About the Course

Course Code: KOM 501E
Term: 2023 Fall
Lecturer: Prof. Dr. M. Turan Söylemez
Control and Automation Eng. Dept.
Room Num: 4207, Tel: 212 - 285 35 70
Course Place - Hours: Z4 - Wednesday (09:00 - 11:59)
Course Books: 1) "Robust Control: Systems with Uncertain Physical Parameters", J Ackermann, 1993, Springer-Verlag.
"Robust Control: The Parameter Space Approach", 2nd ed, J Ackermann, 2002, Springer-Verlag, ISBN:1-85233-514-9.
2) "New Tools for Robustness of Linear Systems", B R Barmish, 1994, Macmillan
3) "Robust Control: The Parametric Approach", S P Bhattacharyya, H Chapellat and L H Keel, 1995, Prentice-Hall
4) "Linear Control Theory: Structure, Robustness and Optimization", 2009, S. P. Bhattacharyya, A Datta, L H Keel, CRC Press, ISBN: 978-0-8493-4063-5
5) "Pole Assignment for Uncertain Systems", M. T. Söylemez, 1999, RSP Press
6) "Robust Control of Uncertain Dynamic Systems", R K Yedavalli, 2014, Springer
Grading Policy: 15% Midterm Exam
35% Homework
20% Final Project
30% Final Exam
Final Exam Enterance Condition: Weighted average of the first two Homework Assignments and the midterm exam must be at least 25.
Home Page: http://web.itu.edu.tr/soylemezm/kom501e

Course Syllabus

Date Topics to be covered
October 4
(Week 1)
INTRODUCTION

  • Motivation
  • Definition of Robust Control
  • Classification of Robust Control Systems
  • Introduction to parametric uncertain systems
  • October 11
    (Week 2)
    MODELING OF PARAMETRIC UNCERTAIN SYSTEMS

  • Examples for modeling systems with parameter uncertainty
  • Introduction to the notation and general concepts
  • Symbolic algebra and parametric uncertain systems
  • Generalization of several control concepts to parametric uncertain systems
    • Stability
    • Controllability & Observability
  • October 18
    (Week 3)
    ROBUST STABILITY ANALYSIS

  • Pole Spread and gridding
  • Boundary crossing theorem
  • Algebraic tests
  • Routh table
    MATHEMATICA TUTORIAL
  • October 25
    (Week 4)
    ROBUST STABILITY ANALYSIS

  • Hurwitz determinants
  • Bialas theorem
  • November 1
    (Week 5)
    FREQUENCY RESPONSE of POLYNOMIALS with PARAMETRIC UNCERTAINTIES

  • Mikhailov Theorem
  • Hermite-Biehler Theorem
  • Value Set Concept
  • Zero Exclusion Theorem
  • Singular Frequency
  • November 8
    (Week 6)
    CLASSIFICATION OF PARAMETRIC UNCERTAIN POLYNOMIALS and TEST SETS

  • Classification
  • Interval polynomials
  • Affine-linear polynomials
  • Multilinear polynomials
  • Polynomials with polynomial coefficients
  • Test Sets
  • Kharitonov theorem
  • November 15
    (Week 7)
    TEST SETS (CONT.)

  • The concept of conservatism
  • Edge theorem
  • November 22
    (Week 8)
    MIDTERM EXAM
    November 29
    (Week 9)
    TEST SETS (CONT.)

  • Test sets for multilinear polynomials
  • Jacobi conditions for uncertain parameters
  • Mapping Theorem
  • Test sets for polynomials with polynomial uncertainties.
  • December 6
    (Week 10)
    CONSTRUCTION OF VALUE SETS

  • Addition and multiplication of value sets
  • Tree structured decomposition
  • December 13
    (Week 11)
    STABILITY RADIUS

  • Tsypkin - Polyak Loci
  • Interval polynomials
  • Affine linear polynomials
  • Largest hypersphere in the parameter space
  • December 20
    (Week 12)
    ROBUSTNESS ANALYSIS of FEEDBACK SYSTEMS

  • Box Theorem
  • Positive interval plants
  • Robustness with respect to nonlinearities
  • December 27
    (Week 13)
    STABILIZING PID CONTROLLER DESIGN

  • Stabilizing P Controllers
  • Stabilizing PI Controllers
  • Stabilizing PID Controllers
  • January 3
    (Week 14)
    FINAL PROJECT PRESENTATIONS