CDS 101/110, Week 3 - Dynamic Behavior
From MurrayWiki
| CDS 101/110a | Schedule | Recitations | FAQ | AM08 (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.
- Lecture handout
- MATLAB code: phaseplot.m, boxgrid.m, L3_1_stability.m, oscillator.m, invpend.m, predprey.m
Wednesday: Stability Analysis using Lyapunov Functions (Notes, MP3)
Lyapunov functions are introduced as a method of proving stability for nonlinear systems. Simple examples are used to explain the concepts.
Friday: Recitations
Reading
- K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Preprint, 2007. Chapter 4 - Dynamic Behavior.
Homework
- Homework #3
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
- How are the z variables defined on slide 10, Lecture 3-1?
- How was V(x) derived on slide 13 of Lecture 3-1?
Wednesday
- Was the equation for V(q) for the spring mass example missing a transpose?
- Where can I find the proof to the Lyapunov Theorem?
Homework
