The University of Texas at
Austin
Deptartment of Electrical
and Computer Engineering
Fall Semester 2012
Some Basic Information
Instructor:
Constantine Caramanis
Email: caramanis AT mail DOT utexas DOT edu
Phone: (512) 4719269
Office: ENS 427
Office Hours: Tuesday 4  5 pm
TA: Xinyang Yi
Email: yixy@utexas.edu
Office: ENS 137
Office Hours: Wednesday, 3:00 pm  5:00 pm.
Lectures:
 Time: Tuesday and Thursday, 5:00  6:30 PM,
 Location: CPE 2.204
Course Overview
The concept of feedback is central in the study of systems and control.
Feedback loops naturally appear in the most basic biological phenomena,
including macroscopic scale (population evolution, extinction, etc.) but
also physiological function, for example, regulation of glucose level in
the blood. In Engineering, feedback has long played an important role in
mechanical, electronic, and now also digital systems. More generally,
systems theory and feedback are central to understanding, analyzing, and
designing systems with interconnected components.
The purpose of this class will be to gain a basic intuition for and
understanding of, linear feedback systems, and also to develop
the mathematical tools to understand the basics of design and analysis
of singleinput singleoutput feedback control systems.
Official Course Description
Analysis of linear automatic
control systems in time and frequency domains; stability analysis;
state variable analysis of continuoustime and discretetime systems;
root locus; Nyquist diagrams; Bode plots; sensitivity;
lead and lag compensation.Important topics we will cover include:
Course Outline (tentative):
What is a dynamical system, control, and feedback?
Concepts from state space design.
Linear algebra review and some new concepts.
Statespace solution to linear systems.
Controllability. Observability.
Review of basics in Laplace transforms.
System diagrams. Significance of pole and zero locations. System stability test.
Basic equations of feedback. Performance measures, such as stability,
disturbance rejection, noise attenuation, and tracking.
ProportionalIntegralDerivative (PID) controller.
Frequency response design. Bode and Nyquist plots, and the Nyquist criterion.
Stability, and stability margins. Robustness.
Time permitting: nonlinear systems, digital control.
There will be a big effort to draw interesting examples
illustrating the basic concepts from a wide area, in order to
give an idea of the applicability and impact ideas from
Systems Theory have had, and are currently continuing to have.
Course Prerequisites
The prerequisites for this class are: Electrical Engineering 438,
as well as Mathematics 340L, with a grade of at least C in each.
Much of what we cover in this class is cumulative. Thus these
prerequisites are strict. Indeed, this class draws heavily on
previous work in: linear algebra, transforms, and differential equations.
In addition to these, part of the assignments will require use of Matlab.
You do not need to have prior exposure to Matlab, but knowledge of basic
programming will be helpful.
General Note: If you are concerned about the prerequisites
or your background, or what the course will cover, please don't
hesitate to contact me by email, or come by
my office hours.
Homework and Exams
In this class there will be roughly weekly
homeworks; there will be three midterm exams in class, and then a final
exam. The weighting will be as follows:
Homework: 15% Midterm Exams: 45% Final Exam: 35%
Class participation: 5%
Policy on Collaboration: Discussion of homework questions is
encouraged. Please be sure to submit your own independent
homework solution. This includes any matlab code required for the assignments.
Late homework assignments will not be accepted.
Text and References
The course will be taught from the book: Feedback Systems: An Introduction for Scientists and Engineers,
by Karl J. Astrom and Richard M. Murray. This book is available (for free) from
Richard Murray's web page.
Please note that this is a different book than what is used
in past years and other sections.
Additional References (Optional)
 Feedback Control of Dynamic Systems by G.F. Franklin, J.D. Powell, and A. EmamiNaeini.
 Control Systems: Principles and Design by M. Gopal.
Other helpful references
 Linear Algebra Done Right by Sheldon Axler.
 Advanced Calculus for Applications by F.B. Hildebrand.
Lecture schedule (tentative)
Lecture No.  Date  Problem Sets  Problem Set Solutions  Assigned Reading  Exam

1  Thu August 30      Chapter 1  

2  Tue September 4      Chapter 1  

3  Thu September 6  problem set 1  solution set 1  Chapter 2  

4  Tue September 11      Chapters 2,3  

5  Thu September 13  problem set 2  solution set 2  Chapters 3,5  

6  Tue September 18      Chapter 5  

7  Thu September 20  problem set 3  solution set 3  Chapter 5  

8  Tue September 25      Chapters 6  

9  Thu September 27  problem set 4  solution set 4  Chapter 6  

10  Tue October 2      Chapter 5  

MIDTERM 1  Thu October 4      Chapter 6  MIDTERM 1

11  Tue October 9      Chapter 6  

12  Thu October 11  problem set 5  solution set 5  Chapter 6 (6.1,6.2)  

13  Tue October 16      Chapter 6 (6.16.3)  

14  Thu October 18  problem set 6  solution set 6  Chapters 6,7 (6.4,7.1)  

15  Tue October 23        

16  Thu October 25  problem set 7  solution set 7    

17  Tue October 30        

MIDTERM 2  Thu November 1      Chapter 7 (7.17.3)  MIDTERM 2

18  Tue November 6      Chapter 7  

19  Thu November 8  problem set 8  solution set 8  Chapter 8 (8.1)  

20  Tue November 13        

21  Thu November 15      Chapter 8 (8.18.3)  

22  Tue November 20  problem set 9    Chapter 8 (8.18.3)  

THANKSGIVING  Thu November 22        

23  Tue November 27      Chapter 8  

MIDTERM 3  Thu November 29      Chapter 9  MIDTERM 3

24  Tue December 4      Chapter 9  

25  Thu December 6  problem set 10    Chapter 9  

Final Exam  Thu December 13 710 pm, ETC 2.136        Final

Homeworks
Homeworks are to be turned in at the beginning of the class when they are due, otherwise are counted as late.
You are allowed to drop two (2) homeworks.
problem set 1. This problem set gets us started on linear systems, stability, and also providing
some linear algebra review.
problem set 2. This problem set continues our work on linear algebra, eigenvalues and eigenvectors and matlab, as well as stability for discrete time and continuous time LTI systems.
problem set 3. This problem set focuses on stability for CT and DT LTI systems, including practice using Jordan Canonical Form.
problem set 4. This problem set is a good review for the midterm.
problem set 5. This problem set focuses on reachable canonical form, and linear state feedback.
problem set 6. This problem set gives more on reachable canonical form, and linear state feedback, and also introduces observability.
problem set 7. This problem set focuses on observability.
problem set 8. This problem set turns our attention to frequency domain: Laplace Transforms and partial fraction expansion.
problem set 9. This problem set builds on the previous one, and focuses on transfer functions, block diagrams, and designing PID controllers.
problem set 10. This problem set focuses on Nyquist plots and Nyquist stability.
Solutions
solution set 1
solution set 2
solution set 3
solution set 4
solution set 5
solution set 6
solution set 7
solution set 8