Modern Control Engineering

905 Pages · 2010 · 5.92 MB · English

  • Modern Control Engineering

    Modern Control


    Fifth Edition

    Katsuhiko Ogata

    Prentice Hall

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    textbook appear on appropriate page within text.

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    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


    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


    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


    • 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


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