EE640
Multivariable Control Systems (Autumn 2012)
ANNOUNCEMENTS: HW 8 uploaded.
Instructor: Dr.
Debraj Chakraborty
Email: dc [AT]
ee.iitb.ac.in
Office: 231D, EE
Lecture Hours:
Wednesday 3:30-5pm; Thurs: 11:30am-1:00pm (EEG 103)
Website: http://www.ee.iitb.ac.in/~dc/EE640/
TA: Sanand Athalye (asanand [AT] ee.iitb.ac.in) and Chirayu Athalye (chirayu [AT] ee.iitb.ac.in)
·
Introduction to State Variables:
Motivation for State Variables, Implementation of Differential Equations,
Formal Definitions
·
Basic Realization Theory:
Similarity Transformation, Canonical Realizations: Jordan and real canonical
forms, Minimal realization
·
Connections to Transfer Functions:
Characteristic/Minimal Polynomials, matrix exponentials, Markov parameters and
other invariants
·
Observability
·
Stability and time response
·
Controllability
·
Canonical Realizations
·
Duality, Decomposition of
Uncontrollable and Unobservable realizations, Popov test
·
State Feedback
·
Asymptotic Observers: Full and
reduced order
·
Separation Principle and Pole
Placement Theorem
·
Discrete Time Systems
·
MIMO: Controllability,
Observability and Pole Placement, Controller/Observer forms, Controllability
indices
·
Matrix Fraction Descriptions:
Hermit form, Coprimeness, Column/row reduced
polynomial matrices, Minimality and relations to Controllablity and observability, MIMO Realization theory
No Text Book is prescribed. Lecture Notes
will be provided.
Evaluation:
Homework assignments will be distributed regularly. The homework
assignments will carry no points. However, homework assignments submitted on
time will be corrected by the TA. Students are requested to regularly clarify
any questions about the homework
correction (only) with the TA
during his office hour.
There will be one midterm (40%) and one end of semester (60%) final
examination. Examination questions will be based on homework problems.
1. The need for state variables
2. State Variables from Differential Equations
3. Similarity Transform and Canonical Forms
4. The transfer function of a realization
6. Time Response and Stability
9. Uncontrollable and Unobservable Realizations
10. State Feedback
12. Observers + Observer-Controller Configuration
13. Discrete Systems
14. Bezout Identity (SISO)
(overview)
15. MIMO Controllability and Observability
16. MIMO Controller form and Pole placement (Subashish’s Notes)
17. Matrices over polynomials, Hermit form and Coprimeness
18.
MIMO Realizations:
Controller form
Homework Assignments
1.
Homework 1+Homework 2:
Hardcopy to be submitted before August 9th ,
2012.
2.
Homework 3+Homework 4:
Hardcopy to be submitted before August 29th, 2012.
3.
Homework 5: Hardcopy to be submitted before September
5th, 2012.
4.
Homework 6 + Homework 7:
Hardcopy to be submitted before October 11, 2012.
5.
Homework
8: This homework has two parts. The first part is in this pdf. The second part is from Kailath,
Linear Systems exercises. The problem numbers are: 6.2-7,6.2-9,6.3-1b,6.3-2a,6.3-10,6.3-13,6.4-1,6.4-5. A scan of
the relevant pages is available here.