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 (ISBN-13: 9780511287428)




DYNAMIC MODELING AND CONTROL OF ENGINEERING SYSTEMS
THIRD EDITION



This textbook is ideal for a course in Engineering System Dynamics and Controls. The work is a comprehensive treatment of the analysis of lumped-parameter physical systems. Starting with a discussion of mathematical models in general, and ordinary differential equations, the book covers input–output and state-space models, computer simulation, and modeling methods and techniques in mechanical, electrical, thermal, and fluid domains. Frequency-domain methods, transfer functions, and frequency response are covered in detail. The book concludes with a treatment of stability, feedback control (PID, lag–lead, root locus), and an introduction to discrete-time systems. This new edition features many new and expanded sections on such topics as Solving Stiff Systems, Operational Amplifiers, Electrohydraulic Servovalves, Using MATLAB® with Transfer Functions, Using MATLAB with Frequency Response, MATLAB Tutorial, and an expanded Simulink® Tutorial. The work has 40 percent more end-of-chapter exercises and 30 percent more examples.

Bohdan T. Kulakowski, Ph.D. (1942–2006) was Professor of Mechanical Engineering at Pennsylvania State University. He was an internationally recognized expert in automatic control systems, computer simulations and control of industrial processes, systems dynamics, vehicle–road dynamic interaction, and transportation systems. His fuzzy-logic algorithm for avoiding skidding accidents was recognized in 2000 by Discover magazine as one of its top 10 technological innovations of the year.

John F. Gardner is Chair of the Mechanical and Biomedical Engineering Department at Boise State University, where he has been a faculty member since 2000. Before his appointment at Boise State, he was on the faculty of Pennsylvania State University in University Park, where his research in dynamic systems and controls led to publications in diverse fields from railroad freight car dynamics to adaptive control of artificial hearts. He pursues research in modeling and control of engineering and biological systems.

J. Lowen Shearer (1921–1992) received his Sc.D. from the Massachusetts Institute of Technology. At MIT, between 1950 and 1963, he served as the group leader in the Dynamic Analysis & Control Laboratory, and as a member of the mechanical engineering faculty. From 1963 until his retirement in 1985, he was on the faculty of Mechanical Engineering at Pennsylvania State University. Professor Shearer was a member of ASME’s Dynamic Systems and Control Division and received that group’s Rufus Oldenberger Award in 1983. In addition, he received the Donald P. Eckman Award (ISA, 1965), and the Richards Memorial Award (ASME, 1966).





DYNAMIC MODELING AND CONTROL OF ENGINEERING SYSTEMS

THIRD EDITION

Bohdan T. Kulakowski
Deceased, formerly Pennsylvania State University

John F. Gardner
Boise State University

J. Lowen Shearer
Deceased, formerly Pennsylvania State University





CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

Cambridge University Press
32 Avenue of the Americas, New York, NY 10013–2473, USA

www.cambridge.org
Information on this title: www.cambridge.org/9780521864350

© John F. Gardner 2007

This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.

First published 2007

Printed in the United States of America

A catalog record for this publication is available from the British Library.

Library of Congress Cataloging in Publication Data
Kulakowski, Bohdan T.
Dynamic modeling and control of engineering systems / Bohdan T. Kulakowski, John F.
Gardner, J. Lowen Shearer. – 3rd ed.
   p. cm.
Includes bibliographical references and index.
ISBN-13: 978-0-521-86435-0 (hardback)
ISBN-10: 0-521-86435-6 (hardback)
1. Engineering – Mathematical models. 2. System engineering – Mathematical models.
I. Gardner, John F. (John Francis), 1958– II. Shearer, J. Lowen. III. Title.
TA342.S54  2007
620.001′1 – dc22      2006031544

Cambridge University Press has no responsibility for
the persistence or accuracy of URLs for external or
third-party Internet Web sites referred to in this publication
and does not guarantee that any content on such
Web sites is, or will remain, accurate or appropriate.

MATLAB® and Simulink® are trademarks of The MathWorks, Inc. and are used with
permission. The MathWorks does not warrant the accuracy of the text or exercises in this
book. This book’s use or discussion of MATLAB® and Simulink® software or related
products does not constitute endorsement or sponsorship by The MathWorks of a particular
pedagogical approach or particular use of the MATLAB® and Simulink® software.





Dedicated to the memories of Professor Bohdan T. Kulakowski (1942–2006), the victims of the April 16, 2007 shootings at Virginia Tech, and all who are touched by senseless violence. May we never forget and always strive to learn form history.





Contents



  Preface page xi
1   INTRODUCTION 1
  1.1  Systems and System Models 1
  1.2  System Elements, Their Characteristics, and the Role of Integration 4
          Problems 9
2   MECHANICAL SYSTEMS 14
  2.1  Introduction 14
  2.2  Translational Mechanical Systems 16
  2.3  Rotational–Mechanical Systems 30
  2.4  Linearization 34
  2.5  Synopsis 44
          Problems 45
3   MATHEMATICAL MODELS 54
  3.1  Introduction 54
  3.2  Input–Output Models 55
  3.3  State Models 61
  3.4  Transition Between Input–Output and State Models 68
  3.5  Nonlinearities in Input–Output and State Models 71
  3.6  Synopsis 76
          Problems 76
4   ANALYTICAL SOLUTIONS OF SYSTEM INPUT–OUTPUT EQUATIONS 81
  4.1  Introduction 81
  4.2  Analytical Solutions of Linear Differential Equations 82
  4.3  First-Order Models 84
  4.4  Second-Order Models 92
  4.5  Third- and Higher-Order Models 106
  4.6  Synopsis 109
          Problems 111
5   NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 120
  5.1  Introduction 120
  5.2  Euler’s Method 121
  5.3  More Accurate Methods 124
  5.4  Integration Step Size 129
  5.5  Systems of Differential Equations 133
  5.6  Stiff Systems of Differential Equations 133
  5.7  Synopsis 138
          Problems 139
6   SIMULATION OF DYNAMIC SYSTEMS 141
  6.1  Introduction 141
  6.2  Simulation Block Diagrams 143
  6.3  Building a Simulation 147
  6.4  Studying a System with a Simulation 150
  6.5  Simulation Case Study: Mechanical Snubber 157
  6.6  Synopsis 164
          Problems 165
7   ELECTRICAL SYSTEMS 168
  7.1  Introduction 168
  7.2  Diagrams, Symbols, and Circuit Laws 169
  7.3  Elemental Diagrams, Equations, and Energy Storage 170
  7.4  Analysis of Systems of Interacting Electrical Elements 175
  7.5  Operational Amplifiers 179
  7.6  Linear Time-Varying Electrical Elements 186
  7.7  Synopsis 188
          Problems 189
8   THERMAL SYSTEMS 198
  8.1  Introduction 198
  8.2  Basic Mechanisms of Heat Transfer 199
  8.3  Lumped Models of Thermal Systems 202
  8.4  Synopsis 212
          Problems 213
9   FLUID SYSTEMS 219
  9.1  Introduction 219
  9.2  Fluid System Elements 220
  9.3  Analysis of Fluid Systems 225
  9.4  Electrohydraulic Servoactuator 228
  9.5  Pneumatic Systems 235
  9.6  Synopsis 243
          Problems 244
10   MIXED SYSTEMS 249
  10.1  Introduction 249
  10.2  Energy-Converting Transducers and Devices 249
  10.3  Signal-Converting Transducers 254
  10.4  Application Examples 255
  10.5  Synopsis 261
          Problems 261
11   SYSTEM TRANSFER FUNCTIONS 273
  11.1  Introduction 273
  11.2  Approach Based on System Response to Exponential Inputs 274
  11.3  Approach Based on Laplace Transformation 276
  11.4  Properties of System Transfer Functions 277
  11.5  Transfer Functions of Multi-Input, Multi-Output Systems 283
  11.6  Transfer Function Block-Diagram Algebra 286
  11.7  MATLAB Representation of Transfer Function 293
  11.8  Synposis 298
          Problems 299
12   FREQUENCY ANALYSIS 302
  12.1  Introduction 302
  12.2  Frequency-Response Transfer Functions 302
  12.3  Bode Diagrams 307
  12.4  Relationship between Time Response and Frequency Response 314
  12.5  Polar Plot Diagrams 317
  12.6  Frequency-Domain Analysis with MATLAB 319
  12.7  Synopsis 323
          Problems 323
13   CLOSED-LOOP SYSTEMS AND SYSTEM STABILITY 329
  13.1  Introduction 329
  13.2  Basic Definitions and Terminology 332
  13.3  Algebraic Stability Criteria 333
  13.4  Nyquist Stability Criterion 338
  13.5  Quantitative Measures of Stability 341
  13.6  Root-Locus Method 344
  13.7  MATLAB Tools for System Stability Analysis 349
  13.8  Synopsis 351
          Problems 352
14   CONTROL SYSTEMS 356
  14.1  Introduction 356
  14.2  Steady-State Control Error 357
  14.3  Steady-State Disturbance Sensitivity 361
  14.4  Interrelation of Steady-State and Transient Considerations 364
  14.5  Industrial Controllers 365
  14.6  System Compensation 378
  14.7  Synopsis 383
          Problems 383
15   ANALYSIS OF DISCRETE-TIME SYSTEMS 389
  15.1  Introduction 389
  15.2  Mathematical Modeling 390
  15.3  Sampling and Holding Devices 396
  15.4  The z Transform 400
  15.5  Pulse Transfer Function 405
  15.6  Synopsis 407
          Problems 408
16   DIGITAL CONTROL SYSTEMS 410
  16.1  Introduction 410
  16.2  Single-Loop Control Systems 410
  16.3  Transient Performance 412
  16.4  Steady-State Performance 418
  16.5  Digital Controllers 421
  16.6  Synopsis 423
          Problems 424
  APPENDIX 1. Fourier Series and the Fourier Transform 427
  APPENDIX 2. Laplace Transforms 432
  APPENDIX 3. MATLAB Tutorial 438
  APPENDIX 4. Simulink Tutorial 463
  Index 481




Preface



From its beginnings in the middle of the 20th century, the field of systems dynamics and feedback control has rapidly become both a core science for mathematicians and engineers and a remarkably mature field of study. As early as 20 years ago, textbooks (and professors) could be found that purported astoundingly different and widely varying approaches and tools for this field. From block diagrams to signal flow graphs and bond graphs, the diversity of approaches, and the passion with which they were defended (or attacked), made any meeting of systems and control professionals a lively event.

   Although the various tools of the field still exist, there appears to be a consensus forming that the tools are secondary to the insight they provide. The field of system dynamics is nothing short of a unique, useful, and utterly different way of looking at natural and manmade systems. With this in mind, this text takes a rather neutral approach to the tools of the field, instead emphasizing insight into the underlying physics and the similarity of those physical effects across the various domains.

   This book has its roots as lecture notes from Lowen Shearer’s senior-level mechanical engineering course at Penn State in the 1970s with additions from Bohdan Kulakowski’s and John Gardner’s experiences since the 1980s. As such, it reveals those roots by beginning with lumped-parameter mechanical systems, engaging the student on familiar ground. The following chapters, dealing with types of models (Chapter 3) and analytical solutions (Chapter 4), have seen only minimal revisions from the original version of this text, with the exception of modest changes in order of presentation and clarification of notation. Chapters 5 and 6, dealing with numerical solutions (simulations), were extensively rewritten for the second edition and further updated for this edition. Although we made a decision to feature the industry-standard software package (MATLAB®) in this book (Appendices 3 and 4 are tutorials on MATLAB and Simulink®), the presentation was specifically designed to allow other software tools to be used.

   Chapters 7, 8, and 9 are domain-specific presentations of electric, thermal, and fluid systems, respectively. For the third edition, these chapters have been extensively expanded, including operational amplifiers in Chapter 7, an example of lumped approximation of a cooling fin in Chapter 8, and an electrohydraulic servovalve in Chapter 9. Those using this text in a multidisciplinary setting, or for nonmechanical engineering students, may wish to delay the use of Chapter 2 (mechanical systems) to this point, thus presenting the four physical domains sequentially. Chapter 10 presents some important issues in dealing with multidomain systems and how they interact.

   Chapters 11 and 12 introduce the important concept of a transfer function and frequency-domain analysis. These two chapters are the most revised and (hopefully) improved parts of the text. In previous editions of this text, we derived the complex transfer function by using complex exponentials as input. For the third edition, we retain this approach, but have added a section showing how to achieve the same ends using the Laplace transform. It is hoped that this dual approach will enrich student understanding of this material. In approaching these, and other, revisions, we listened carefully to our colleagues throughout the world who helped us see where the presentation could be improved. We are particularly grateful to Sean Brennan (of Penn State) and Giorgio Rizzoni (of Ohio State) for their insightful comments.

   This text, and the course that gave rise to it, is intended to be a prerequisite to a semester-long course in control systems. However, Chapters 13 and 14 present a very brief discussion of the fundamental concepts in feedback control, stability (and algebraic and numerical stability techniques), closed-loop performance, and PID and simple cascade controllers. Similarly, the preponderance of digitally implemented control schemes necessitates a discussion of discrete-time control and the dynamic effects inherent in sampling in the final chapters ( 15 and 16). It is hoped that these four chapters will be useful both for students who are continuing their studies in electives or graduate school and for those for which this is a terminal course of study.

   Supplementary materials, including MATLAB and Simulink files for examples throughout the text, are available through the Cambridge University Press web site (http://www.cambridge.org/us/engineering) and readers are encouraged to check back often as updates and additional case studies are made available.

   Outcomes assessment, at the program and course level, has now become a fixture of engineering programs. Although necessitated by accreditation criteria, many have discovered that an educational approach based on clearly stated learning objectives and well-designed assessment methods can lead to a better educational experience for both the student and the instructor. In the third edition, we open each chapter with the learning objectives that underlie each chapter. Also in this edition, the examples and end-of-chapter problems, many of which are based on real-world systems encountered by the authors, were expanded.

   This preface closes on a sad note. In March of 2006, just as the final touches were being put on this edition, Bohdan Kulakowski was suddenly and tragically taken from us while riding his bicycle home from the Penn State campus, as was his daily habit. His family, friends, and the entire engineering community suffered a great loss, but Bohdan’s legacy lives on in these pages, as does Lowen’s. As the steward of this legacy, I find myself “standing on the shoulders of giants” and can take credit only for its shortcomings.

JFG
Boise, ID
May, 2007





DYNAMIC MODELING AND CONTROL
OF ENGINEERING SYSTEMS


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