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INEL 6000 Introduction to Nonlinear Control, Spring 2002

INEL 6000 INTRODUCTION TO NONLINEAR CONTROL

First Semester 2005-2006

Catalog Data: / Analysis and synthesis of nonlinear control systems; phase plane and describing function techniques; Lyapunov's second method and its application in the design and stability determination of nonlinear systems.
Textbook: / H. Khalil, Nonlinear Systems, 3rd Edition, Prentice Hall, 2002.
References: /
  1. H.J. Marquez, Nonlinear Control Systems: Analysis and Design, Wiley, 2003.
  2. A. Isidori, Nonlinear Control Systems II, Third Edition, Springer-Verlag, 1999.
  3. S. Sastry, Nonlinear Systems: Analysis, Stability, and Control, Springer-Verlag, 1999.
  4. C.T. Chen, Linear System Theory and Design, 3rd Edition, OxfordUniversity Press, 1999.
  5. T.L. Vincent and W.J. Grantham, Nonlinear and Optimal Control Systems, John Wiley & Sons, 1997.
  6. C.I. Byrnes, F.D. Priscoli, and A. Isidori, Output Regulation of Uncertain Nonlinear Systems, Birkhäuser, 1997.
  7. I. Mareels and J.W. Polderman, Adaptive Systems: An Introduction, Birkhäuser, 1996.
  8. R. Marino and P. Tomei, Nonlinear Control Design: Geometric, Adaptive, Robust, Prentice Hall, 1995.
  1. M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, John Wiley, 1995.
  1. A. Isidori, Nonlinear Control Systems, Third Edition, Springer-Verlag, 1995.
  1. M. Vidyasagar, Nonlinear Systems Analysis, Second Edition, Prentice Hall, 1993
  1. J. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, 1991.
  1. R.H. Mohler, Nonlinear Systems, Vols. 1 y 2, Prentice Hall, 1991
  1. H. Nijermeijer and A.J. van der Schaft, Nonlinear Dynamical Control Systems, Springer-Verlag, 1990
  1. S. Sastry and M. Bodson, Adaptive Control, Prentice Hall, 1989
  1. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, Second Edition, Clarendon Press, 1987.
  2. L.O. Chua, C.A. Desoer, and E.S. Kuh, Linear and Nonlinear Circuits, McGraw Hill, 1987.
  1. D.G. Luenberger, Introduction to Dynamic Systems: Theory, Models, and Applications, John Wiley & Sons, 1979

Instructor: / Dr. Miguel Vélez-Reyes, Professor of Electrical and Computer Engineering.
Office: / S-404, Ext. 2888
e-mail:

Office Hours: / M-W 10:30 to 12:00, and by appointment. I can also answer your questions via e-mail.YOU HAVE TO READ YOUR E-MAIL FOR CLASS ANOUNCEMENTS!!
Goals: / This course introduces theory and techniques for the analysis of nonlinear dynamical systems and the design of nonlinear control. It emphasizes rigorous analysis supplemented with computer simulation.
Exams (50%): / There will be three tests during the course of the term. The lowest grade partial exam will be counted half as much as each of the two higher grades. If you miss a test, you may take a makeup test at a designated time near the end of the semester.
Homework (25%): / Required problem sets will be assigned and will be due at the beginning of each class period on the due date. Unless otherwise instructed, you must work by yourself on the homework.
Project (25%): / A term project will be required. Subject and scope of the project will be discussed during the course of the term.
Computer Usage: / The software package MATLABTM and SIMULINKTM will be used for analysis and design of simple nonlinear systems. These toolboxes could be of great help in design or analysis projects and their use is highly encouraged.
A student version of MATLAB and SIMULINK are available from Mathworks ( MATLAB Student Version Highlights:
  • Full-featured MATLAB (Same as expensive professional version)
  • Includes Simulink (with model sizes up to 300 blocks) &
  • the Symbolic Math Toolbox
  • Available on PC & Linux platforms
  • Add-on products also available
Do not purchase the Prentice Hall version. Students in the U.S. or Canada can purchase the MATLAB Student Version direct from The MathWorks or at UPRM bookstore. Students who own the MATLAB Student Version can purchase add-on products to extend its capabilities and they are available for download only. (Will not work with the Student Edition of MATLAB from Prentice Hall.)
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Grading Policy: / Your final grade will be based in Tests (50%), Homework (25%), and a Project (25%). Grades:
At least 90A
At least 80B
At least 70C
At least 60D
59 or lessF
There will be a “gray area” between letter grades in the final distribution, so that two people getting the same weighted average grade could get different letter grades. If you are in one of these gray areas, whether your get a higher or lower grade depends on whether your test performance has been improving (your grade goes up) or declining (it will not change), and class participation.
If you cheat in your homework or take home exams, you will get an F in the course and I will report your case to the Dean of Student Affairs for further disciplinary actions.
An incomplete grade is given only for a valid reason when arrangements have been made with me and, in that case, only if the student was passing the course.

Prerequisites by topic:

  1. Fundamentals of linear systems and control theory:
  2. Ordinary differential equations
  3. Elementary matrix algebra and matrix notation
  4. Taylor series expansions
  5. Multivariable Calculus

Course Outline:

Topics: / Assigned Readings
(based on 2nd ed., I will update as soon as I get the 3rd) / Lectures

Analysis

  1. Introduction
/ Chapter 1 / 1
  1. Second Order Systems
/ Sections 1.2, Section 7.1 / 4
  1. Fundamental Properties
/ Chapter 2 / 2
  1. Lyapunov Stability
/ Chapter 3, Section 5.3 / 9
  1. Input-Output Stability
/ Chapter 6, Section 10.2 / 3
  1. Passivity
/ Section 10.3 / 4
  1. Frequency Domain Analysis of Nonlinear Systems
  2. Absolute Stability
  3. Describing Function Method
/ Section 10.1
Section 10.4 / 5
Feedback Control
  1. Linearization and Integral Control
/ Chapter 11 / 3
  1. Feedback Linearization
/ Chapter 12 / 5
  1. Nonlinear Control Tools
  • Sliding mode control
  • High-gain feedback
  • Lyapunov redesign
  • Passivity-based control
  • Backstepping
  • Observers
/ Section 13.3
Notes
Section 13.1
Notes
Section 13.2
Notes / 9

Revised by Dr. Miguel Vélez Reyes in May 5, 2005.