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 |