Ferdowsi university of Mashhad

Department of Electrical Engineering

MC87882    Modern Control Systems

Fall 2008


Course Description :

This course aims to introduce the state space methods in modeling and feedback control of linear time invariant systems. The concepts induced in this framework such as controllability, stabilize ability, observe ability and detect ability is defined and elaborated in this course. Next the system transformation, stability and realization and state controller and observer design will be explained.

Instructor:     Dr. Naghibi Sistani

                        ( mb-naghibi@ferdowsi.um.ac.ir)

Room and Time:    

*                      Saturday    , 16:00 - 17:30 pm , Room  122

*                      Monday    ,  16:00 - 17:30 pm , Room  122


*                      Majid Mazouchi (Majid_Mazouchi@gmail.com)

Required Text:  

*                      Linear system theory and design by chi tsong chen, state university of New York.

*                      Fundamentals of Modern Control, Ali K. Sedigh, Tehran University Publication, 2nd edition, 2004.

Other References:

*          The Essentials of linear state-space systems, J.D. Aplevich, John Wiley & Sons, 2000.

*           Modern control theory, William L. Brogan, 3rd ed.,.Englewood Cliffs, N.J., Prentice Hall, 1991.

*           State Variables for Engineers, P.M.Derusso et.al, John Wiley & Sons, 1998.

*           Modern control engineering, Katsuhiko Ogata, 4th edition, NJ, Prentice Hall, 2001.



*                      Linear Control Systems- Linear Algebra 

Web Page: 

*                      http://www.um.ac.ir/~mb-naghib

Course Mailing List:

*                      mc8788@gmail.com

(To register in the class list, send an email including your complete Name & Student No. to the above address.  )


*                      The CAE supported package MATLAB will be useful.

Exams and Quizzes : 

*                      Will be determined in class or web page .

 (Quizzes and Exams will all be closed book and notes)

Grading Policy:

*                      Quiz 15%;

*                      Assignments + MATLAB Projects  15%;

*                      Mid-term exam  30%;

*                      Final exam 40%.

The tentative course contents are as following.


 Teaching Contents

Week 1

Introduction: Why Feedback, Conceptual components of feedback systems, Physical components of Feedback systems, State definition, and state feedback.

Week 2

LTI System Representation: State space representation, modeling based on physical principles, electrical systems, electromechanical systems, mechanical systems.

Week 3

LTI System Representation: Hydraulic systems, modeling based on Lagrange equation, mathematical linearization, modeling uncertainty.

Week 4

Linear system theory: Linear system properties, solution to linear system D.E., zero-input solution, zero state solution, state transition matrix.

Week 5

Linear system theory: State transition matrix derivation methods: Laplace, Dynamical modes, Caley-Hamilton, Silvester methods, similarity transformations.

Week 6

Linear system theory: System poles and transmission zeros, diagonalization, Jordan forms,  block-Jordan forms.

Week 7

Controllability and Observability: Observability, observability matrix, eigenvector test, controllability, duality, Kalman cannonical  decomposition.

Week 8


Week 9

Realization and Stability:  Controllable and Observable canonical form, realization of MISO systems, realization of SIMO systems, MIMO realizations.

Week 10

Realization and Stability:  Stability definitions, internal stability, BIBO stability, Lyapunov matrix equation.

Week 11

State feedback: State feedback properties, tracking objective, pole placement methods, pole placement for MIMO systems.

Week 12

State feedback: Optimal state feedback LQR, applied gain selection, diturbance rejection, State integral feedback.

Week 13

State Observer: State observer general idea, full state observer, Luengerger Observer.

Week 14

State Observer: Optimal state Observer LQE, Kalman Filter.

Week 15

State Observer: Optimal state Observer LQE, Kalman Filter.

Assignments :

Assignments (pdf)

Projects (pdf)

Exams (pdf)

Assignment 1


Assignment 2


Assignment 3


Assignment 4


Assignment 5


Assignment 6


Assignment 7























Course Documents :

*                      Text Book: linear system theory and design by chi tsong chen, state university of new York

*                      Matlab Primer (.pdf)

*                      Linear Algebra Text Book: Matrix Analysis and Applied Linear Algebra