Modern Control Engineering Fifth Edition Katsuhiko Ogata Prentice 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 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 Sandin Credits and acknowledgments borrowed from other sources and reproduced,with permission,in this 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 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