Curtis D. Johnson. University of Houston. Heidar A. Malki

Transcription

1 CONTROL SYSTEMS TECHNOLOGY Curtis D. Johnson University of Houston Heidar A. Malki University of Houston

2 Library of Congress Cataloging-in-Publication Data Johnson, Curtis D. Control systems technology / Curtis Johnson & Heidar Malki. p.cm. Includes index. ISBN Process control. I. Malld, Heidar. II. Title. TSI56.8.J dc "2348. Editor in Chief: Stephen Helba Assistant Vice President and Publisher: Charles Stewart Assistant Editor: Delia K. Uherec Production Editor: Tricia L. Rawnsley Design Coordinator: Robin G. Chukes Production Coordination: Carlisle Publishers SeIVices Cover art!photo: Visual Edge Imaging Studios Cover Designer: Linda Fares Production Manager: Matthew Ottenweller This book was set by Carlisle Communications, Ltd. It was printed and bound by R. R. Donnelley & Sons Company. The cover was printed by Phoenix Color Corp. Pearson Education Ltd., London Pearson Education Australia Pty. Limited, Sydney Pearson Education Singapore Pte. Ltd. Pearson Education North Asia Ltd., Hong Kong Pearson Education Canada, Ltd., Toronto Pearson Educaci6n de Mexico, S.A de C.V. Pearson Education-Japan, Tokyo Pearson Education Malaysia Pte. Ltd. Pearson Education, Upper Saddle River, New Jersey Copyright 2002 by Pearson Education, Inc., Upper Saddle River, New Jersey All rights reserved. Printed 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. For information regarding permission(s), write to: Rights and Permissions Department ISBN

3 This text was written to fill a very important educational niche in the broad spectrum of control systems knowledge. That niche lies between the hands-on electromechanical knowledge and skills needed by technicians and the highly abstract and theoretical knowledge required by scholars who research and develop new control strategies. This book focuses on the knowledge required by control systems practitioners to enable them to both understand and evaluate an existing control system and devise and design new control system applications. The text presents classical and digital control systems with an emphasis on careful explanations of the concepts. Many examples illustrate key topics and the operations required to solve problems. The text is an outgrowth of many years of teaching control systems to students in an engineering technology program. It is written for a two-semester course, nominally separated into analog and digital control. The difficulty with this approach is that much of digital control is a spinoff of analog concepts. Therefore, the analog material by itself is more extensive than the digital. In practice, we have found that some of the material on analog control must be delayed to the second course. Although patterned after the course sequence expected for a particular educational program, this text can be adapted to other approaches. For example, Chapter 2 (Measurement) can be omitted by those who prefer to cover sensors and measurement in other courses. Likewise, if Laplace transforms are covered in an independent course, that section in Chapter 3 can be omitted or assigned as review. It would be important to include, however, the last section of Chapter 3, Analog Simulation. The text emphasizes an understanding of control system concepts, but also requires the use of computers to implement practical solutions to problems. There are a number of control and mathematical software packages which are of great value in the study of control systems. Throughout the text, the use of these packages to facilitate solving problems is emphasized, and Mathcad or MATLAB is used to illustrate computer-based mathematical procedures. An attempt has been made to emphasize the use of computers as a tool to implement the mathematical and graphical operations required to solve a problem. A Web page ( will be set up for this text as a means for communication between users and authors, and also for sharing ideas and techniques related to teaching control systems. A solutions manual (ISBN: ) is available. It contains examples of physical and simulation experiments that can be conducted to enhance learning. Dr. Malki would like to thank his parents, his wife Layla, and his son Armeen for their support and patience during the long task of writing this book. Dr. Johnson would like to thank his wife Helene and his mother-in-law Lois for their continuing kindness while he undertook this task.

4 1 INTRODUCTION TO CONTROL SYSTEMS Purpose Introduction Control System Strategy Examples of Control Systems Analytical Issues Analytical Descriptions Block Diagram Transfer Functions Computer Applications Software Analog and Digital Control System Design Objectives 17 Summary 19 Problems Dynamic Response Instability 17 2 MEASUREMENT Purpose Measurement Principles Sensor Signal Conditioning Sensors 38 Summary 47 Problems Temperature Displacement Motion 45 vii

5 viii I CONTENTS 3 LAPLACE TRANSFORMS Purpose Introduction Definition of the Laplace Transform Computer Applications Properties of Laplace Transforms Inverse Laplace Transform Partial-fraction Expansion Convolution Analog Simulation 77 Summary 87 Problems The Operational Amplifier Simulation of Physical Systems Simulation of Control Systems 85 4 CONTROL SYSTEM MODELS B 4.1 Purpose Transfer Functions Block Transfer Functions Transfer Function Properties Graphing Block Diagrams Canonical Form Block Diagram Reduction Multiple Inputs Mason's Gain Formula Controller/Compensator Transfer Functiom 128 Summary 132 Problems Proportional, Integral, and Derivative Contro~ Lead and Lag Compensation STATIC AND DYNAMIC RESPONSE 13! 5.1 Purpose Static Response Steady-State Error Disturbance Error 148

6 CONTENTS I ix 5.3 Dynamic Response of First- and Second-Order Plants First-Order Plant Second-Order Plant Characteristics of Dynamic Response Steady-State Error Versus Stability 165 Summary 167 Problems STABILITY Purpose Definitions of Stability Formal Definition of Stability Routh-Hurwitz Stability Criterion 178 Summary 184 Problems Special Cases FREQUENCY RESPONSE ANALYSIS Purpose Basic Principles Frequency Response Analysis Exact Analysis Bode Plot Control System Bode Plots Manual Construction Computer Construction Bode Plot Applications 210 Summary 216 Problems Gain and Phase Margins Transportation Delay ROOT LOCUS Purpose Introduction to Root Locus Closed-Loop Poles Root Locus Graph 224

7 x I CONTENTS 8.3 Root Locus Construction Manual Construction Computer Construction Root Locus Applications Gain and Phase Margin Transient Response 242 Summary 249 Problems STATE-SPACE ANALYSIS Purpose State-Space Definition Solving State-Space Equations Laplace Transform Solutions Series Expansion Solution Computer Simulation Solution Simulation Diagrams and State-Space Equations Simulation Diagram Definition Generalized Rules of Simulation Diagram Construction Transfer Function in State Space Controllability and Observability 277 Summary 281 Problems Controllability Observability INTRODUCTION TO DIGITAL CONTROL SYSTEMS Purpose Definition of a Digital Control System Digital Control System Hardware Digital Control System Software Simulations Using Computers The Difference Equation 294 Summary 302 Problems Finding the Difference Equation Solution of the Difference Equation 298

8 CONTENTS I xi 11 z-transform AND THE DIFFERENCE EQUATION Purpose Definition of the z-transform Properties of z-transforms Linearity Advance Theorem (Shift Left) Delay Theorem (Shift Right) Final Value Theorem Initial Value Theorem Inverse z-transform Partial-Fraction Expansion for Real Poles Partial-Fraction Expansion for Complex Poles Partial-Fraction Expansion for Repeated Poles Direct Method: Long Division Inverse z- Transforms by Software Difference Equation Solution 330 Summary 334 Problems DISCRETE CONTROL SYSTEMS Purpose Discrete Transfer Function Open-Loop Transfer Functions Closed-Loop Transfer Functions Static and Dynamic Response 355 Summary 365 Problems Static Response Dynamic Response STABILITY OF DISCRETE CONTROL SYSTEMS Purpose Conditions for Stability Stability Tests Routh-Hurwitz Test with the Bilinear Transformation Jury's Stability Test 376

9 xii I CONTENTS 13.4 Discrete System Root Locus Root Locus Construction Rules 381 Summary 387 Problems DISCRETE STATE SPACE Purpose State-Space Equations in the Discrete Domain Discrete State Equations Solution by Recursion Solution by z- Transforms Discrete State-Space Transfer Function Generation of State-Vector Equations Observability and Controllability Discrete Simulation Diagrams 406 Summary 410 Problems 410 APPENDIX A: COMPLEX NUMBERS 413 APPENDIX B: MATRICES 417 GLOSSARY 423 SOLUTIONS TO SELECTED ODD PROBLEMS 427 INDEX 459

10 CONTROL SYSTEMS TECHNOLOGY