Date |
Topics to be covered |
September 20
(Week
1)
|
INTRODUCTION
 |
Motivation |
 |
Definition
of Robust Control |
 |
Classification
of
Robust Control Systems |
 | Introduction
to parametric uncertain systems |
|
September
27
(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
|
|
ROBUST
STABILITY ANALYSIS
 |
Pole
Spread and gridding |
ROBUST
STABILITY ANALYSIS
 | Boundary
crossing theorem" |
MATHEMATICA TUTORIAL |
October
4
(Week
3)
|
ROBUST
STABILITY ANALYSIS
 |
Algebraic
tests
 |
Routh
table |
 |
Hurwitz
determinants |
 |
Bialas
theorem |
|
|
October 11
(Week
4)
|
FREQUENCY
RESPONSE of POLYNOMIALS with PARAMETRIC UNCERTAINTIES
 |
Mikhailov
Theorem |
 | Hermite-Biehler
Theorem |
 | Value
Set Concept |
 |
Zero Exclusion Theorem |
 |
Singular Frequency |
|
October 18
(Week
5)
|
CLASSIFICATION
OF PARAMETRIC UNCERTAIN POLYNOMIALS and TEST SETS
 | Classification
 |
Interval
polynomials |
 |
Affine-linear
polynomials |
 |
Multilinear
polynomials |
 |
Polynomials
with polynomial coefficients |
|
 | Test
Sets |
 | Kharitonov
theorem |
|
October
25
(Week
6)
|
TEST SETS
(CONT.)
 | The
concept of concervatism |
 | Edge
theorem |
|
November
1
(Week
7)
|
TEST SETS
(CONT.)
 | Test
sets for multilinear polynomials |
 | Jacobi
conditions for uncertain parameters |
|
November
8
(Week
8)
|
NO CLASS! |
November
15
(Week
9)
|
MIDTERM
EXAM |
November
22
(Week 10)
|
TEST SETS
(CONT.)
 | Mapping
Theorem |
 | Test
sets for polynomials with polynomial uncertainties. |
|
November
29
(Week
11)
|
CONSTRUCTION OF VALUE SETS
 |
Addition and multiplication of value
sets |
 |
Tree structured decomposition |
|
December
6
(Week
12)
|
STABILITY
RADIUS
 | Tsypkin - Polyak Loci
 | Interval polynomials |
 | Affine linear polynomials |
 | Largest hypersphere in the
parameter space |
|
|
December
13
(Week
13)
|
ROBUSTNESS ANALYSIS of
FEEDBACK SYSTEMS
 | Box Theorem |
 | Positive interval plants |
 | Robustness with respect to
nonlinearities |
|
December
20
(Week
14)
|
STABILIZING
PID CONTROLLER
DESIGN
 |
Stabilizing
P
Controllers |
 | Stabilizing
PI
Controllers |
 | Stabilizing
PID
Controllers |
|
December
27
(Week
15)
|
FINAL PROJECT PRESENTATIONS |