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Nonlinear Control-Khalil.pdf

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    Cover
    Title Page
    Copyright Page
    Contents
    Preface
    1 Introduction
    1.1 Nonlinear Models
    1.2 Nonlinear Phenomena
    1.3 Overview of the Book
    1.4 Exercises
    2 Two-Dimensional Systems
    2.1 Qualitative Behavior of Linear Systems
    2.2 Qualitative Behavior Near Equilibrium Points
    2.3 Multiple Equilibria
    2.4 Limit Cycles
    2.5 Numerical Construction of Phase Portraits
    2.6 Exercises
    3 Stability of Equilibrium Points
    3.1 Basic Concepts
    3.2 Linearization
    3.3 Lyapunov’s Method
    3.4 The Invariance Principle
    3.5 Exponential Stability
    3.6 Region of Attraction
    3.7 Converse Lyapunov Theorems
    3.8 Exercises
    4 Time-Varying and Perturbed Systems
    4.1 Time-Varying Systems
    4.2 Perturbed Systems
    4.3 Boundedness and Ultimate Boundedness
    4.4 Input-to-State Stability
    4.5 Exercises
    5 Passivity
    5.1 Memoryless Functions
    5.2 State Models
    5.3 Positive Real Transfer Functions
    5.4 Connection with Stability
    5.5 Exercises
    6 Input-Output Stability
    6.1 L Stability
    6.2 L Stability of State Models
    6.3 L[sub(2)] Gain
    6.4 Exercises
    7 Stability of Feedback Systems
    7.1 Passivity Theorems
    7.2 The Small-Gain Theorem
    7.3 Absolute Stability
    7.3.1 Circle Criterion
    7.3.2 Popov Criterion
    7.4 Exercises
    8 Special Nonlinear Forms
    8.1 Normal Form
    8.2 Controller Form
    8.3 Observer Form
    8.4 Exercises
    9 State Feedback Stabilization
    9.1 Basic Concepts
    9.2 Linearization
    9.3 Feedback Linearization
    9.4 Partial Feedback Linearization
    9.5 Backstepping
    9.6 Passivity-Based Control
    9.7 Control Lyapunov Functions
    9.8 Exercises
    10 Robust State Feedback Stabilization
    10.1 Sliding Mode Control
    10.2 Lyapunov Redesign
    10.3 High-Gain Feedback
    10.4 Exercises
    11 Nonlinear Observers
    11.1 Local Observers
    11.2 The Extended Kalman Filter
    11.3 Global Observers
    11.4 High-Gain Observers
    11.5 Exercises
    12 Output Feedback Stabilization
    12.1 Linearization
    12.2 Passivity-Based Control
    12.3 Observer-Based Control
    12.4 High-Gain Observers and the Separation Principle
    12.5 Robust Stabilization of Minimum Phase Systems
    12.5.1 Relative Degree One
    12.5.2 Relative Degree Higher Than One
    12.6 Exercises
    13 Tracking and Regulation
    13.1 Tracking
    13.2 Robust Tracking
    13.3 Transition Between Set Points
    13.4 Robust Regulation via Integral Action
    13.5 Output Feedback
    13.6 Exercises
    A: Examples
    A.1 Pendulum
    A.2 Mass–Spring System
    A.3 Tunnel-Diode Circuit
    A.4 Negative-Resistance Oscillator
    A.5 DC-to-DC Power Converter
    A.6 Biochemical Reactor
    A.7 DC Motor
    A.8 Magnetic Levitation
    A.9 Electrostatic Microactuator
    A.10 Robot Manipulator
    A.11 Inverted Pendulum on a Cart
    A.12 Translational Oscillator with Rotating Actuator
    B: Mathematical Review
    C: Composite Lyapunov Functions
    C.1 Cascade Systems
    C.2 Interconnected Systems
    C.3 Singularly Perturbed Systems
    D: Proofs
    Bibliography
    Symbols
    Index
    A
    B
    C
    D
    E
    F
    G
    H
    I
    J
    K
    L
    M
    N
    O
    P
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    R
    S
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    U
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    Z
    Nonlinear Control
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    Nonlinear Control Hassan K. Khalil Department of Electrical and Computer Engineering Michigan State University
    Vice President and Editorial Director, ECS: Marcia J. Horton Executive Editor: Andrew Gilfillan Marketing Manager: Tim Galligan Managing Editor: Scott Disanno Project Manager: Irwin Zucker Art Director: Jayne Conte Cover Designer: Bruce Kenselaar Cover Image: Reconstruction of a clepsydra water clock invented by Ctesibius of Alexandria c270 BC 1857 c The Print Collector / Alamy Full-Service Project Management/ Composition: SPI Global Printer/Binder: Courier Westford Cover Printer: Courier Westford Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear on appropriate page within text. Copyright c 2015 by Pearson Education, Inc., publishing as Prentice Hall, 1 Lake Street, Upper Saddle River, NJ 07458. All rights reserved. Manufactured in the United States of America. This publication is protected by Copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. To obtain permission(s) to use material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, imprint permissions address. Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks. Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps. MATLAB and Simulink are registered trademarks of The Math Works, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098 The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs. Library of Congress Cataloging-in-Publication Data on file 10 9 8 7 6 5 4 3 2 1 ISBN-10: 0-13-349926-X ISBN-13: 978-0-13-349926-1
    To my parents Mohamed and Fat-hia and my grandchildren Maryam, Tariq, Aya, and Tessneem
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    Contents Preface 1 Introduction 1.1 Nonlinear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Nonlinear Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Overview of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Two-Dimensional Systems 2.1 Qualitative Behavior of Linear Systems . . . . . . . . . . . . . . . . . . 2.2 Qualitative Behavior Near Equilibrium Points . . . . . . . . . . . . . . 2.3 Multiple Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Limit Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Numerical Construction of Phase Portraits . . . . . . . . . . . . . . . . 2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Stability of Equilibrium Points 3.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Lyapunov’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 The Invariance Principle . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Exponential Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Region of Attraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Converse Lyapunov Theorems . . . . . . . . . . . . . . . . . . . . . . . 3.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Time-Varying and Perturbed Systems 4.1 Time-Varying Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Perturbed Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Boundedness and Ultimate Boundedness . . . . . . . . . . . . . . . . . 4.4 Input-to-State Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii xi 1 1 8 9 10 15 17 21 24 27 31 33 37 37 43 45 54 58 61 68 70 75 75 80 85 94 99
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