Sharif University of Technology
Department of Electrical Engineering
Parametric Robust Control
Spring 2011 (1389-90)
Course Information
- 25-420 Parametric Robust Control
- Credits: 3
- Level: Graduate, 600
- Prerequisite: Linear Control Systems & Modern Control
- Instructor: H. Karimi
- Hours & Locations:
- Lecture: Sat. & Mon., 18:00 - 19:30, Classroom 1, EE Dept. (old building)
Course Description:
This is a graduate course for students who passed Linear Control and Modern Control Systems. The outline of the course is:
- A Global Overview: robustness problems, historical perspective, Kharitonov's THM, uncertainty structure,
mathematical programming approach, the value set concept, family paradigm, robustness analysis, robustness margin,
robust synthesis, conclusion.
- Notation for Uncertain Systems: notations for uncertain parameters, uncertainty bounding sets and norms,
notation for families, real versus complex.
- Case Study: The Fiat Engine, and Some Microgrid Examples: modeling, control, transfer function matrix for the engine,
uncertain parameters in the model, closed-loop polynomial
- Robust Stability with a Single Parameter: stability and robust stability, basic definitions and examples, generalized root locus,
invariant degree concept, eigenvalue criteria for robustness, introduction to robust D-stability
- Kharitonov's Theorem: interval polynomial family, Kharitonov polynomials, Kharitonov's theorem, graphical interpretation, overbounding via interval polynomials,
extensions with degree dropping, frequency sweeping function, Kharitonov's THM with complex coeeficients
- The Value Set Concept: the value set, the zero exclusion condition, zero exclusion for robust D-stability, boundary sweeping functions
- Polytopes of Polynomials: affine linear uncertainty structure, introduction to polytopes of polynomials, polygonal value sets.
- The Edge Theorem: lack of extreme points results for polytopes, the edge THM, Fiat Example.
- Distinguished Edges: parallelotopes, parpolygons, setup with an interval plant, the Thirty-Two Edge THM.
- The Sixteen Plant Theorem: Sixteen distinguished plants, the Sixteen Plant THM, Controller synthesis technique.
- Multilinear Uncertainty Structure: multilinear and polynomic uncertainty, interval matrix family, lack of extreme point
and edge results, the mapping THM, geometric interpretation, value set interpretation
- Spherical Polynomial Families: boxes versus spheres, Soh-Berger-Dabke THM, value set for spherical polynomial family, overbounding via spherical family,
spherical set, Barmish and Tempo THM, affine linear uncertainty structures, testing function for robust stability.
Text Book:
B. R. Barmish, New Tools for Robustness of Linear Systems, MacMillan, New York, 1994.
References:
- S. P. Bhattacharyya, H. Chapellat, L.H. Keel, Robust Control - The Parametric Approach, Prentice Hall, Englewood Cliffs, New Jersey, 1995.
- S. P. Bhattacharyya, A. Datta, L. H. Keel, Linear Control Theory: Structure, Robustness, and Optimization, CRC Press, Taylor & Francis Group, 1 Edition, January 30, 2009.