# CDS 101/110 - System Modeling

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 CDS 101/110a Schedule Recitations FAQ ()

## 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)

This lecture will provide a review of key concepts from linear algebra and differential equations, tuned to the needs of the course.

## Handouts

 Monday Lecture handout MATLAB files: L2_1_modeling.m, springmass.m HW #2 Wednesday (CDS 110) Lecture handout MATLAB files: Friday

• K. J. Åström and R. M. Murray,, Preprint, 2006..

## 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 MATLAB-based analysis of dynamical systems.

Monday

Wednesday

Friday

Homework