CDS 101/110 - Dynamic Behavior

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CDS 101/110a

Schedule

Recitations

FAQ

AM06 (errata)

Overview

Monday: Qualitative Analysis and Stability (Slides, MP3)

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 (Notes, MP3)

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

Friday: Lyapunov Stability (Notes, MP3)

Handouts

Monday Lecture handout MATLAB code: phaseplot.m, boxgrid.m, L3_1_stability.m, oscillator.m, pendulum.m, predprey.m Homework #3

Wed/Fri (CDS 110) Lecture notes

Reading

• K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Preprint, 2006. Chapter 4 - Dynamic Behavior.

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.

FAQ

Monday <ncl>CDS 101/110 FAQ - Lecture 3-1</ncl> Wednesday <ncl>CDS 101/110 FAQ - Lecture 3-2</ncl> Friday <ncl>CDS 101/110 FAQ - Lecture 3-3</ncl> Homework <ncl>CDS 101/110 FAQ - Homework 3</ncl>