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

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{{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}}, {{cds101 mp3|cds101-2007-10-29.mp3|MP3}})
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'''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|L5-1_reachability_h.pdf|Lecture handout}}
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<!--{{cds101 handouts placeholder|L5-1_reachability_h.pdf|Lecture handout}}-->
* MATLAB code: {{cds101 matlab|L5_1_reachability.m}}, {{cds101 matlab|predprey.m}}, {{cds101 matlab|predprey_rh.m}}
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* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L4-1_statefbk.pdf Lecture handout]
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* 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 ({{cds101 mp3|cds101-2007-10-31.mp3|MP3}})
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'''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 control using state feedback.  The material from this lecture will not be covered on the homework.
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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. -->
 
* Midterm: available in class or outside 102 Steele
 
 
'''Friday:''' Midterm review (sorry, forgot to press 'record' on MP3 recorder)
 
* [[Media:Sawyer_reviewnotes.pdf|Midterm review]] Note: the plots at the end show the example problem before (unstable) and after (stable) applying state feedback.
 
  
 
== Reading ==
 
== Reading ==
  
* {{AM06|Chapter 6 - State Feedback}}
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* {{AM08|Chapter 6 - State Feedback}}
 
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== Midterm ==
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The exam will consist of 3-5 problems, covering the material in the first five weeks of the course (including reachability and state feedback).  The exam will be open book. You may use the course notes, any of the optional texts (Friedland, Franklin-Powell and Emami-Naeni, Lewis), course handouts, lecture notes, course problem sets and solutions, and your own handwritten notes. ''No other books are allowed.''
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== Homework ==
  
You may use a computer or calculator for carrying out ''numerical'' computations. MATLAB may be used but is not required. You are not allowed to use the Internet during the exam (except for accessing local computing resources, such as MATLAB/SIMULINK), but you may download or print out copies of presentations, notes, FAQs, or other material posted on the course web site (CDS 101 or 110). You are not allowed to print out contents of other sites for use while taking the exam (although you can take handwritten notes on the sites and use your own notes in the exam).
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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.
  
The exam will be due by 5 p.m. Tuesday, 6 November, in the box outside 102 Steele. Please write your solutions in a fresh exam book (blue book). We have to grade a large collections of exams in a short time and it makes things much simpler to manage if everyone uses a bluebook.
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* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw4-101-fa08.pdf hw4 - 101]
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* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw4-110-fa08.pdf hw4 - 110]
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* [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw4-210-fa08.pdf hw4 - 210]
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* [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 5-1, Fall 2007</ncl>
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<ncl>CDS 101/110 FAQ - Lecture 4-1, Fall 2008</ncl>
 
'''Wednesday'''
 
'''Wednesday'''
<ncl>CDS 101/110 FAQ - Lecture 5-2, Fall 2007</ncl>
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<ncl>CDS 101/110 FAQ - Lecture 4-2, Fall 2008</ncl>
 
'''Friday'''
 
'''Friday'''
<ncl>CDS 101/110 FAQ - Lecture 5-3, Fall 2007</ncl>
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<ncl>CDS 101/110 FAQ - Lecture 4-3, Fall 2008</ncl>
'''Midterm'''
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'''Homework'''
<ncl>CDS 101/110 FAQ - Midterm</ncl>
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<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 ()

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.

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,, Princeton University Press, 2008..

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.

FAQ

Monday

Wednesday

Friday

Homework