CDS 101/110 - Dynamic Behavior: Difference between revisions

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{{cds101-fa06}}
{{cds101-fa08 lecture|prev=Introduction and Review|next=Linear Systems}}


{{righttoc}}
{{righttoc}}
== Overview ==
== Overview ==
The learning objectives for this week are:
* Students should be able to use a phase portraits to describe the behavior of dynamical systems and determine the stability of an equilibrium point
* Students should be able to find equilibrium points for a nonlinear system and determine whether they are stable using linearizations (all) and Lyapunov functions (CDS 110/210)
* Students should be able to explain the difference between stability, asymptotic stability, and global stability


'''Monday:'''  Qualitative Analysis and Stability (Slides, MP3)
'''Monday:'''  Qualitative Analysis and Stability ({{cds101 handouts|L2-1_stability.pdf|Slides}}, [http://www.cds.caltech.edu/~murray/courses/cds101/fa07/mp3/cds101-2007-10-15.mp3 MP3]- due to technical difficulties, this is last year's lecture)
<p>
:This lecture provides an introduction to stability  of (nonlinear) control systems. Formal definitions of stability are given and phase portraits are introduced to help visualize the concepts. Local and global behavior of nonlinear systems is discussed, using a damped pendulum and the predator-prey problem as examples.


This lecture provides an introduction to stability of (nonlinear) control systems. Formal definitions of stability are given and phase portraits are introduced to help visualize the concepts. Local and global behavior of nonlinear systems is discussed, using a damped pendulum and the predator-prey problem as examples.  
:* {{cds101 handouts|L2-1_stability_h.pdf|Lecture handout}}
:* MATLAB code: {{cds101 matlab|phaseplot.m}}, {{cds101 matlab|boxgrid.m}}, {{cds101 matlab|L2_1_stability.m}}, {{cds101 matlab|oscillator.m}}, {{cds101 matlab|invpend.m}}, {{cds101 matlab|predprey.m}}
</p>
'''Wednesday:''' Stability Analysis using Lyapunov Functions ({{cds101 handouts|L2-2_lyapunov.pdf|Notes}}, [http://www.cds.caltech.edu/~murray/courses/cds101/fa07/mp3/cds101-2007-10-17.mp3 MP3]- due to technical difficulties, this is last year's lecture)
:Lyapunov functions are introduced as a method of proving stability for nonlinear systems. Simple examples are used to explain the concepts.


'''Wednesday:''' Stability Analysis (Slides, MP3)
:* {{cds101 handouts|L2-2_lyapunov.pdf|Lecture notes}}


Lyapunov functions are introduced as a method of proving stability for nonlinear systems. Simple examples are used to explain the concepts; domain specific examples will be presented in individual recitation sections.
'''Friday:''' [[CDS 101/110a, Fall 2008 - Recitation Schedule|Recitations]]
 
:* [[CDS 210 - Stability Analysis]]
'''Friday:''' Lyapunov Stability (Slides, MP3)
 
 
== Handouts ==
 
{| width=100%
|- valign=top
| width=33% | Monday
* {{cds101 handouts|L3-1_dynsys_h.pdf|Lecture handout}}
* MATLAB code: {{cds101 matlab|L3_1_stability.m}}, {{cds101 matlab|oscillator.m}}, {{cds101 matlab|pendulum.m}}, {{cds101 matlab|predprey.m}}
* {{cds101 handouts|hw3.pdf|Homework #3}}
| width=33% | Wednesday (CDS 110)
* {{cds101 handouts|L3-2_stability_h.pdf|Lecture handout}}
* MATLAB code:
| width=33% | Friday
* {{cds101 handouts|L3-3_lyapunov_h.pdf|Lecture handout}}
 
|}


== Reading ==
== Reading ==


* {{AM06|Chapter 3 - Dynamic Behavior}}
* {{AM08|Chapter 4 - Dynamic Behavior}}  
** CDS 101: Read sections 4.1-4.3 [30 min]
** CDS 110: Read sections 4.1-4.4, up to Krasolvski-Lasalle (p 118) [60 min]
** CDS 210: Review sections 4.1-4.3, read sections 4.4-4.5 [60 min]


== Homework ==
== Homework ==


This homework set covers stability and performance through a series of application examples. The first problem provides a set of three real-world models in which the student must identify the equilibrium points and determine stability of the equilibrium points (through simulation). The second problem explores performance specification in the conext of the cruise control example, including step response and frequency response.
* {{cds101 handouts|hw2-fa08.pdf|Homework #2}}
 
<!-- Links to homework materials -->


== FAQ ==
== FAQ ==
'''Monday'''
'''Monday'''
<ncl>CDS 101/110 FAQ - Lecture 3-1</ncl>
<ncl>CDS 101/110 FAQ - Lecture 2-1, Fall 2008</ncl>
'''Wednesday'''
'''Wednesday'''
<ncl>CDS 101/110 FAQ - Lecture 3-2</ncl>
<ncl>CDS 101/110 FAQ - Lecture 2-2, Fall 2008</ncl>
'''Friday'''
<ncl>CDS 101/110 FAQ - Lecture 3-3</ncl>
'''Homework'''
'''Homework'''
<ncl>CDS 101/110 FAQ - Homework 3</ncl>
<ncl>CDS 101/110 FAQ - Homework 2, Fall 2008</ncl>

Latest revision as of 05:56, 9 December 2008

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

Overview

The learning objectives for this week are:

  • Students should be able to use a phase portraits to describe the behavior of dynamical systems and determine the stability of an equilibrium point
  • Students should be able to find equilibrium points for a nonlinear system and determine whether they are stable using linearizations (all) and Lyapunov functions (CDS 110/210)
  • Students should be able to explain the difference between stability, asymptotic stability, and global stability

Monday: Qualitative Analysis and Stability (Slides, MP3- due to technical difficulties, this is last year's lecture)

This lecture provides an introduction to stability of (nonlinear) control systems. Formal definitions of stability are given and phase portraits are introduced to help visualize the concepts. Local and global behavior of nonlinear systems is discussed, using a damped pendulum and the predator-prey problem as examples.

Wednesday: Stability Analysis using Lyapunov Functions (Notes, MP3- due to technical difficulties, this is last year's lecture)

Lyapunov functions are introduced as a method of proving stability for nonlinear systems. Simple examples are used to explain the concepts.

Friday: Recitations

Reading

Homework

FAQ

Monday <ncl>CDS 101/110 FAQ - Lecture 2-1, Fall 2008</ncl> Wednesday <ncl>CDS 101/110 FAQ - Lecture 2-2, Fall 2008</ncl> Homework <ncl>CDS 101/110 FAQ - Homework 2, Fall 2008</ncl>

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