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Modern Control Engineering

905 Pages · 2010 · 6.56 MB · English

  • Modern Control Engineering

    Modern Control


    Engineering


    Fifth Edition


    Katsuhiko Ogata


    Prentice Hall


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    Credits and acknowledgments borrowed from other sources and reproduced,with permission,in this


    textbook appear on appropriate page within text.


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    Copyright © 2010,2002,1997,1990,1970 Pearson Education,Inc.,publishing as Prentice Hall,One Lake


    Street,Upper Saddle River,New Jersey 07458.All rights reserved.Manufactured in the United States of


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    Lake Street,Upper Saddle River,New Jersey 07458.


    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.


    Library of Congress Cataloging-in-Publication Data on File


    10 9 8 7 6 5 4 3 2 1


    ISBN 10: 0-13-615673-8


    ISBN 13: 978-0-13-615673-4 C


    Contents


    Preface ix


    Chapter 1 Introduction to Control Systems 1


    1–1 Introduction 1


    1–2 Examples of Control Systems 4


    1–3 Closed-Loop Control Versus Open-Loop Control 7


    1–4 Design and Compensation of Control Systems 9


    1–5 Outline of the Book 10


    Chapter 2 Mathematical Modeling of Control Systems 13


    2–1 Introduction 13


    2–2 Transfer Function and Impulse-Response Function 15


    2–3 Automatic Control Systems 17


    2–4 Modeling in State Space 29


    2–5 State-Space Representation of Scalar Differential


    Equation Systems 35


    2–6 Transformation of Mathematical Models with MATLAB 39


    iii 2–7 Linearization of Nonlinear Mathematical Models 43


    Example Problems and Solutions 46


    Problems 60


    Chapter 3 Mathematical Modeling of Mechanical Systems


    and Electrical Systems 63


    3–1 Introduction 63


    3–2 Mathematical Modeling of Mechanical Systems 63


    3–3 Mathematical Modeling of Electrical Systems 72


    Example Problems and Solutions 86


    Problems 97


    Chapter 4 Mathematical Modeling of Fluid Systems


    and Thermal Systems 100


    4–1 Introduction 100


    4–2 Liquid-Level Systems 101


    4–3 Pneumatic Systems 106


    4–4 Hydraulic Systems 123


    4–5 Thermal Systems 136


    Example Problems and Solutions 140


    Problems 152


    Chapter 5 Transient and Steady-State Response Analyses 159


    5–1 Introduction 159


    5–2 First-Order Systems 161


    5–3 Second-Order Systems 164


    5–4 Higher-Order Systems 179


    5–5 Transient-Response Analysis with MATLAB 183


    5–6 Routh’s Stability Criterion 212


    5–7 Effects of Integral and Derivative Control Actions


    on System Performance 218


    5–8 Steady-State Errors in Unity-Feedback Control Systems 225


    Example Problems and Solutions 231


    Problems 263


    iv Contents Chapter 6 Control Systems Analysis and Design


    by the Root-Locus Method 269


    6–1 Introduction 269


    6–2 Root-Locus Plots 270


    6–3 Plotting Root Loci with MATLAB 290


    6–4 Root-Locus Plots of Positive Feedback Systems 303


    6–5 Root-Locus Approach to Control-Systems Design 308


    6–6 Lead Compensation 311


    6–7 Lag Compensation 321


    6–8 Lag–Lead Compensation 330


    6–9 Parallel Compensation 342


    Example Problems and Solutions 347


    Problems 394


    Chapter 7 Control Systems Analysis and Design by the


    Frequency-Response Method 398


    7–1 Introduction 398


    7–2 Bode Diagrams 403


    7–3 Polar Plots 427


    7–4 Log-Magnitude-versus-Phase Plots 443


    7–5 Nyquist Stability Criterion 445


    7–6 Stability Analysis 454


    7–7 Relative Stability Analysis 462


    7–8 Closed-Loop Frequency Response of Unity-Feedback


    Systems 477


    7–9 Experimental Determination of Transfer Functions 486


    7–10 Control Systems Design by Frequency-Response Approach 491


    7–11 Lead Compensation 493


    7–12 Lag Compensation 502


    7–13 Lag–Lead Compensation 511


    Example Problems and Solutions 521


    Problems 561


    Chapter 8 PID Controllers and Modified PID Controllers 567


    8–1 Introduction 567


    8–2 Ziegler–Nichols Rules for Tuning PID Controllers 568


    Contents v 8–3 Design of PID Controllers with Frequency-Response


    Approach 577


    8–4 Design of PID Controllers with Computational Optimization


    Approach 583


    8–5 Modifications of PID Control Schemes 590


    8–6 Two-Degrees-of-Freedom Control 592


    8–7 Zero-Placement Approach to Improve Response


    Characteristics 595


    Example Problems and Solutions 614


    Problems 641


    Chapter 9 Control Systems Analysis in State Space 648


    9–1 Introduction 648


    9–2 State-Space Representations of Transfer-Function


    Systems 649


    9–3 Transformation of System Models with MATLAB 656


    9–4 Solving the Time-Invariant State Equation 660


    9–5 Some Useful Results in Vector-Matrix Analysis 668


    9–6 Controllability 675


    9–7 Observability 682


    Example Problems and Solutions 688


    Problems 720


    Chapter 10 Control Systems Design in State Space 722


    10–1 Introduction 722


    10–2 Pole Placement 723


    10–3 Solving Pole-Placement Problems with MATLAB 735


    10–4 Design of Servo Systems 739


    10–5 State Observers 751


    10–6 Design of Regulator Systems with Observers 778


    10–7 Design of Control Systems with Observers 786


    10–8 Quadratic Optimal Regulator Systems 793


    10–9 Robust Control Systems 806


    Example Problems and Solutions 817


    Problems 855


    vi Contents Appendix A Laplace Transform Tables 859


    Appendix B Partial-Fraction Expansion 867


    Appendix C Vector-Matrix Algebra 874


    References 882


    Index 886


    Contents vii This page intentionally left blank P


    Preface


    This book introduces important concepts in the analysis and design of control systems.


    Readers will find it to be a clear and understandable textbook for control system courses


    at colleges and universities.It is written for senior electrical,mechanical,aerospace,or


    chemical engineering students.The reader is expected to have fulfilled the following


    prerequisites:introductory courses on differential equations,Laplace transforms,vector-


    matrix analysis,circuit analysis,mechanics,and introductory thermodynamics.


    The main revisions made in this edition are as follows:


    • The use of MATLAB for obtaining responses of control systems to various inputs


    has been increased.


    • The usefulness of the computational optimization approach with MATLAB has been


    demonstrated.


    • New example problems have been added throughout the book.


    • Materials in the previous edition that are of secondary importance have been deleted


    in order to provide space for more important subjects.Signal flow graphs were


    dropped from the book.A chapter on Laplace transform was deleted. Instead,


    Laplace transform tables,and partial-fraction expansion with MATLAB are pre-


    sented in Appendix A and Appendix B,respectively.


    • A short summary of vector-matrix analysis is presented in Appendix C;this will help


    the reader to find the inverses of n x n matrices that may be involved in the analy-


    sis and design of control systems.


    This edition of Modern Control Engineeringis organized into ten chapters.The outline of


    this book is as follows:Chapter 1 presents an introduction to control systems.Chapter 2


    ix


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