ECE685 Introduction to Robust Control

Fall 2005

Course Information

Instructor: Sarah Koskie
Email: skoskie@iupui.edu
Lectures: MW 5:45–7 pm in SL 165 or SL 174
Office Hours: MW 7–8:30 pm in SL 164F or by appointment
Textbook: A Course in Robust Control Theory: A Convex Approach by Geir E. Dullerud and Fernando Paganini. Springer, 2000. ISBN: 0-387-98945-5.
*** Note to students: The notation in this text is very mathematical but the explanations are excellent. Please do not let the notation alarm you. I will explain it in class. The alternative texts listed below use simpler notation but give very little explanation.
Suggested references:
- Linear Matrix Inequalities in System and Control Theory, S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Vol. 15 in SIAM Studies in Applied Mathematics, 1994.
- Robust and Optimal Control by K. Zhou, J.C. Doyle and K. Glover, Prentice-Hall, 1996.
- Essentials of Robust Control by Kemin Zhou and John C. Doyle, Prentice-Hall, 1998.
- ECE685 Fall 2003 Lecture notes by Prof. V. Balakrishnan of Purdue, W. Lafayette
Prerequisites: ECE602, or consent of instructor. (Topics required: finite-dimensional linear algebra, exposure to control and system theory, and basic concepts from functional analysis.)
Objectives: Students will become familiar with the basic concepts and methods of robust control and be able to apply them appropriately to the analysis and design of control systems.
Course requirements/exams
- Occasional homework assignments, which may involve some simple Matlab programming
- One take-home midterm exam
- One take-home final exam

Students are allowed, even encouraged, to work on the homework in small groups, but each student must write up his or her own homework to hand in.

Grading:
- homework 34%
- midterm 33%
- final exam 33%

Course description

One of the most useful qualities of a properly designed feedback control system is robustness, i.e., the ability of the closed-loop system to continue performing satisfactorily despite large variations in the (open-loop) plant dynamics. This course will provide an introduction to the analysis and design of robust feedback control systems. Topics covered: modeling and paradigms for robust control; robust stability and measures of robust performance; analysis of robust stability and performance; design for robust stability and performance.

Course outline

Robust control -- motivation and overview

Why robust control?
Examples of important robust control problems

Paradigms for robust control

Sources of uncertainties
Parametric families of polynomials or matrices
Multi-model and polytopic systems
Systems with feedback perturbations: Linear fractional transformations; structured perturbations

Measures of robustness

Robust stability; quadratic stability; stability margins; invariant ellipsoids; decay rate
Reachable sets with input constraints
Output energy and peak
H₂ and H_∞ performance

Computation of robustness measures

Complexity issues
Exact methods for parametric families: Kharitonov and Edge theorems
Polytopic systems: LMI methods
Systems with feedback uncertainties: Small-gain and passivity methods
Systems with structured uncertainties: μ, Km and LMI analysis

Robust synthesis

Polytopic systems: LMI methods
Systems with feedback uncertainties
Systems with structured uncertainties
Gain-scheduled control

Bibliography

Where appropriate, journal papers may be referenced. In addition to the references listed above, the instructor has consulted the following texts which are out of print.

New Tools for Robustness of Linear Systems, B.R. Barmish, MacMillan, 1994.
Linear Robust Control, M. Green and D.J.N. Limebeer, Prentice Hall, 1995.

Last modified May 15,2007.