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)

Syllabus

·       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

Text Book

No Text Book is prescribed. Lecture Notes will be provided.

Reference Books

  1. T. Kailath, “Linear Systems”, Prentice-Hall, New Jersey, 1980, xxi+682 pages (2 copies in IITB Library study room)
  2. C.T. Chen, “Linear System theory and design”, Holt, Rinehart and Winston, New York, 1984, xxii,662 p. (2 copies in IITB library)

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.

Lecture Notes

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

5.      Observability

6.      Time Response and Stability

7.      Controllability

8.      Canonical Realizations

9.      Uncontrollable and Unobservable Realizations

10.   State Feedback

11.   Stabilizable Systems

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.