalue placement. The performance of the system as a function of the placement of the closed loop eigenvalues will be described. The use of integral action and a brief introduction to LQR control will also be given. --> | <!-- This lecture will describe how to design state feedback controllers via eigenvalue placement. The performance of the system as a function of the placement of the closed loop eigenvalues will be described. The use of integral action and a brief introduction to LQR control will also be given. --> | ||

## Revision as of 17:01, 20 October 2008

CDS 101/110a | Schedule | Recitations | FAQ | AM08 (errata) |

## Contents |

## Overview

**Monday:** Reachability and State Feedback (Slides, MP3)

This lecture introduces the concept of reachability and explores the use of state space feedback for control of linear systems. Reachability is defined as the ability to move the system from one condition to another over finite time. The reachability matrix test is given to check if a linear system is reachable, and the test is applied to several examples. The concept of (linear) state space feedback is introduced and the ability to place eigenvalues of the closed loop system arbitrarily is related to reachability. A cart and pendulum system and the predator prey problem are used as examples.

- Lecture handout
- MATLAB code: L5 predprey_calcs.m, predprey.m, predprey_rh.m,

**Wednesday:** State Feedback Design (MP3)

This lecture will present more advanced analysis on reachability and on control using state feedback.

## Reading

- K. J. Åström and R. M. Murray,, Preprint, 2007..

## Homework

This homework set covers reachability and state feedback. The Whipple bicycle model is used as an example to illustrate state feedback with pole placement, and the dependence of both the tracking behaviour and the command response on the location chosen for the closed-loop poles.

- hw4 - 101
- hw4 - 110
- hw4 - 210
- bike_linmod.m - Mass, damping and stiffness matrices for Whipple bicycle model

## FAQ

**Monday**

**Wednesday**

**Friday**

**Homework**