# Difference between revisions of "CDS 101/110 - System Modeling"

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* [http://www.cds.caltech.edu/~murray/courses/cds101/fa07/mp3/cds101-demo.mp4 cds101-demo.mp4] spring-mass system frequency response demonstration video from lecture | * [http://www.cds.caltech.edu/~murray/courses/cds101/fa07/mp3/cds101-demo.mp4 cds101-demo.mp4] spring-mass system frequency response demonstration video from lecture | ||

− | '''Wednesday:''' Modeling using Ordinary Differential Equation ({{cds101 handouts placeholder|L2-2_odes_h.pdf|Slides}}, {{cds101 mp3 | + | '''Wednesday:''' Modeling using Ordinary Differential Equation ({{cds101 handouts placeholder|L2-2_odes_h.pdf|Slides}}, {{cds101 mp3|cds101-2007-10-10.mp3|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). | 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). |

## Revision as of 23:56, 10 October 2007

WARNING: This page is for a previous year.See current course homepage to find most recent page available. |

CDS 101/110a | Schedule | Recitations | FAQ | () |

## Contents |

## 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.

- Lecture handout
- MATLAB files: L2_1_modeling.m, springmass.m
- cds101-demo.mp4 spring-mass system frequency response demonstration video from lecture

**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:** SIMULINK Tutorial - George Hines

This tutorial will provide an overview of the SIMULINK modeling tool.

## Reading

- K. J. Åström and R. M. Murray,, Preprint, 2007..

## 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 problem (CDS 110 only) explore discrete time modeling techniques.

## FAQ

**Monday**

- How do we read the simulated predator-prey graph?
- Is there any open source software we can use instead of MATLAB?
- What are the Di parameters in the power grid model?
- What is a finite state machine and how does it relate to the traffic example?
- Where can I find a theoretical definition of dynamical system?
- Why was there only one damper in the mass/spring model?

**Wednesday**

**Friday**

**Homework**