Mechanical Engineering Series

Frederick F. Ling Series Editor

Advisory Board

Applied Mechanics F.A. Leckie University of California, Santa Barbara

Biomechanics V.C. Mow Columbia University

Computational Mechanics H.T. Yang Purdue University

Dynamic Systems and Control KM. Marshek University of Texas, Austin

Energetics J. Welte University of Oregon, Eugene

Mechanics of Materials 1. Finnie University of California, Berkeley

Processing KK Wang Cornell University

Thermal Science A.E. Bergles Rennselaer Polytechnic Institute

Tribology W.O. Winer Georgia Institute of Technology Mechanical Engineering Series

Laser Machining: Theory and Practice G. Chryssolouris

Theory of Wire Rope G.A Costello

Balancing of High-Speed Machinery M.S. Darlow

Analysis of Material Removal Processes W.R. DeVries (Springer Texts in Mechanical Engineering)

Principles of Heat Transfer in Porous Media M. Kaviany

Underconstrained Structural Systems E.N. Kuznetsov

Mechatronics: Electromechanics and Contromechanics D.K. Miu

Introductory Attitude Dynamics F.P. Rimrott

Theory of Vibration Vol. I Introduction Vol. II Discrete and Continuous Systems AA Shabana Denny K. Miu

Mechatronics Electromechanics and Contromechanics

With 127 Figures

fllustmtions by Viktoria Temesvary

Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest Denny K. Miu, Ph. D Department of Mechanical, Aerospace and Nuclear Engineering University of California, Los Angeles Los Angeles, CA 90024-1597

Series Editor Frederick F. Ling President, Institute for Productivity R.esea.rch New York, NY 10010 and Distinguished William Howard Hart Professor Emeritus Department of Mechanical Engineering, Aeronautical Engineering, and Mechanics Rensselaer Polytechnic Institute Troy, NY 12180-3590 USA

Library of Congress Cataloging-in_Publication Data Miu, Denny K. MecllatroniCII: e lectromechaniCII and contromechanlCII/Denny K. Miu. p. cm.-{Mech.&nicaJ engineering ""riee) Includee bibliographical ref",...,nces a nd index.

IS BN - ' 3 '97 8 - ' - 46. :> - 874 6 - 9 001, 10. 007/978- 1 - .... 6 1 :Z - 4 358 - 8

1. Electromechanical devices. 2. Automatic control. I. Title. II. Seriee: Mechanical engineering aeriee (Berlin, Germany) TJI63.M5 1992 621-dc20 92-1604

Printed On &eid-free pa.per.

@1993Springer-Verlag Ne.... York, Inc. AU righta reserved. This work may not be translated or copied in whOle or in part without the written permi88ion of the publisher (Spring<:!r_Vetlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpta in connection with revie.... s or BCholar. Iy anal)'1lis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or diNimilar methodology now known or her... after developed is forbidden. The u.se of general deBCriptive namee, trade names, trademarka, etc., in this publication, even if the former a re not especially identified, is not to be taken ... a sign that such names, as understood by the Trade Marka and Merchandiae Marka Act, may accordingly be u.sed freely by anyone .

Production managed by Natalie JohlllKln; manuf&eturing l uperv;Sf!d by Vincent Scelta. Camera-ready copy prepared by the author; Illustration. by Viktoria Temesvary.

98765 4 321 To my friend Paul who opened my eyes so I can hear, To my friend Dom who opened my heart so I can speak. To my Mom and Dad who gave me the means, To my Melodies who show me the way. Series Preface

Mechanical engineering, an engineering discipline born of the needs of the industrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound is• sues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series features graduate texts and research monographs intended to address the need for information in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that will cover a broad range of concentrations important to mechanical engineering graduate ed• ucation and research. We are fortunate to have a distinguished roster of consulting editors, each an expert in one of the areas of concentration. The names of the consulting editors are listed on the front page of the volume. The areas of concentration are applied mechanics, biomechanics, compu• tational mechanics, dynamic systems and control, energetics, mechanics of material, processing, thermal science, and tribology. Professor Marshek, the consulting editor for dynamic systems and con• trol, and I are pleased to present this volume of the series: Mechatronics: Electromechanics and Contromechanics by Professor Denny K. Miu. The selection of this volume underscores again the interest of the Mechanical Engineering Series to provide our readers with topical monographs as well as graduate texts.

New York, New York Frederick F. Ling

vii Preface

While I was writing this book, I was constantly reminded of a story told by a dear friend of mine and it goes something like this: "Sometime in the not too distant past, there was a modern art exhibit being held somewhere at the outskirts of town. It was the first of its kind. It was not well attended. Several fellow artists and the art critics were there to examine the works of a few unknown but rather- high-spirited individuals. Toward the end of the day, in one corner of the room, there emerged a heated discussion. The critics were arguing whether some of the paintings should, in fact, be considered impressionistic, while others were merely classically inspired. At the same time, at the opposite end of the room, the artists themselves were engaging in an equally important discussion. They were heatedly debating where they could get the cheapest turpentine .... " Similarly, in the field of mechatronics, there is a never-ending discus• sion on whether it is a new field or merely an extension or a combina• tion of some existing fields. There seems to be no agreement on what the field should be called. Is it mechatronics, mechano-informatics, intelligent mechanisms, smart products, computerized machines, information-driven mechanical systems, or computer-controlled electromechanical systems? On the other hand, fortunately, there is almost perfect agreement among the researchers themselves. Although due to a variety of packaging reasons, we still disagree on the name, at least we are in agreement that in recent years, much efforts and resources from both industry and academia have been focused on an exciting body of activities which in the most simplis• tic sense can be categorized as those involving interaction of mechanics, electronics, and information. We recognize that similar to other emerging technologies during their infancy stage, these activities are driven to exis• tence by real-world needs rather than by pure intellectual curiosity. And as such, they inevitably, and indeed necessarily, cross the existing boundaries of well-established academic disciplines. Those of us who work in the field are excited about the future, but unlike the critics, none of us can accurately predict how mechatronics is going to

ix x Preface evolve or what it will eventually be called. All we know is that there are materials that need to be taught at our universities that have not been taught before, there are concepts that ought to be integrated that have not been integrated before, and there are research opportunities that can be exploited that have not been exploited before. Until the dust settles and the historians have their final say, all we can do now is be guided by our own experience, vision, and intuition. In that sense, this book is a reflection of my own personal aspiration and limitation. My purpose in writing this book is based on my desire to share them with my fellow artisans.

This book evolved from a set of classnotes that I had prepared at UCLA for a graduate course on computer-controlled electromechanical systems. Over the years, the students who attended this course had come from a variety of technical backgrounds and therefore had different needs and ex• pectations. Many of the students majored in aerospace control, especially those who were interested in control of large flexible space structures and aerospace vehicles. For them, this course provided a unique opportunity to explore, ob• serve, and appreciate the interaction between control and electromechanics. In the process, they also gained some intuitive understanding of the physics behind electromechanical sensors and actuators which they otherwise would not have received from the typical control curriculum. A small minority of the students majored in structural mechanics but had an interest in control. They therefore were in the class for the same reason, except they saw things from a mechanics perspective. The majority of the students who attended this course were interested in doing research on electromechanical systems, robotics, precision engineer• ing, or manufacturing automation. They are the primary audience of this book.

In this book, I try to present materials that are both elementary and fundamental. Whenever possible, mathematical modeling is combined with physical understanding and the working equations are almost always de• rived from first principles. From experience, I have found that students typically need very little in the way of prerequisites, except a solid under• graduate education in mechanical engineering. The skills that they need are calculus, physics, vibration, strength of material, and classical control. This book is divided into two parts as suggested by the title: electrome• chanics and contromechanics. The main focus of Part I is to explore various issues related to electromechanical sensors and actuators. After a brief re• view of the fundamental concepts of classical mechanics in Chapter 2, we xii Preface

Obviously, this book is not meant to be the final word on the subject of mechatronics. The best that I can say is that, in my mind, it represents a small step toward establishing mechatronics as a stand-alone respectable academic discipline, which has long been my desire. In addition to my friends and my family to whom I have dedicated this book, the people whom I wish to thank the most are my former graduate students and friends, Greg, Sudarshan, Makato, and Shan-Shuong; I only hope that they have learned from me as much as I have learned from them. I also wish to thank the students who have attended my graduate class at UCLA for giving me the opportunity to teach so I can learn.

DENNY K. MIU UCLA,1992 Preface xi begin this book by dealing with the important topic of electromagnetics in Chapters 3 and 4. The emphasis here is not on electromagnetic radiation as in most available textbooks, but rather on concepts related to work and energy. I attempt to teach students basic principles in order to illustrate the physics beh!nd electrostatic and electrodynamic devices. In Chapter 5, we apply this fundamental understanding to simple devices such as DC motors and stepper motors. In Chapter 6, we investigate the connection between electricity and mechanics by way of piezoelectric ef• fects. Unlike earlier chapters which deal with discrete spring-mass systems, here we introduce continuous systems such as elastic layers under dynamic transverse loading. In Part II, the focus is shifted to the interaction between electromechanics and control. Similar to Chapter 2, a brief review of the fundamental con• cepts in classical control is presented in Chapter 7. In Chapter 8, students learn about the stability of colocated and noncolocated computer-controlled electromechanical systems. Specifically, we explore the physical interpreta.• tion of transfer function poles and zeros of electromechanical systems with multiple in-the-Ioop energy storage elements. The materials presented here include both discrete and continuous systems. The last two chapters are more research-oriented; Chapter 9 is on resid• ual vibration and Chapter 10 active damping. Finally, in Appendix D, some real-world electromechanics and contromechanics problems involving a commercial mechatronic system, the magnetic recording computer rigid disk drive, are described. This book is presented in the format of a research monograph but can be and has been used as a graduate textbook; some short problem sets are included in the earlier chapters.

Emerging fields are inherently interdisciplinary. In the case of mechatron• ics, at the very least, it is a field that combines electromagnetics, mechanics, and control. None of the researchers I know who are currently doing research in the field of mechatronics are formally trained in all three disciplines. We typically start with a solid education in one field and acquire the other skills as needed. However, I feel very strongly that in order for mechatron• ics to evolve into a single discipline suitable for teaching at a university, our understanding of the physical phenomena that exist in and between these separate domains must be unified. Only then, can mechatronics progress from a field that inherently involves multiple disciplines into a single disci• pline that happens to involve multiple energy storage media. Contents

Series Preface vii

Preface ix

1 Introduction 1 1.1 Background ...... 1 1.2 The concept of energy flow 2 1.3 Exercises ...... 5

Part I Electromechanics 7

2 Review of Classical Mechanics 9 2.1 Newton's second law 9 2.2 Rigid bodies .... 12 2.3 Deformable bodies 15 2.4 References . . . . . 20

3 Fundamentals of Electromagnetics 22 3.1 Coulomb's law 22 3.2 Lorentz's law 25 3.3 Biot-Savart law 25 3.4 Faraday's law . 26 3.5 Maxwell's equations 30 3.6 Conservation of charge . . 32 3.7 Maxwell's equations (continued) 33 3.8 References ...... 35

xiii xiv Contents

4 Electromagnetic Energy 36 4.1 Electrostatics . . . . 36 4.2 Electrostatic energy 38 4.3 Dielectrics . . . 40 4.4 Magnetostatics ... 43 4.5 Ferromagnetics .... 44 4.6 Induction and inductance 48 4.7 Electromagnetic energy 51 4.8 Kirchhoff's laws...... 56 4.9 Maxwell's equations (revisited) 57 4.10 Exercises 59 4.11 References ...... 60

5 Examples of Electric Machines 61 5.1 DC motors .. 61 5.2 Stepper motors 66 5.3 Exercises 71 5.4 References . . . 72

6 Introduction to Piezoelastics 74 6.1 Dynamics of elastic layer . . 76 6.2 Dynamics of dielectric layer 83 6.3 Dynamics of piezoelastic layer . 84 6.4 Exercises 90 6.5 References ...... 92

Part II Contromechanics 95

7 Review of Classical Control 97 7.1 Dynamic systems . 97 7.2 Laplace transforms 100 7.3 Transfer functions 102 7.4 Time response 104 7.5 Feedback control 107 7.6 Other topics . . . 111 Contents xv

7.7 Exercises . 111 7.8 References. 112

114 8 Poles and Zeros 8.1 Discrete systems 115 8.2 Continuous systems 122 8.3 Migration of zeros 126 804 Pole/zero pairing . . 131 8.5 Discrete systems (nonminimum phase) 134 8.6 Continuous systems (nonminimum phase) 138 8.7 Summary 150 8.8 Exercises 150 8.9 References . 155

9 Residual Vibration 157 9.1 Point-to-point control ...... 157 9.2 Necessary and sufficient condition. 159 9.3 Relevance to existing techniques 160 9.4 Laplace domain synthesis technique. 163 9.5 Minimum energy control . . . . 164 9.6 Minimum jerk control ..... 172 9.7 Frequency band-limited control 175 9.8 Summary 180 9.9 Exercises 182 9.10 References . 182

10 Active Damping 185 10.1 Background . 185 10.2 Problem definition ...... 186 10.3 Three-dimensional piezoelasticity 187 lOA Laminated piezopolymer plate theory 190 10.5 Dynamics of a simple PVDF laminar . 195 10.6 References ...... 198 xvi Contents

Part III Appendices 201

A Units and Constants 203

B Review of Vector Calculus 205 B.1 Differential vector calculus . 205 B.2 Integral vector calculus . 207

C Elasticity Tensor 211 C.1 Definition of tensors 211 C.2 Elasticity tensor ... 212

D Disk Drive Mechatronics 214 D.1 System description ...... 214 D.2 Electromechanics: moving-coil actuator. . . . . 215 D.3 Contromechanics: read/write head suspension. 218 D.4 Contromechanics: track-seeking servo .. 223 D.5 References...... 228

Index 231