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EE-361: Feedback Control Systems


Dr. Abubakr Muhammad, Assistant Professor of Electrical Engineering

Email: abubakr [at]

Office: Room 9-311A, 3rd Floor, SSE Bldg

Mr. Zeeshan Shareef, Teaching fellow

Email: zeeshan.sharif [at]

Office: Room 9-309, 3rd Floor, SSE Bldg

Mr. Talha Manzoor, Teaching Assistant

Email: talha.manzoor [at]

Office: Room 9-309, 3rd Floor, SSE Bldg

Course Details

Year: 2010-11

Semester: Spring

Category: Undergrad

Credits: 4

Core course for electrical engineering majors

Course Website:

Course Description

Design of linear feedback control systems for command-following, disturbance rejection, stability, and dynamic response specifications. Root-locus and frequency response design (Bode) techniques. Nyquist stability criterion. Design of dynamic compensators. State-space methods. Digitization and computer implementation issues. Integrated laboratory exercises on practical applications of control.


The students should learn

  • Use of control for achieving desired behavior in unstable and uncertain systems.
  • Advantages and disadvantages of feedback in a system.
  • Open- and closed-loop control and their respective merits/demerits.
  • Stability and its relationship with feedback.
  • Techniques of linear time-invariant (LTI) control system design.
  • Pervasiveness of feedback and control in science & engineering.
  • Systems engineering tools for solving complex problems.

Learning Outcomes

The students will be able to:

  • Model physical systems, sensors and actuators in various settings using the language of signals and systems.
  • Identify state, measurement and control in a given problem.
  • Design controllers for linear models of systems using MATLAB and SIMULINK.
  • Implement digital controllers for various mechanical and electrical systems.
  • Predict and test control system performance.



Enforced: EE-210. Signals and Systems

Recommended: MATH2xx Linear Algebra-I


Laplace transform, differential equations, programming in MATLAB and C.

Text book

The course will be taught from the following textbook.

  • Feedback control of dynamical systems by Franklin, Powell and Emami-Naeni, Prentice Hall, 2006.

Other important references include

  • Feedback Systems: An Introduction for Scientists and Engineers by Karl Astrom and Richard Murray, Princeton University Press, 2008.
  • Signals and Systems by Alan V. Oppenheim, Alan S. Willsky with S. Hamid, 2nd edition, Prentice Hall, 1997.
  • Computer controlled systems by Karl Astrom and Bjorn Witternmark, Prentice Hall, 1997.

Grading Scheme

Homeworks+Quiz : 15%

Lab Performance: 20%

Midterm: 30%

Final : 35%

Policies and Guidelines

  • Quizzes will be announced. There will be no makeup quiz.
  • Homework will be due at the beginning of the class on the due date. Late homework will not be accepted.
  • You are allowed to collaborate on homework. However, copying solutions is absolutely not permitted. Offenders will be reported for disciplinary action as per university rules.
  • Any appeals on grading of homeworks, quiz or midterm scores must be resolved within one week of the return of graded material.
  • Attendance is in lectures and tutorials strongly recommended but not mandatory. However, you are responsible for catching the announcements made in the class.
  • Attendance in lab exercises is compulsory.
  • Many of the homeworks will include MATLAB based computer exercise. Some proficiency in programming numerical algorithms is essential for both the homework and project.

Course Delivery Method

Lectures. Tues, Thurs: 12:00pm-1:15pm. SC-1.

Labs. Mon, Wed: 9:30:00am-12:00 pm, 2pm-4pm. EE-Lab4. 5th Floor. SSE Bldg.


Week 1. January 24 Jan 25. Classes begin. Lecture 1. Introduction to concepts of control, feedback, feedforward, uncertainty and robustness; Franklin Ch1; Astrom Ch.1;
Week 2. January 31 Feb 1. Add/drop with full refund; Feb 5. Kashmir Day. Lecture 2. advantages of feedback control; process, plant, sensor, actuator, control and disturbance; cruise control example;

Lecture 3. Dynamical models; cruise control example revisited; introduction to On-Off and PID controllers

Lecture 4. Review of Laplace transforms; impulse response; convolution;

Lab 1. Introduction to SIMULINK environment and real-time data acquisition.

Franklin Ch 2, Appendix A; Astrom Ch 1;
Week 3. February 7 Feb 10. Second payment deadline Lecture 5. Block diagrams; modeling examples; electromechanical systems;

Lecture 6. Uses of feedback; robustness against parameter variation; creating inversion via feedback;

Lab 2. Modeling systems and control in SIMULINK. Cruise control and water tank systems.

Franklin Ch 2; Oppenheim Sec 11.2;
Week 4. February 14 Feb 16. Eid Milad-un-Nabi Lecture 7. Second order models of electrical and mechanical systems; rational transfer functions; poles and zeros;

Lecture 8. Dynamic response. Unit impulse, step and ramp responses of first order systems; impulse and unit responses of second order system; damping ratio, natural frequency, Q-factor of 2nd order systems; effects of pole positions in the complex plane;

Lecture 9. Modeling examples; Atomic Force Microscopy (AFM); voltage clamp in neuroscience; internet congestion control (TCP).

Franklin Ch 3; Astrom Ch 2,3;

Extras. Hodgkin Huxley Model; Slides on AFM.

Week 5. February 21

Lecture 10. Control specifications via rise time, overshoots, settling time; Meeting control specifications via a second order response;

Lecture 11. Internal stability and BIBO stability; stability of LTI systems; Effects of Zeros on response; Pole-Zero cancellation.

Lab 3. Position control of a DC motor.

Franklin Ch 3;
Week 6. February 28 March 1. Drop with penalty

Lecture 12. Routh's criterion for stability; examples on computing Routh's array. Examples on using Routh's criterion;

Lecture 13. Errors in open loop and closed loop control; Robustness against disturbances; Bode's sensitivity function; Watt's problem of disturbance rejection.

Lab 3 (contd.) Position control of a DC motor.

Franklin Ch3, 4;

Extras. Proof of Routh-Hurtwitz

Week 7. March 7 Lecture 14. Bode's sensitivity function; Black's feedback amplifier design problem; comparing open loop and feedback topologies;

Lecture 15 compensating steady state errors; systems types.

Lab 4. Digital control of an HVAC-like thermal system.

Franklin Ch4.
Week 8. March 14 Midterm exams

Lecture 16. Dynamic errors; PID control; Limitations of P, PI, PD controllers; Introduction to root locus design;

Lecture 17. Motivational examples; MATLAB commands for drawing root-locus; general properties of root loci;

Midterm Exam.

Franklin Ch4, 5; Astrom 10.1;
Week 9. March 21 Mid semester break
Week 10. March 28 Lecture 18. Examples of design using root locus; effects of additional poles and zeros;

Lecture 19. introduction to dynamic compensation;

Lab 5. Anti windup in controller design.

Franklin Ch 5;
Week 11. April 4 Lecture 20. Examples of root-locus design;

Lecture 21. Lead, lag and notch compensators using root locus.

Lab 6. Digital speed control of DC motor.

Franklin Ch 5;
Week 12. April 11 Lecture 22. Frequency domain design methods; Frequency response of a control system; bandwidth; Overshoots

Lecture 23. Frequency response (contd.); Second order systems; Bode plots; Neutral stability

Lab 7. Discrete-time controller implementation.

Franklin Ch 6;
Week 13. April 18 Lecture 24. Cauchy's residue theorem; Encirclement property

Lecture 25. Argument principle; Nyquist plots; Examples

Lab 8. Practical system identification.

Franklin Ch 6;
Week 14. April 25 Lecture 26. Gain and Phase Margins; Frequency based control design basics

Lecture 27. Minimum phase systems; Bode's gain-phase relationship; PD control re-interpreted;

Lab 9. Inverted pendulum stabilization using state space methods.

Franklin Ch 6;
Week 15. May 2 Lecture 28. PD control by lead compensation; design examples

Lecture 29. PI control; lag compensation; lag-lead compensation; PID control

Lab 10. Case Study on Control System Design.

Franklin Ch 6;
Week 16. May 9 May 9. Last day of classes; May 10-11. Reading and Reviewing period; May 12-18. Final Exams.
Week 17. May 16 May 14-21. Final Exams
Week 18. May 23 May 19-27. Semester break; May 31. Final grades submission
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