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ME 677 SYLLABUS

NONLINEAR CONTROLLER DESIGN Fall Semester 2013

INSTRUCTORS: Professor Bin Yao, ME 3061L, 494-7746 byao@purdue.edu https://engineering.purdue.edu/~byao Lectures: TuTh 9:00 - 10:15 AM in ME2004 Office Hours: TuTh 10:15 - 11:30 AM, or individual appointments COURSE TEXT:

Nonlinear Systems, H. K. Khalil, Prentice-Hall, Inc., Third Edition, 2002 REFERENCES:

[1] Nonlinear Systems: Analysis, Stability, and Control, Shankar Sastry, Springer-Verlag, New York, Inc., 1999. (A good theoretically oriented reference book)

[2] Applied Nonlinear Control, J.J.E. Slotine and Weiping Li, Prentice-Hall, 1991 (Application oriented and easy to read, but tends to be sloppy on theoretical development). [3] Nonlinear Control Systems, Alberto Isidori, 3rd Ed., 1995.

[4] Nonlinear and Adaptive Control Design, M. Krstic, I. Kanellakopoulos, and P.V.Kokotovic, John Wiley, New York, 1995 (An excellent reference for adaptive control of nonlinear systems)

PREREQUISITE:

A course on Modern Control Theory (ME575 or AAE564 or EE602 or equivalent) GOALS:

This course is designed to provide a graduate level introductory treatment of the standard analysis tools for nonlinear systems and the common design methodologies in synthesizing nonlinear feedback controllers. The course emphasizes not only the usefulness and the practicality of various nonlinear feedback controller design methodologies but also the rigorous theoretical development so that, upon the completion of the course, the student is equipped with adequate theoretical background to be able to read published research papers on nonlinear controls.

CONTENTS:

Common nonlinear behaviors and standard analysis tools for nonlinear systems are covered, including frequency domain analysis of nonlinear systems via describing function method and the absolute stability concepts. Lyapunov stability concepts for equilibrium points are introduced, along with various advanced Lyapunov type stability theorems and converse theorems. System level input-output (I/O) stability and passivity concepts are also presented with corresponding stability theorems. The feedback linearization method for known nonlinear systems is covered. Common nonlinear controller design methodologies for systems with uncertainties are then introduced and experimentally compared, including the state-space nonlinear system dynamics based deterministic robust controls (DRC) (e.g., the sliding mode control and the Lyapunov min-max method), and the recently developed nonlinear adaptive

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robust control approach. High-gain observers and adaptive robust observers are briefly touched to synthesize output feedback or partial state feedback nonlinear controllers.

GRADING POLICY:

Homework 60% Project 40%

CAMPUS EMERGENCIES

In the event of a major campus emergency, course requirements, deadlines, and grading policy are subject to changes that may be necessitated by a revised semester calendar or other circumstances beyond the instructor’s control. Any changes to the course will be announced on the course webpage. Consult http://www.purdue.edu/emergency_preparedness/ for emergency preparedness. If you are absent due to medical emergencies (e.g., H1N1 flu), alert instructor via email that you will be absent for the period and provide a medical release proof upon returning. Arrangement will be made to the grading policy to accommodate your absence during the period so that you will not be adversely punished for the course.

COURSE WEBPAGE:

https://mycourses.purdue.edu/ login using Career Account username and password. Then select ME677 and go to the course website.

HOMEWORK POLICY:

Homework will be assigned regularly. Each student is expected to complete the homework individually but group discussions are allowed to have a better understanding of the materials covered and the problems to be solved. It is to be turned in by the specified deadlines. Late homework will receive no credit (or partial credit if approved by the instructor in advance).

PROJECT:

Topics of the project are flexible and could be anything related to the materials covered in the course; examples like a focused theoretical research study on a particular nonlinear control methodology introduced in the course, application of nonlinear control techniques to a particular system in your research,…. The project report should follow a journal paper format and will be graded based on innovations, theoretical soundness, completeness, practicality, and knowledge of the subject covered.

COMPUTER USAGE:

Students will be expected to use MATLAB for some of the homework assignments. You are expected to secure a computer account having MATLAB within the first week of class.

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ME 677 TENTATIVE COURSE OUTLINE Period Date Topic Reading

Assignment HW Due

1 08/20/Tu. Nonlinear Models and Phenomena Chap.1 2 08/22/Th. Second-Order Systems: local behavior via

linearization Chap.2

3 08/27/Tu. Limit Cycles, Bifurcation, & Global Behavior Chap.2 4 08/29/Th. Existence & Uniqueness of Solutions Chap. 3 #15 09/03/Tu. Sensitivity & Comparison Principle Chap.3 6 09/05/Th. Lyapunov Stability – Autonomous System Chap.4 #2 7 09/10/Tu. - Invariance Principle &Linearization Chap.4 8 09/12/Th. - Comparison function & stability concept

for Non-autonomous systems Chap.4

#3

9 09/17/Tu. Stability Theorems for non-autonomous systems

Chap.4

10 09/19/Th. Linear time-varying systems & linearization Chap.4 #4 11 09/24/Tu. Converse Theorems Chap.4 12 09/26/Th. Boundedness & Ultimate Boundedness Chap. 4 #5 13 10/01/Tu. Input-to-State Stability Chap.4 14 10/03/Th. Input-Output (I/O) L-Stability Chap.5 #6

10/08/Tu. October Break 15 10/10/Th. L2 Gain & Small Gain Theorem Chap. 5 16 10/15/Tu. Passivity and Positive Real TF Concepts Chap.6 17 10/17/Th Passivity Theorems Chap.6 #7 18 10/22/Tu. Absolute Stability & Circle and Popov

Criterion Chap.7

19 10/24/Th. Describing Function Method Chap.7 #8 20 10/29/Tu. Control Problems; Integral Control & Gain

Scheduling Chap.12

21 10/31/Th. Relative Degree, Zero Dynamics, I/O Linearization

Chap.13 #9

22 11/05/Tu. Lie Bracket & Full-State Linearization Chap.13 23 11/07/Th. Design via Feedback Linearization Chap. 13 #10 24 11/12/Tu. Integrator Backstepping Chap.14 25 11/14/Th. Control Systems with Matched Uncertainties Chap.14 #11 26 11/19/Tu. - Sliding Mode Control (SMC) Chap.14 27 11/21/Th. - Lyapunov Re-Design Chap.14 #12 28 11/26/Tu. - Adaptive Control Notes

11/28/Th. Thanksgiving Holiday 29 12/03/Tu. - Adaptive Robust Control (ARC) Notes 30 12/05/Th. High-Gain and Adaptive Robust Observer

Designs Chap.14