Week 3: Stability and Performance
Overview
Monday: This lecture provides an introduction to stability and performance 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. Performance of control systems is presented for transient and steady state specifications.
Wednesday: Lyapunov functions are introduced as a method of proving stability for nonlinear systems. Simple examples are used to explain the concepts; domain specific examples will be presented in individual recitation sections.
Friday: Prof. Tim Colonius will give a lecture on flow instabilities in fluid systems.Handouts
Monday (CDS 101/110)
Wednesday (CDS 110 only)
Friday
- Friday lecture handout
- Additional references:
- Drazin & Reed, Hydrodynamic Stability. Cambridge Univ. Press, 1981
- Collis, S.S., Joslin, R.D., Seifert, A., and Theofilis, V., Issues in Active Flow control: Theory, computation, simulation, and experiment, 2004.
- Flow control: new challenges for a new renaissance. Prog. Aerosp. Sci. 37:21-58. 2001
- Annaswamy AM, Ghoniem AF, Active control of combustion instability: Theory and practice. IEEE CONTROL SYSTEMS MAGAZINE 22 (6): 37-54 DEC 2002
Reading
-
K. J. Åström and R. M. Murray, Analysis and Design of Feedback Systems, Preprint, 2004. Chapter 3 . (Caltech access only).
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.
- HW #3
- MATLAB functions: phaseplot.m, boxgrid.m
- SIMULINK models: hw1cruise.mdl, hw3cruise_sat.mdl
Additional Information