SUGGESTED SYLLABUS FOR

CONTROL of SYSTEMS with PARAMETER UNCERTAINTIES

Fall 2016

 

Date Topics to be covered

September  20

(Week 1)

INTRODUCTION

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Motivation

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Definition of Robust Control

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Classification of Robust Control Systems

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Introduction to parametric uncertain systems

September  27

(Week 2)

MODELING OF PARAMETRIC UNCERTAIN SYSTEMS

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Examples for modeling systems with parameter uncertainty

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Introduction to the notation and general concepts

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Symbolic algebra and parametric uncertain systems

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Generalization of several control concepts to parametric uncertain systems
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Stability

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Controllability & Observability

ROBUST STABILITY ANALYSIS

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Pole Spread and gridding

ROBUST STABILITY ANALYSIS

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Boundary crossing theorem"

 MATHEMATICA TUTORIAL

October  4

(Week 3)

ROBUST STABILITY ANALYSIS

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Algebraic tests
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Routh table

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Hurwitz determinants

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Bialas theorem

October 11

(Week 4)

FREQUENCY RESPONSE of POLYNOMIALS with PARAMETRIC UNCERTAINTIES

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Mikhailov Theorem

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Hermite-Biehler Theorem

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Value Set Concept

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Zero Exclusion Theorem

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Singular Frequency

October 18

(Week 5)

CLASSIFICATION OF PARAMETRIC UNCERTAIN POLYNOMIALS and TEST SETS

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Classification
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Interval polynomials

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Affine-linear polynomials

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Multilinear polynomials

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Polynomials with polynomial coefficients

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Test Sets

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Kharitonov theorem

October 25

(Week 6)

TEST SETS (CONT.)

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The concept of concervatism

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Edge theorem

November 1

(Week 7)

TEST SETS (CONT.)

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Test sets for multilinear polynomials

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Jacobi conditions for uncertain parameters

November 8

(Week 8)

NO CLASS!

November 15

(Week 9)

MIDTERM EXAM

November 22

(Week 10)

TEST SETS (CONT.)
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Mapping Theorem

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Test sets for polynomials with polynomial uncertainties.

November 29

(Week 11)

CONSTRUCTION OF VALUE SETS

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Addition and multiplication of value sets

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Tree structured decomposition

December 6

(Week 12)

STABILITY RADIUS
bulletTsypkin - Polyak Loci
bulletInterval polynomials
bulletAffine linear polynomials
bulletLargest hypersphere in the parameter space

December 13

(Week 13)

ROBUSTNESS ANALYSIS of FEEDBACK SYSTEMS
bulletBox Theorem
bulletPositive interval plants
bulletRobustness with respect to nonlinearities

December 20

(Week 14)

STABILIZING PID CONTROLLER DESIGN
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Stabilizing P Controllers

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Stabilizing PI Controllers

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Stabilizing PID Controllers

December 27

(Week 15)

FINAL PROJECT PRESENTATIONS

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