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CMPE-432: Feedback Control Design


Dr Abubakr Muhammad, Assistant Professor of Electrical Engineering

Email: abubakr [at]

Office: Room L310, 3rd Floor, SSE Bldg

Office Hours: Mon, Wed: 11am-12pm. Tue, Thurs: 9:30am-12pm

Hasan Arshad Nasir, Teaching Assistant

Email: hasan.nasir [at]

Office: Room L314, 3rd Floor, SSE Bldg

Course Details

Year: 2009-10

Semester: Spring

Category: Undergrad

Credits: 3

Elective course for electrical & computer 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. Digitization and computer implementation issues. Course will include a design project on digital controller design.



Enforced: CMPE2xx. Signals and Systems OR CMPE2xx. Circuits and Systems-II

Recommended: MATH2xx Linear Algebra-I


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

Text book

The course will be taught from a combination of the following textbooks.

  • Feedback control of dynamical systems by Franklin, Powell and Emami-Naeni, Prentice Hall, 2006.
  • Computer controlled systems by Karl Astrom and Bjorn Witternmark, Prentice Hall, 1997.

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.
  • Modern Control Engineering by Ogata.

Grading Scheme

Homeworks+Quiz : 15%

Design Project: 25%

Midterm: 20%

Final : 40%

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.
  • Separate tutorials on software tools such as SIMULINK and MATLAB real-time workshop can be arranged if there is significant demand for it.

Course Delivery Method

Lectures. Mon, Wed: 9:30am-10:45am. 10-402. SSE Bldg.

Labs. Wed: 9:00am-11:00 am (Week 2, 4, 6). EE-Lab2. SSE Bldg.


Week 1. January 25 Jan 25. Classes begin. Lecture 1. Introduction to concepts of control, feedback, feedforward, uncertainty and robustness;

Lecture 2. Review of Laplace transforms; impulse response; convolution; frequency response;

Week 2. February 1 Feb 1. Add/drop with full refund; Feb 5. Kashmir Day. Lab 1. Lecture 3. Block diagrams; modeling examples: cruise control; car suspension;

Lab 1 Handouts. Simulink Basics. Cruise Control Problem. [Courtesy. University of Michigan control tutorials.]

Homework. HW #1.

Week 3. February 8 Feb 10. Second payment deadline List of projects posted. Lecture 4. Modeling examples (contd.); Firsr order models; linearization of nonlinear models; pendulum; model of internet congestion control (TCP);

Extra Material. Modeling and control of internet congestion. A control theoretic look at internet congestion control.

Lecture 5. Second order models of electrical and mechanical systems; rational transfer functions; poles and zeros; effects of pole positions in the complex plane; second order response; damping and natural frequency;

Week 4. February 15 Hw 1 due. Lecture 6. Dynamic response. Unit impulse, step and ramp responses of first order systems; impulse and unit responses of second order system.

Lecture 7. (Guest Lecturer: Mr. Hasan Arshad Nasir). Second order responses; rise time; peak time; overhoot; effect of zeros on response.

Homework. HW #2.

Week 5. February 22 Feb 27. Eid Milad-un-Nabi Lecture 8. Internal stability and BIBO stability; stability of LTI systems; Routh's criterion for stability; examples on computing Routh's array.

Lecture 9. Examples on Routh's criterion (contd.); Errors in open loop and closed loop control; Robustness against disturbances; Bode's sensitivity function; Watt's problem of disturbance rejection.

Week 6. March 1 March 1. Drop with penalty March 1. Hw#2 due; March 3. Quiz #1. Lecture 10. Bode's sensitivity function; Black's feedback amplifier design problem; comparing open loop and feedback topologies; compensating steady state errors; systems types.

Lecture 11. Problem solving session and Quiz.

Homework. HW #3.

Week 7. March 8 March 8. Project proposals due. Lecture 12. Dynamic errors; PID control

Lab 2 Handouts. Using Real time Workshop in Simulink. Example: Speed control of DC motor. Slides.

Week 8. March 15 Midterm exams March 15. Hw#3 due.

March 17. Midterm exam

Lecture 13. Limitations of P, PI, PD controllers; Implementation issues in PID; integrator anti-windup; digital implementaion of PID controller;

Midterm Exam.

Week 9. March 22 Mid semester break
Week 10. March 29 Lecture 14. Introduction to root locus design; motivational examples; MATLAB commands for drawing root-locus;

Lecture 15. Mathematical derivation of the six rules for drawing a general root-locus; connections with Routh Hurtwitz;

Week 11. April 5 Lecture 16. Examples of design using root locus; effects of additional poles and zeros; introduction to dynamic compensation;

Lecture 17. Lead, lag and notch compensators.

Homework. HW #4.

Week 12. April 12 Lecture 18. Introduction to state space analysis; block diagrams to state-space; canonical forms; state transformations;

Lecture 19. Controllability matrix; control canonical form; relation of poles and zeros to eigendecomposition;

Week 13. April 19 Lecture 20. Dynamic response in SS; full state feedback; derivation of control law; reference tracking;

Lecture 21. Pole placement; Ackermann's formula; feedback gains and controllability; estimators; observability; separation principle; design examples;

Week 14. April 26 Lecture 22. Guest lecture by Dr Raza Samar.
Week 15. May 3
Week 16. May 10 May 10. Last day of classes; May 11-13. Reading and Reviewing period; May 14-21. Final Exams. Project presentations.
Week 17. May 17 May 14-21. Final Exams
Week 18. May 24 May 24-38. Semester break; May 31. Final grades submission .


A major requirement for this course is a project on digital controller design. The project will carry a weight of 25% in the final grade. A list of project ideas will be distributed at the start of the course. You can also suggest your own project idea, with the permission of the instructor. Projects will be done in groups of two. Students are expected to design, simulate and implement a real-time digital controller with analog or digital I/O using either a PC based environment or an embedded DSP/microcontroller/FPGA system.

A tentative list of projects is as follows:


A heater heats a small home made cavity by resistive heating. The heater is controlled by a solid-state relay. Temperatures from R.T. to 600 deg C are achievable. The temperature is continuously monitored with a J type thermocouple attached to the inside of the cavity/oven. The aim is to demonstrate two kinds of controls on the heating: proportional and PID using Labview.

Problem posed by SSE [Physics Lab].


A sample is placed inside the flowing vapour of nitrogen, that has a temperature between 77 K and R.T. A silicon diode is glued to the sample and is used as a cryogenic thermometer. The goal is to keep the temperature constant through a low wattage heater that is wrapped around a chamber holding the sample. This is achieved by two simultaneous methods: controlling the current through the heater and maintaining the level of liquid nitrogen inside the dewar.

Problem posed by [Physics Lab].


A laser diode is driven by a current source. The project involves building the current source that drives the laser whose intensity is held constant. The intensity is measured by a photodetector which provides feedback error for correction.

Problem posed by [Physics Lab].


In this project you will design a control algorithm that drives a tricycle robot. Two wheels of the robot are driven independently by DC motors. Your task is to enable a differential drive for the robot, to enable it to drive, brake and turn in a controlled fashion. You will work on a real robot. Work includes modeling tire friction, turning and drive, DC motor speed control, and tuning a controller for best performance.

Problem posed by. CYPHYNETS at LUMS for research.


In this project you will learn how to apply feedback control methods to robustly stabilize a pendulum in an inverted position. This will be done on a real apparatus. Work includes modeling an inverted pendulum, sensory feedback by an optical encoder, a motorized linear drive, errors and electronic feedback.

Problem posed by. CYPHYNETS and SSE Electrical Engineering for curriculum development.


In this project, you will learn to stabilize a multiple degree of freedom platform based on visual input from a camera. The project will involve both an emphasis on the vision system and in using feedback control for pose correction.

Problem posed by. CYPHYNETS and RICE for research.


In this project, you will learn how chemical wastes are treated for excessive acidic or basic contents before disposal into sewerage. You will model the chemical reaction rates, mixing models, opening and closing of valves and fluid flow in tanks. Your controller will implement an automatic adjustment of pH for a real system in current use.

Problem posed by SSE facilities and engineering department.

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