Difference between revisions of "CDS 101/110  System Modeling"
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This lecture provides a more detailed introduction to the use of ordinary differential equations (ODEs) for modeling dynamical systems. A brief review of the solutions of second order linear ODEs is provided to make connection with prior coursework. The general form of nonlinear and linear ODEs is provided, along with an overview of some of the techniques for solving linear ODEs in special forms (scalar and diagonal systems). Analysis tools, including stability and frequency response, are illustrated. Finally, the use of block diagrams in control systems is introduced, including the standard symbology used in the text and an extended example (insect flight).  This lecture provides a more detailed introduction to the use of ordinary differential equations (ODEs) for modeling dynamical systems. A brief review of the solutions of second order linear ODEs is provided to make connection with prior coursework. The general form of nonlinear and linear ODEs is provided, along with an overview of some of the techniques for solving linear ODEs in special forms (scalar and diagonal systems). Analysis tools, including stability and frequency response, are illustrated. Finally, the use of block diagrams in control systems is introduced, including the standard symbology used in the text and an extended example (insect flight).  
−  '''Friday:'''  +  '''Friday:''' Review of Linear Algebra and ODE  Mary Dunlop ([[Media:ODE_review.pdfLecture Notes]]) 
This lecture will provide a review of key concepts from linear algebra and differential equations, tuned to the needs of the course.  This lecture will provide a review of key concepts from linear algebra and differential equations, tuned to the needs of the course. 
Revision as of 03:55, 10 October 2006
See current course homepage to find most recent page available. 
CDS 101/110a  Schedule  Recitations  FAQ  AM06 (errata) 
Overview
Monday: Introduction to Modeling (Slides, MP3)
This lecture provides an overview of modeling for control systems. We discuss what a model is and what types of questions it can be used to answer. The concepts of state, dynamics, inputs and outputs are described, including running examples to demonstrate the concepts. Several different modeling techniques are summarized, with emphasis on differential equations. Two examples are included to demonstrate the main concepts.
Wednesday: Modeling using Ordinary Differential Equation (Slides, MP3)
This lecture provides a more detailed introduction to the use of ordinary differential equations (ODEs) for modeling dynamical systems. A brief review of the solutions of second order linear ODEs is provided to make connection with prior coursework. The general form of nonlinear and linear ODEs is provided, along with an overview of some of the techniques for solving linear ODEs in special forms (scalar and diagonal systems). Analysis tools, including stability and frequency response, are illustrated. Finally, the use of block diagrams in control systems is introduced, including the standard symbology used in the text and an extended example (insect flight).
Friday: Review of Linear Algebra and ODE  Mary Dunlop (Lecture Notes)
This lecture will provide a review of key concepts from linear algebra and differential equations, tuned to the needs of the course.
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 2  System Modeling.
Homework
This homework set demonstrates the construction and use of models for control systems. The first problem asks the student to identify the states, inputs, outputs, and dynamics for a sample systems. The second problem consists of a detailed construction of a vehicle model that can be used for cruise control. The last two problems (CDS 110 only) explore different modeling techniques, including both discrete time, analytical, and MATLABbased analysis of dynamical systems.
 SIMULINK speed control module (for problem #2): hw1cruise.mdl, documentation
FAQ
Monday <ncl>CDS 101/110 FAQ  Lecture 21</ncl> Wednesday <ncl>CDS 101/110 FAQ  Lecture 22</ncl> Friday <ncl>CDS 101/110 FAQ  Lecture 23</ncl> Homework <ncl>CDS 101/110 FAQ  Homework 2</ncl>