Sharif University of Technology
Department of Electrical Engineering
Parametric Robust Control
Spring 2011 (1389-90)
- 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)
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.
B. R. Barmish, New Tools for Robustness of Linear Systems, MacMillan, New York, 1994.
- 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.