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

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− | {{cds101- | + | {{cds101-fa08 lecture|prev=Linear Systems|next=Output Feedback}} |

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== Overview == | == Overview == | ||

− | '''Monday:''' Reachability and State Feedback ({{cds101 handouts|L5-1_reachability.pdf|Slides}}, MP3) | + | '''Monday:''' Reachability and State Feedback ({{cds101 handouts placeholder|L5-1_reachability.pdf|Slides}}, {{cds101 mp3|cds101-2008-10-20.mp3|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. | 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. | ||

− | + | <!--{{cds101 handouts placeholder|L5-1_reachability_h.pdf|Lecture handout}}--> | |

+ | * [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L4-1_statefbk.pdf Lecture handout] | ||

+ | * MATLAB code: [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/predprey_calcs.m L5 predprey_calcs.m], {{cds101 matlab|predprey.m}}, [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/predprey_rh.m predprey_rh.m], | ||

− | + | '''Wednesday:''' State Feedback Design: [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L4-2_statefbk.pdf Lecture notes] ({{cds101 mp3|cds101-2008-10-22.mp3|MP3}}) | |

− | + | 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. --> | ||

− | == | + | == Reading == |

− | + | * {{AM08|Chapter 6 - State Feedback}} | |

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− | * {{ | ||

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− | == | + | == 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. | |

− | + | * [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw4-101-fa08.pdf hw4 - 101] | |

+ | * [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw4-110-fa08.pdf hw4 - 110] | ||

+ | * [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw4-210-fa08.pdf hw4 - 210] | ||

+ | * [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/bike_linmod.m bike_linmod.m] - Mass, damping and stiffness matrices for Whipple bicycle model | ||

== FAQ == | == FAQ == | ||

'''Monday''' | '''Monday''' | ||

− | <ncl>CDS 101/110 FAQ - Lecture | + | <ncl>CDS 101/110 FAQ - Lecture 4-1, Fall 2008</ncl> |

'''Wednesday''' | '''Wednesday''' | ||

− | <ncl>CDS 101/110 FAQ - Lecture | + | <ncl>CDS 101/110 FAQ - Lecture 4-2, Fall 2008</ncl> |

'''Friday''' | '''Friday''' | ||

− | <ncl>CDS 101/110 FAQ - Lecture | + | <ncl>CDS 101/110 FAQ - Lecture 4-3, Fall 2008</ncl> |

'''Homework''' | '''Homework''' | ||

− | <ncl>CDS 101/110 FAQ - | + | <ncl>CDS 101/110 FAQ - Homework 4, Fall 2008</ncl> |

## Latest revision as of 05:57, 9 December 2008

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

## 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: Lecture notes (MP3)

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

## Reading

- K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, 2008. Chapter 6 - State Feedback.

## 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**
<ncl>CDS 101/110 FAQ - Lecture 4-1, Fall 2008</ncl>
**Wednesday**
<ncl>CDS 101/110 FAQ - Lecture 4-2, Fall 2008</ncl>
**Friday**
<ncl>CDS 101/110 FAQ - Lecture 4-3, Fall 2008</ncl>
**Homework**
<ncl>CDS 101/110 FAQ - Homework 4, Fall 2008</ncl>