Difference between revisions of "CDS 101/110  Linear Systems"
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This lecture gives an introduction to linear input/output systems. The main properties of linear systems are given and the matrix exponential is used to provide a formula for the output response given an initial condition and input signal. Linearization of nonlinear systems as an approximation of the dynamics is also introduced.  This lecture gives an introduction to linear input/output systems. The main properties of linear systems are given and the matrix exponential is used to provide a formula for the output response given an initial condition and input signal. Linearization of nonlinear systems as an approximation of the dynamics is also introduced.  
−  '''Wednesday:''' Linearization (  +  '''Wednesday:''' Linearization ([[Media:Lecture32.pdfNotes]], [[Media:18Oct06.mp3MP3]], Note: the recorder's batteries died 4 minutes into lecture) 
Further analysis of linear systems, including a derivation of the convolution integral and the use of Jordan form. This lecture also covers the use of linearization to approximate the dynamics of a nonlinear system by a linear system.  Further analysis of linear systems, including a derivation of the convolution integral and the use of Jordan form. This lecture also covers the use of linearization to approximate the dynamics of a nonlinear system by a linear system. 
Revision as of 18:37, 19 October 2006
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CDS 101/110a  Schedule  Recitations  FAQ  AM06 (errata) 
Overview
Monday: Linear TimeInvariant Systems (Slides, MP3)
This lecture gives an introduction to linear input/output systems. The main properties of linear systems are given and the matrix exponential is used to provide a formula for the output response given an initial condition and input signal. Linearization of nonlinear systems as an approximation of the dynamics is also introduced.
Wednesday: Linearization (Notes, MP3, Note: the recorder's batteries died 4 minutes into lecture)
Further analysis of linear systems, including a derivation of the convolution integral and the use of Jordan form. This lecture also covers the use of linearization to approximate the dynamics of a nonlinear system by a linear system.
Friday: Performance measures (Notes, MP3)
This lecture defines the standard performance measures for linear systems in terms of the step and frequency responses. Second order systems are considered in detail.
Handouts
Monday

Wednesday (CDS 110)  Friday 
Reading
 K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Preprint, 2006. Chapter 5  Linear Systems.
Homework
This homework set covers linear control systems. The first problem asks for stability, step and frequency response for some common examples of linear systems. The second problem considers stabilization of an inverted pendulum on a cart, using the local linaerization. The remaining problems (for CDS 110 students) include derivation of discrete time linear systems response functions and derivation of a linearized model for internet congestion. Supplemental problems for flight control and robotics are available.
 Homework #4
 hw4balance.mdl  SIMULINK model of a balance system
FAQ
Monday <ncl>CDS 101/110 FAQ  Lecture 41</ncl> Wednesday <ncl>CDS 101/110 FAQ  Lecture 42</ncl> Friday <ncl>CDS 101/110 FAQ  Lecture 43</ncl> Homework <ncl>CDS 101/110 FAQ  Homework 4</ncl>