Linear Control Course

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Dr. Hamid D. Taghirad


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Course Description



Course Name:

 Linear Control Systems

Course No.

 EE - 411


 Dr. Hamid D. Taghirad


 Fall 94

Room and Time:

 Mon. and Wed. 10:30 - 12:00 Room 304

Office Hours:

 Mon. and Wed. :8:00 - 9:00

Course Contents:

This course aims to introduce the basic concept of linear feedback control to the students. As the first and main course in control, special emphasis is on the analysis of feedback control systems, especially on the stability analysis. First modeling of the systems with transfer functions, and block diagrams are introduced, and flow graphs and Mason rule for its simplification is taught. Then the time response characteristics of first and second order system are explained, and the stability analysis is started using Roth-Horowitz criteria. Next static feedback compensation, and stability analysis through Root Locus method is detailed, and then frequency response method and Bode, Nyquist and Nichols charts are elaborated. Finally, Dynamic compensation, and general method of feedback controller design for lead-lag and PID's are explained, based on the frequency response method. The expertise obtained by the students in this course is examined in a thorough and comprehensive design task as a term project.

The tentative course contents are as following.


     Teaching Contents

Week 1

Introduction: Why feedback, conceptual components of feedback systems, physical components of feedback systems, the magic of feedback.

Week 2

Introduction: the characteristics of feedback systems, stability, tracking, disturbance attenuation, noise rejection and insensitivity to model uncertainty.

Week 3

System Representation: Laplace transform, modeling of the systems with transfer functions, block diagrams, rules and simplifications, flow graph, Mason rule.

Week 4

Linear system time response: impulse and step response, first and second order time response characteristics, rise time, settling time, steady state error, overshoot, decay ratio, time and frequency domain relation.

Week 5

Stability analysis: BIBO stability definition, characteristic polynomials, poles, stability condition, Routh - Horwitz stability criteria.

Week 6

Root Locus: Closed-loop pole relation to the loop gain, Root locus graphical method of pole representation, magnitude and angle laws.

Week 7

Root Locus: Rules of root locus representation, gain selection, static feedback design, desired characteristics, time and frequency domain relation.

Week 8


Week 9

Frequency Response:  Bode response, Bode theorem,  the relation between magnitude and phase, cross over frequency, bandwidth, and frequency domain characteristics of second order systems.

Week 10

Frequency Response:  Nyquist diagram, encirclements and number of closed loop poles, Nyquist contour, nyquist stability criteria.

Week 11

Frequency Response:  Ultimate point, stability characteristics,  poles and zeros on imaginary axis, controller design based on nyquist diagram, relation between Bode and Nyquist plot.

Week 12

Frequency Response:  Nichols chart, M circles, sensitivity, and complementary sensitivity transfer functions, loop gain and feedback characteristics in  Nichols chart.

Week 13

Dynamic feedback design: Basic definitions, stability margins, gain and phase margin, bandwith, cross over frequencies, relation between time and frequency response.

Week 14

Dynamic feedback design: P controller design based on stability margin,  PI controller design based on steady state characteristics or disturbance rejection in steady state.

Week 15

Dynamic feedback design: Lag controller design, PD controller and closed loop bandwidth, lead controller, PID and lead-lag controller, comprehensive example.





Modern control Systems, R.C. Dorf and R.H. Bishop, 12th Edition, Prentice Hall, TJ 216.D67 2010.


Automatic Control Systems, 8th Edition,  Farid Golnaraghi and Benjamin C. Kuo, Wiley, TY 213.K8354 2010.


Modern control engineering, Katsuhiko Ogata, 5th ed., NJ, Prentice Hall, TJ 213.O28 2010.


Control engineering: a modern approach, Pierre Bélanger, Saunders College Pub., 1995.


 سيستمهاي کنترل خطي، دکتر علي خاکي صديق، انتشارات دانشگاه پيام نور، 1381


Assignments (pdf) Projects (pdf) Exams (pdf)
Assignment 1 17/07/91 Solution  Project,


Assignment 2 26/07/91 Solution  
Assignment 3 10/08/91 Solution Quizz 1 Quizz 5  Final
Assignment 4 22/08/91 Solution Quizz 2 Quizz 6  
Assignment 5 22/09/91 Solution Quizz 3 Quizz 7  Final scores
Assignment 6 06/10/91 Solution Quizz 4  

Extra Problems:

 Chapter 1: Solved problems, Extra problems

 Chapter 2: Solved problems, Extra problems

 Chapter 3: Solved problems, Extra problems

 Chapter 4: Solved problems, Extra problems

 Chapter 5: Solved problems, Extra problems

 Chapter 6: Solved problems, Extra problems



Course Evaluation:

Dear Students: Please kindly provide me your precious feedback by completing this survey.

Course Documents

 Principle of Argument

 Comprehensive Design Example: Non_min system, mfile.


 Dr. Zames Handout on Bode Theorem and Non-min phase systems


 Mathworks Matlab:

 Control Toolbox.

Selected Papers 


H.D. Taghirad and H. Memarzadeh and M. Younesi, Design and implementation of Electronic system and computer control of a 4DOF Robot D&A 401, in the proceeding of 11th International conference of Electrical Engineering, Tabriz, 2002.


H.D. Taghirad, A. Ghaffari, S.A.A. Moosavian and M. Khalkhali, Design and implementation of the computer control system of casting Robot D&A 101, in the proceeding of 10 International Conference of Mechanical Engineering, Tehran, June 2002.


H.D. Taghirad and M.A. Khosravi, Stability analysis and robust PID design for flexible joint manipulators, Proceedings of the 31st International Symposium on Robotics, Vol 1, pp 144-149, May 2000, Montreal, Canada.


H.D. Taghirad and S. Afshar, Linear identification and PID controller design and implementation on a SCARA robot, Proceedings of 8th International Conference on Electrical Engineering, May 1999, Isfahan.



Description  Contents  References  Assignments  Documents  Software  Papers

Copyright © Dr. Hamid D. Taghirad

K.N. Toosi University of Technology

Last Updated Monday September 14, 2015