The University of Texas at Austin
Deptartment of Electrical and Computer Engineering

EE362K: Introduction to Automatic Control

Fall Semester 2009


Some Basic Information

Instructor: Constantine Caramanis

Email: caramanis AT mail DOT utexas DOT edu
Phone: (512) 471-9269
Office: ENS 426
Office Hours: M: 9:00-10:00 am. Tu: 3:30-4:30 pm.

TA: Praneeth Netrapalli

Email: praneethn@gmail.com
Office: ENS 119
Office Hours: Tue: 4:30-6:30 pm

Lectures:

Time: Monday and Wednesday, 5:00 - 6:30 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)

    Other helpful references

    Lecture schedule (tentative)

    Lecture No.

    Date

    Homework out

    Homework in

    Assigned Reading

    Exam

    1

    Wed Aug 26

    ---

    ---

    Chapter 1

    ---

    2

    Mon Aug 31

    Problem Set #1

    PS #1 Solutions

    Chapter 1

    ---

    3

    Wed Sep 2

    ---

    ---

    Chapter 2

    ---

    4

    Wed Sep 9

    Problem Set #2

    PS #2 Solutions

    Chapters 2,3

    ---

    5

    Mon Sep 14

    ---

    ---

    Chapters 3,4

    ---

    6

    Wed Sep 16

    ---

    ---

    Chapter 4

    ---

    7

    Mon Sep 21

    ---

    ---

    Chapter 4

    ---

    8

    Wed Sep 23

    Problem Set #3

    PS #3 Solutions

    Chapters 4,5

    ---

    9

    Mon Sep 28

    ---

    ---

    Chapter 5

    ---

    10

    Wed Sep 30

    Problem Set #4

    PS #4 Solutions

    Chapter 5

    ---

    11

    Mon Oct 5

    ---

    ---

    Chapter 5

    ---

    MIDTERM 1

    Wed Oct 7

    ---

    ---

    Chapter 5

    MIDTERM 1

    12

    Mon Oct 12

    ---

    ---

    Chapter 6 (6.1,6.2)

    ---

    13

    Wed Oct 14

    Problem Set #5

    PS #5 Solutions

    Chapter 6 (6.1-6.3)

    ---

    14

    Mon Oct 19

    ---

    ---

    Chapters 6,7 (6.4,7.1)

    ---

    15

    Wed Oct 21

    Problem Set #6

    PS #6 Solutions

    Chapter 6,7

    ---

    16

    Mon Oct 26

    ---

    ---

    ---

    ---

    17

    Wed Oct 28

    Problem Set #7 , Diagrams

    ---

    ---

    ---

    18

    Mon Nov 2

    ---

    ---

    Chapter 7 (7.1-7.3)

    ---

    19

    Wed Nov 4

    ---

    ---

    Chapter 7

    ---

    MIDTERM 2

    Mon Nov 9

    ---

    ---

    Chapter 8 (8.1)

    MIDTERM 2

    20

    Wed Nov 11

    Problem Set #8

    ---

    ---

    ---

    21

    Mon Nov 16

    ---

    ---

    Chapter 8 (8.1-8.3)

    ---

    22

    Wed Nov 18

    Problem Set #9

    ---

    Chapter 8 (8.1-8.3)

    ---

    23

    Mon Nov 23

    ---

    ---

    ---

    ---

    MIDTERM 3

    Wed Nov 25

    ---

    ---

    Chapter 8

    MIDTERM 3

    24

    Mon Nov 30

    ---

    ---

    Chapter 9

    ---

    25

    Wed Dec 2

    ---

    ---

    Chapter 9

    ---

    Final Exam

    TBA

    ---

    ---

    ---

    Final

    Homeworks

    Homeworks are to be turned in 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: First concepts of feedback, and linear systems. Review of basic linear algebra.
  • Homework #2: More review of basic linear algebra, examples of discrete time LTI systems, using Matlab.
  • Homework #3: Stability, and stability of nonlinear systems, using both a Lyapunov function approach, as well as linearization.
  • Homework #4: Good review for the first midterm.
  • Homework #5: Reachable canonical form (RCF). Eigenvalue placement (aka root locus). Robust stability.
  • Homework #6: Reachable canonical form (RCF) and Integral Action. Observability, OCF, and state estimation.
  • Problem Set #7 , Diagrams : First problem set for frequency domain. Routh-Hurwitz, Block diagrams, etc.
  • Problem Set #8: Frequency domain, system interconnection, some Bode plots.
  • Problem Set #9: Stability and Nyquist plots.


    Solutions

  • PS #1 Solutions
  • PS #2 Solutions
  • PS #3 Solutions
  • PS #4 Solutions
  • PS #5 Solutions
  • PS #6 Solutions

    Announcements

  • Wed, Aug 26: Welcome to EE362K! Please look to this page for announcement, homeworks, solutions, etc. More information will be posted soon.

    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.