ECE 415 Control System Theory and Design

Synthesis of feedback control systems to meet design specifications, including sensitivity; multivariable systems; introduction to systems with random inputs; state variable techniques; and nonlinear systems.
This is a fundamental graduate-level course on the modern theory of control of dynamical systems, building upon a first-level course in control such as ECE 386. State space techniques are emphasized in the analysis of dynamical systems and in the synthesis of control laws meeting given design specifications. The course also develops some mathematical tools required for further study in control and communication. To follow the course, some familiarity with vector spaces and matrix algebra is strongly recommended. Some of this material will, however, be reviewed during the course in proper contexts.
Prerequisite: Electrical and Computer Engineering 386 or equivalent, or consent of instructor.


Office Hours


Office Hours will be held on Wednesdays from 10:30 -- 12:00 in 351 EL (Phone: 3-4212) -- Other times by appointment. I can be reached for questions by electronic mail at s-meyn@uiuc.edu I will collect representative questions that have been electronically posed, and broadcast the questions together with my answers to all of you by electronic mail. Of course, the identity of the author of a question will be kept confidential.

Teaching assistant: To be announced.

Assignments

To appear!

References

C-T Chen, Linear System Theory and Design, 3rd edition, Oxford Universiy Press, 1999.

Additional references

The following three books are on reserve at Grainger Library, and should be useful supplements to the course notes.
  • B.D.O. Anderson and Moore, J.B., Linear Optimal Control, Prentice Hall, 1990.
  • Athans, M. and Falb, P.L., Optimal Control, McGraw Hill, 1966.
  • Bellman, R.E., Matrix Analysis, 2nd ed., McGraw Hill, 1968.
  • Brogan, W.L., Modern Control Theory, Prentice Hall, 1991.
  • Bryson, A.E. and Ho, Y.C., Applied Optimal Control, 2nd ed., Blaisdell, 1979.
  • C-T Chen, Linear System Theory and Design, Holt, Rinehart and Winston, In c., 1984.
  • Cruz, J.B., Jr., Feedback Systems, McGraw Hill, 1972.
  • Cruz, J.B., Jr., System Sensitivity Analysis, Dowden, Hutchinson & Ross, 1973.
  • Dorato, P. and C. Abdallah, and V. Cerone, Linear-Quadratic Control, Prentice Hall, 1995.
  • Frank, P.M., Introduction to System Sensitivity Theory, Academic Press, 1978.
  • Kailath, T., Linear Systems, Prentice Hall, 1980.
  • Kwakernaak, H. and R. Sivan, Linear Optimal Control Systems, Wiley, 1972.
  • Rosenbrock, H.H., State Space and Multivariable Theory, Wiley, 1970.
  • Skogestad, S. and I. Postlethwaite, Multivariable Feedback Control, Wiley, 1996.
  • Wiberg, D.M., State Space and Linear Systems, Schaum's Outline Series, McGraw Hill, 1972.


    • Outline

  • Modeling and Analysis of Control Systems
    Linear and nonlinear state space models
    Linear algebra and linear operators
    State transition matrix and solutions of linear state equations
  • Structural Properties of Control Systems

    Stability (Lyapunov, Input-Output)
    Stability tests for linear systems

    EXAM 1 (Wednesday, October 13, 1999)


    Controllability
    Observability
  • Feedback Controller Design
    Role of feedback in controller design
    Pole placement by state and output feedback
    Full-order and reduced-order observers
    Tracking, disturbance rejection, and the Internal Model Principle

    EXAM 2 (Wednesday, November 17, 1999)

  • Optimal Feedback Control
    Dynamic optimization: Dynamic programming and the HJB equation
    Optimal feedback control for linear-quadratic (LQ) systems
    Infinite horizon problems and steady-state analysis
    Minimum principle for continuous-time systems



    Other useful information: Exams, homeworks, and grading

    Homework problems will be assigned on a weekly basis, to be handed in at the beginning of class on the date due. They will be graded and returned the following week. Late homework cannot be accepted. There will be two term exams and one final exam. In the first term exam you will be allowed 1 sheet of notes, and in the second term exam two sheets of notes; but otherwise they will be closed-book and closed-notes. The final exam will be open-notes, but closed-book. Homework problems will count 10%, each of the term exams 25%, and the final exam will count 40% towards the final grade in the course.

    Note: Class will be cancelled on September 23rd so that all of us can attend the 37th Allerton Conference on Communication, Control, and Computing

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