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  • 1.Modern Control Engineering Fifth Edition Katsuhiko OgataPrentice Hall Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo

2. VP/Editorial Director, Engineering/Computer Science: Marcia J. Horton Assistant/Supervisor: Dolores Mars Senior Editor: Andrew Gilfillan Associate Editor: Alice Dworkin Editorial Assistant: William Opaluch Director of Marketing: Margaret Waples Senior Marketing Manager: Tim Galligan Marketing Assistant: Mack Patterson Senior Managing Editor: Scott Disanno Art Editor: Greg Dulles Senior Operations Supervisor: Alan Fischer Operations Specialist: Lisa McDowell Art Director: Kenny Beck Cover Designer: Carole Anson Media Editor: Daniel SandinCredits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear on appropriate page within text. MATLAB is a registered trademark of The Mathworks, Inc., 3 Apple Hill Drive, Natick MA 01760-2098. 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 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, One 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 File10 9 8 7 6 5 4 3 2 1ISBN 10: 0-13-615673-8 ISBN 13: 978-0-13-615673-4 3. C ContentsPreface Chapter 1 11 12 13 14 1526Introduction to Control Systems1Introduction 1 Examples of Control Systems 4 Closed-Loop Control Versus Open-Loop Control 7 Design and Compensation of Control Systems 9 Outline of the Book 10Chapter 2 21 22 23 24 25ixMathematical Modeling of Control SystemsIntroduction 13 Transfer Function and Impulse-Response Function 15 Automatic Control Systems 17 Modeling in State Space 29 State-Space Representation of Scalar Differential Equation Systems 35 Transformation of Mathematical Models with MATLAB1339iii 4. 27Linearization of Nonlinear Mathematical Models Example Problems and Solutions ProblemsChapter 3434660Mathematical Modeling of Mechanical Systems and Electrical Systems31Introduction32Mathematical Modeling of Mechanical Systems33Mathematical Modeling of Electrical Systems63Example Problems and Solutions Problems Chapter 463 728697Mathematical Modeling of Fluid Systems and Thermal Systems41Introduction42Liquid-Level Systems43Pneumatic Systems Hydraulic Systems12345Thermal Systems10010644100 101136Example Problems and Solutions Problems Chapter 5140152Transient and Steady-State Response Analyses51Introduction52First-Order Systems53Second-Order Systems Higher-Order Systems17955Transient-Response Analysis with MATLAB56Rouths Stability Criterion57Effects of Integral and Derivative Control Actions on System Performance 21858Steady-State Errors in Unity-Feedback Control Systems15916454159 161Problems Contents263183212Example Problems and Solutionsiv63231225 5. Chapter 6Control Systems Analysis and Design by the Root-Locus Method61Introduction62Root-Locus Plots63Plotting Root Loci with MATLAB64Root-Locus Plots of Positive Feedback Systems65Root-Locus Approach to Control-Systems Design66Lead Compensation67Lag Compensation68LagLead Compensation69Parallel Compensation269269 270Chapter 7303 308311 321 330 342Example Problems and Solutions Problems290347394Control Systems Analysis and Design by the Frequency-Response Method71Introduction72Bode Diagrams73Polar Plots74Log-Magnitude-versus-Phase Plots75Nyquist Stability Criterion76Stability Analysis77Relative Stability Analysis78Closed-Loop Frequency Response of Unity-Feedback Systems 47779Experimental Determination of Transfer Functions398398 403427 443445454 462486710 Control Systems Design by Frequency-Response Approach 711 Lead Compensation 712 Lag Compensation493 502713 LagLead Compensation511Example Problems and Solutions Problems Chapter 8521561PID Controllers and Modified PID Controllers81Introduction82ZieglerNichols Rules for Tuning PID ControllersContents491567567 568 v 6. 83 84 85 86 87Design of PID Controllers with Frequency-Response Approach 577 Design of PID Controllers with Computational Optimization Approach 583 Modifications of PID Control Schemes 590 Two-Degrees-of-Freedom Control 592 Zero-Placement Approach to Improve Response Characteristics 595 Example Problems and Solutions 614 ProblemsChapter 9 91 92 93 94 95 96 97Control Systems Analysis in State SpaceChapter 10vi648Introduction 648 State-Space Representations of Transfer-Function Systems 649 Transformation of System Models with MATLAB 656 Solving the Time-Invariant State Equation 660 Some Useful Results in Vector-Matrix Analysis 668 Controllability 675 Observability 682 Example Problems and Solutions 688 Problems101 102 103 104 105 106 107 108 109641720Control Systems Design in State SpaceIntroduction 722 Pole Placement 723 Solving Pole-Placement Problems with MATLAB 735 Design of Servo Systems 739 State Observers 751 Design of Regulator Systems with Observers 778 Design of Control Systems with Observers 786 Quadratic Optimal Regulator Systems 793 Robust Control Systems 806 Example Problems and Solutions 817 Problems 855Contents722 7. Appendix ALaplace Transform Tables859Appendix BPartial-Fraction Expansion867Appendix CVector-Matrix Algebra874References882Index886Contentsvii 8. This page intentionally left blank 9. P PrefaceThis 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, vectormatrix 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 presented 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 analysis and design of control systems. This edition of Modern Control Engineering is organized into ten chapters.The outline of this book is as follows: Chapter 1 presents an introduction to control systems. Chapter 2 ix 10. deals with mathematical modeling of control systems. A linearization technique for nonlinear mathematical models is presented in this chapter. Chapter 3 derives mathematical models of mechanical systems and electrical systems. Chapter 4 discusses mathematical modeling of fluid systems (such as liquid-level systems, pneumatic systems, and hydraulic systems) and thermal systems. Chapter 5 treats transient response and steady-state analyses of control systems. MATLAB is used extensively for obtaining transient response curves. Rouths stability criterion is presented for stability analysis of control systems. Hurwitz stability criterion is also presented. Chapter 6 discusses the root-locus analysis and design of control systems, including positive feedback systems and conditionally stable systems Plotting root loci with MATLAB is discussed in detail. Design of lead, lag, and lag-lead compensators with the rootlocus method is included. Chapter 7 treats the frequency-response analysis and design of control systems. The Nyquist stability criterion is presented in an easily understandable manner.The Bode diagram approach to the design of lead, lag, and lag-lead compensators is discussed. Chapter 8 deals with basic and modified PID controllers. Computational approaches for obtaining optimal parameter values for PID controllers are discussed in detail, particularly with respect to satisfying requirements for step-response characteristics. Chapter 9 treats basic analyses of control systems in state space. Concepts of controllability and observability are discussed in detail. Chapter 10 deals with control systems design in state space. The discussions include pole placement, state observers, and quadratic optimal control. An introductory discussion of robust control systems is presented at the end of Chapter 10. The book has been arranged toward facilitating the students gradual understanding of control theory. Highly mathematical arguments are carefully avoided in the presentation of the materials. Statement proofs are provided whenever they contribute to the understanding of the subject matter presented. Special effort has been made to provide example problems at strategic points so that the reader will have a clear understanding of the s