The University of Texas at
Austin
Deptartment of Electrical
and Computer Engineering
Spring Semester 2012
Some Basic Information
Instructor:
Constantine Caramanis
Email: caramanis AT mail DOT utexas DOT edu
Phone: (512) 471-9269
Office: ENS 427
Office Hours: Monday 4:30 pm and Thursday 11 am.
TA: Aparna Sripada
Email: aparna.sripada@utexas.edu
Office: ENS 137
Office Hours: Tuesday, 11:30 am - 1:30 pm.
Lectures:
- Time: Monday and Wednesday, 3:00 - 4:30 PM,
- Location: ENS 116
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 single-input single-output feedback control systems.
Official Course Description
Analysis of linear automatic
control systems in time and frequency domains; stability analysis;
state variable analysis of continuous-time and discrete-time 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.
State-space 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.
Proportional-Integral-Derivative (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 e-mail, or come by
my office hours.
Homework and Exams
In this class there will be roughly weekly
homeworks; there will be three mid-term 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. Emami-Naeini.
- 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 | Wed January 18 | --- | --- | Chapter 1 | ---
|
2 | Mon January 23 | --- | --- | Chapter 1 | ---
|
3 | Wed January 25 | Problem Set #1 | Solution Set #1 | Chapter 2 | ---
|
4 | Mon January 30 | --- | --- | Chapters 2,3 | ---
|
5 | Wed February 1 | Problem Set #2 | Solution Set #2 | Chapters 3,5 | ---
|
6 | Mon February 6 | --- | --- | Chapter 5 | ---
|
7 | Wed February 8 | Problem Set #3 | --- | Chapter 5 | ---
|
8 | Mon February 13 | --- | --- | Chapters 5 | ---
|
9 | Wed February 15 | --- | --- | Chapter 5 | ---
|
MIDTERM 1 | Mon February 20 | --- | --- | Chapter 5 | MIDTERM 1
|
10 | Wed February 22 | --- | --- | Chapter 6 | ---
|
11 | Mon February 27 | --- | --- | Chapter 6 | ---
|
12 | Wed February 29 | --- | --- | Chapter 6 (6.1,6.2) | ---
|
13 | Mon March 5 | --- | --- | Chapter 6 (6.1-6.3) | ---
|
14 | Wed March 7 | --- | --- | Chapters 6,7 (6.4,7.1) | ---
|
SPRING BREAK | Mon March 12 | --- | --- | --- | ---
|
SPRING BREAK | Wed March 14 | --- | --- | --- | ---
|
15 | Mon March 19 | --- | --- | --- | ---
|
16 | Wed March 21 | --- | --- | Chapter 7 (7.1-7.3) | ---
|
17 | Mon March 26 | --- | --- | Chapter 7 | ---
|
MIDTERM 2 | Wed March 28 | --- | --- | Chapter 8 (8.1) | MIDTERM 2
|
19 | Mon April 2 | --- | --- | --- | ---
|
20 | Wed April 4 | --- | --- | Chapter 8 (8.1-8.3) | ---
|
21 | Mon April 9 | --- | --- | Chapter 8 (8.1-8.3) | ---
|
22 | Wed April 11 | --- | --- | --- | ---
|
23 | Mon April 16 | --- | --- | Chapter 8 | MIDTERM 3
|
24 | Wed April 18 | --- | --- | Chapter 9 | ---
|
MIDTERM 3 | Mon April 23 | --- | --- | Chapter 9 | ---
|
25 | Wed April 25 | --- | --- | Chapter 9 | ---
|
26 | Mon April 30 | --- | --- | Chapter 9 | ---
|
27 | Wed May 2 | --- | --- | Chapter 9 | ---
|
Final Exam | TBA | --- | --- | --- | 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 focuses on some basics of linear algebra,
and also gets us started looking at trajectories of continuous time and discrete time systems in Matlab.
Problem Set #2. This problem set continues the focus on linear algebra and on linear time systems and stability.
Problem Set #3. This problem set brings in Jordan Canonical Form.
Solutions
Solution Set #1
Solution Set #2