The University of Texas at
Austin
Deptartment of Electrical
and Computer Engineering
Spring Semester 2007
Some Basic Information
Instructor:
Constantine Caramanis
Email: cmcaram AT ece DOT utexas DOT edu
Phone: (512) 471-9269
Office: ENS 426
Office Hours: W: 2:30 pm - 3:30 pm.
Open Question/Answer Session: M: 5:00 - 7:00 pm, in ENS 537 (tentative)
TA: Amirshahed Mehrtash
Email: mehrtash AT mail DOT utexas DOT edu
Phone:
Office: ENS 142A
Office Hours: Tues: 5-6:30 pm, Fri: 2-3:30 pm.
Problem Solving Session: Thurs: 5-6:30 pm, in RLM 7.124.
Lectures:
- Time: Monday and Wednesday, 3:30 - 5:00 PM,
- Location: BUR 224
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?
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) controler.
Root locus design.
Frequency reponse design. Bode and Nyquist plots, and the Nyquist criterion.
Stability, and stability margins. Robustness.
Concepts from state space design.
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. 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 Control of Dynamic Systems,
5th edition, by G.F. Franklin, J.D. Powell, and A. Emami-Naeini, Prentice Hall, 2006.
Unless otherwise noted, reading assignments and homework assignments refer to this
book.
Lecture schedule (tentative)
Lecture No. | Date | Homework out | Homework in | Assigned Reading | Exam
|
1 | Wed Jan 17 | --- | --- |
Chapter 1.1-1.4 | ---
|
2 | Mon Jan 22 | --- | --- | Chapter 1.1-1.4 | ---
|
3 | Wed Jan 24 | #1. | --- | Chapter 2.1-2.2 | ---
|
4 | Mon Jan 29 | --- | --- | Chapter 2.3, 3.1 | ---
|
5 | Wed Jan 31 | --- | #1. | Chapter 3.1,3.2 | ---
|
6 | Mon Feb 5 | --- | --- | Chapter 3.1-3.3 | ---
|
7 | Wed Feb 7 | #2. | --- | Chapter 3.4-3.7 | ---
|
8 | Mon Feb 12 | --- | --- | --- | ---
|
9 | Wed Feb 14 | #3. | #2. | Chapter 4.1-4.2 | ---
|
MIDTERM #1 | Mon Feb 19 | --- | --- | --- | MIDTERM #1
|
11 | Wed Feb 21 | --- | #3. | Chapter 4.2-4.3 | ---
|
12 | Mon Feb 26 | #4. | --- | Chapter 5 | ---
|
13 | Wed Feb 28 | --- | --- | Chapter 5 | ---
|
14 | Mon Mar 5 | --- | --- | Chapter 6 | ---
|
15 | Wed Mar 7 | --- | #4. | Chapter 6 | ---
|
SPRING BR | Mon Mar 12 | --- | --- | --- | ---
|
SPRING BR | Wed Mar 14 | --- | --- | --- | ---
|
16 | Mon Mar 19 | #5. | --- | Chapter 6 | ---
|
--- | Wed Mar 21 | --- | --- | --- | ---
|
MIDTERM #2 | Mon Mar 26 | --- | --- | --- | MIDTERM #2
|
19 | Wed Mar 28 | #6. | #5. | Chapter 7 | ---
|
20 | Mon Apr 2 | --- | --- | Chapter 7 | ---
|
21 | Wed Apr 4 | #7. | #6. | Chapter 7 | ---
|
22 | Mon Apr 9 | --- | --- | Chapter 7 | ---
|
23 | Wed Apr 11 | #8. | #7. | Chapter 7 | ---
|
25 | Mon Apr 16 | --- | --- | --- | ---
|
MIDTERM #3 | Wed Apr 18 | --- | #8. | --- | MIDTERM #3
|
26 | Mon Apr 23 | --- | --- | --- | ---
|
27 | Wed Apr 25 | #9. | --- | --- | ---
|
28 | Mon Apr 30 | --- | --- | --- | ---
|
29 | Wed May 2 | --- | --- | --- | ---
|
Final Exam | Friday May 11: 7-10 pm | --- | --- | --- | Final
|
Homeworks
Homeworks are at the beginning of the class when they are due.
Early assignments are fine, but no late
homeworks will be accepted. You are allowed to drop one (1) homework.
Homework #1:
Basic concepts of feedback, and linear systems.
Homework #2: Laplace
transform, inverse Laplace transform, transfer functions, block diagrams.
Homework #3: A good set
of review problems to wrap up chapter 3, and prepare for the first midterm.
Homework #4: This problem
set focuses on the concepts introduced in Chapter 4 of the text.
Homework #5: This problem
set focuses on the concepts introduced in Chapter 6 of the text, in addition to a problem on the small gain theorem.
Homework #6: This problem
set focuses on the use of the small gain theorem. Also, there is one problem on state-space representation of
a third-order system. Use the matrix exponential function in Matlab for the final part where you are asked to plot the
autonomous trajectories of the system.
Homework #7: This short problem
set focuses time domain solution to linear systems, including the matrix exponential.
Homework #8: This problem set focuses
on the state space material we have been covering, including linear algebra background, the matrix exponential,
stability, and reachability. Also, there is a review problem to remind you of the small gain theorem which will
be on the third (and final!) midterm.
Homework #9: This problem set focuses
on reachability, observability, and state space feedback.
Solutions
(Have been taken off-line)
Solution Set #1
Solution Set #2
Solution Set #3
Solution Set #4
Solution Set #5
Solution Set #6
Solution Set #7
Solution Set #8
Solution Set #9
Announcements
Sat. April 14: The re-do for the second midterm will now be due on Friday in my office by 5 pm (slip under the
door if I am not there). You are welcome to hand it in on Wednesday in class. Problem set 8 is still due on Wednesday
in class.
Sat. April 14: The final Midterm (#3) will be on Wednesday, April 18th. There will be a review session
on Tuesday the 17th at 6 pm. The location will be announced in class on Monday. For the test you may bring
in 2+2+2 faces of hand-written notes. There will be NO calculators allowed for the midterm.
Wed. April 4: Office hours today are canceled.
Tue. March 27: The Final Exam schedule is now available. The final for this class will be on Friday, May 11,
from 7-10 pm in CPE 2.216.
Fri. March 23: On Thursday Amirshahed (the TA) held a review. He covered again the basics of the Nyquist plot,
and also he went over parts of three problems. For the problems and the solutions,
click here. One word of warning:
these problems cover things that we did not emphasize in class. When reviewing for the test, make sure to focus
on things that were emphasize in the lecture, and in the problem sets.
Wed. Jan 31: Due to some technical difficulties, the annimation has not worked
out as promised. Instead I am posting simply the (non-animated...) notes for the class.
I have written up notes in the context of Monday's class as well, so that it will
tie everything together. You can download the pdf of the lecture notes
here.
Mon. Jan 29: The class for this Wednesday will be recorded, and posted to the web.
It will remain on line for at least one week. Your feedback as to the usefulness of
posting the class recording will be greatly appreciated.
Mon. Jan 29: There were a few typos/mistakes on problem set 1. The corrected
is now posted to the web page.
Mon. Jan 22: Welcome to 2006_7/ee362k...take 2!
Mon. Jan 15: Welcome to 2006_7/ee362k. I have posted a tentative lecture, homework, and exam
schedule above. If you have any questions about the class, please feel free to e-mail me, or to
drop by my office (ENS 426) if you prefer.
Questions, Comments, Answers
If you have questions/comments, I encourage you to e-mail me.
I will post questions/comments/answers that might be useful to the entire
class here.