ELEE 4220/6220: Feedback Controls


This course will be offered in Spring 2018.


Course Description
The analysis and design of continuous and time-discrete linear feedback control systems with a focus on frequency domain models. Simulation using Scilab/xcos to design controllers for steady-state error reduction and optimal transient response to varied inputs.
Prerequisites: ENGR/ELEE 4210 (Linear Systems) or Permission of Department.



Feedback controls are ubiquitous and fundamental to modern engineering. Whether a component in a simple water tank or the sophisticated control systems in aeronautics and robotics, feedback controls make technology safer, faster, more reliable, if not possible in the first place. Feedback systems can also be found in unexpected areas, for example in biology or economics. In this class, we will understand what feedback controls are, and we will learn how to master feedback controls in three major steps:

  1. We will learn how to describe and characterize the process to be controlled
  2. We will learn how to determine the performance of feedback systems in terms of stability and dynamic response
  3. We will learn how to design feedback controls to meet desired performance criteria.
Linear systems and feedback controls make extensive use of mathematical models. However, in this class, we will always stay close to practical applications. The class is strongly based on hands-on projects where the theoretical concepts can be tested in practice.

Consistent with this philosophy, there will be quizzes and a semester project. The quizzes can be regarded as short homeworks with a theoretical emphasis. These will allow you to strengthen your understanding of the theory and to assess your preparation for the exams. The semester project allows you to build an actual feedback control system. All aspects are covered, from design of the process (or plant) and the sensors to the theory of the necessary control system to the controller implementation. No specific path to the solution is prescribed, and you have wide design flexibility.


This course syllabus is a general plan for the course. Deviations may be necessary and will be announced.

Block Topic
1 Introduction to feedback control systems
Feedback control examples
2 Formal description of feedback systems
Block diagrams and signal flow graphs
3 Description of feedback systems in the Laplace domain
4 Numerical simulation of control systems with XCos
5 Performance and response of feedback systems
6 Stability criteria
7 Stability criteria cont'd
8 The root locus design method
9 Frequency-domain design methods
Bode diagrams and Nyquist design
10 State-variable description of feedback systems
11 Time-discrete linear systems
12 The z transform
13 Stability of time-discrete systems
14 Design of time-discrete feedback systems
15 Presentation of the semester projects


Suggested reading: Linear Feedback Controls -- The Essentials (M. Haidekker, Elsevier 2013),
Link to publisher's web site
This book is available through the UGA library! The link has changed and goes through a proxy, which means that I can't provide a simple link here. However, access is straightforward:

Recommended additional textbooks:


All student computers in Driftmier have Scilab/xcos installed.

Xcos/Scilab is Free Software. You may download and install a copy free of charge and with the right to access the source code. I encourage you to download your own copy and install it on your laptops or home computers.


The grade will be based about equally on short quizzes, the homeworks, the midterm exam, the final exam, and the semester project. You will receive score points based on the fill-the-bucket principle, i.e. for each homework assignment and for each test, you accrue score points. Your final grade will be determined from the score you achieved relative to the maximum score achievable. For a rough idea, you receive a maximum of 20-40 points per quiz, 100 points per exam, and 150 points for the semester project, resulting in a maximum score of around 500 points.

We use a fixed grading system. There will be no adjustment based on the overall class performance. To get a passing grade, you will have to achieve an overall score of at least 45%. The following table shows the percentage of your score you need to reach for a specific grade:

GradeMinimum percentage GradeMinimum percentage GradeMinimum percentage
A95% A-90%   
B+85% B80% B-75%
C+70% C65% C-60%
D+50% D45%   



Quiz assignments

NOTE: Quizzes must be turned in electroncially via eLC dropbox! Two points will be deduced if you want a non-eLC turnin to be considered (e.g., missed deadline or sent via e-mail)

For the self-grading policy, use this document.

Quiz No. Topic Date assigned Date due Score due
Quiz 1        

(*) There seems to be very little demand for the blog -- let me know if you want me to resume offering blog/discussion pages.

Semester project:

  1. Build the process and describe the process mathematically (i.e., determine its transfer function and step response)
  2. Design and build a suitable controller. Describe the closed-loop feedback system mathematically.
  3. Optimize the controller according to your performance criteria
  4. Present your design and demonstrate a working system in front of the class and invited faculty, staff, and students. For large class sizes, the presentation takes the form of a short video.

Grading Milestone Due Date
1: Team nomination  

Grading Milestone #1 requires paper turnin! Create a formal cover page for your project report. The cover page should contain the names of all team members and the project you decide to pursue. Turn in a paper copy in class.

Team presentations are a short video approximately between 5 and 7 minutes long. The video should capture the following topics:

Teamwork and presentations are peer-evaluated. You also vote for two awards. Use this sheet for scoring and award votes. Fill out this sheet and submit it through eLC for up to 15 points toward your score. Items 6 through 10 on this sheet are for your information only. These are awards that are based on measurable and demonstrated performance.


Here are some interesting links, most of them to Free software (with a capital F):

ABET information

Overall Course Contribution to Program Outcomes:

a) An ability to apply knowledge of mathematics, science, and engineering. Extensive  
b) An ability to design and conduct experiments, as well as to analyze and interpret data. Moderate
c) An ability to design a system, component, or process to meet desired needs. Extensive
d) An ability to function on multi-disciplinary teams. Marginal
e) An ability to identify, formulate, and solve engineering problems. Extensive
f) An understanding of professional and ethical responsibility. Not at all
g) An ability to communicate effectively. Marginal
h) the broad education necessary to understand the impact of engineering
Not at all
i) a recognition of the need for, and an ability to engage in life-long learning Marginal
j) a knowledge of contemporary issues Moderate
k) an ability to use the techniques, skills, and modern engineering tools
necessary for engineering practice

Course Learning Objectives Matrix

Course Learning Objectives Relationship to ABET criteria
Upon succesful completion of this course, the student will be able to The objective relates to the ABET criteria
extensively:3, moderately:2, marginally:1, not at all:0
Prepare a model of the system (block diagram, quantitative description) a:3, b:0, c:1, d:0, e:2, f:0, g:0, h:0, i:0, j:1, k:2
Quantify stability of a system using various criteria a:3, b:0, c:2, d:0, e:2, f:0, g:0, h:0, i:0, j:1, k:2
Design a feedback control system to meet given criteria a:3, b:0, c:3, d:0, e:2, f:0, g:0, h:0, i:1, j:1, k:3
Simulate a feedback control system in software a:3, b:2, c:2, d:1, e:3, f:0, g:1, h:0, i:2, j:2, k:3
Develop a lab prototype of a feedback control system in a team a:3, b:2, c:3, d:2, e:3, f:0, g:2, h:0, i:1, j:2, k:3