Preview Continuous System Modeling
Continuous System Modeling Fran9ois E. Cellier Continuous System Modeling With 288 Figures Springer Science+Business Media, LLC Fran~ois E. Cellier, Ph.D. Deparbnent of Electrical and Computer Engineering and Applied Mathematics Program University of Arizona Tucson, AZ 85721 USA Library of Congress Cataloging-in-Publication Data Cellier, Fran~ois E. Continuous system modeling I Fran~ois E. Cellier. p. em. Includes bibliographical references (p. ) and index. Contents: Modeling ISBN 978-1-4757-3924-4 ISBN 978-1-4757-3922-0 (eBook) DOI 10.1007/978-1-4757-3922-0 l. Simulation methods. 2. Computer simulation. 3. Mathematical models. I. Title. T57.62.C26 1991 620'.00l'l3-dc20 90-25286 Printed on acid-free paper. © 1991 Springer Science+Business Media New York Originally published by Springer-Verlag New York, Inc. in 1991 Softcover reprint of the hardcover l st edition 1991 All rights reserved. This work may not be translated or copied in whole or in part without the written per mission of the publisher Springer Science+ Business Media, LLC. except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the for mer are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Camera-ready copy prepared by the author. 987654321 ISBN 978-l-4757-3924-4 to Ursula for all these years of friendship Parasitism: In the beginning, there was Chaos. Chaos nurtures Progress. Progress enhances Order. Order tries to defy Chaos at all cost . . . . But the day Order wins the final battle against Chaos, there will be mourning. 'Cause Progress is dead. Fran~ois E. Cellier September, 1990 Preface Modeling and simulation have become endeavors central to all dis ciplines of engineering and science. They are used in the analysis of physical systems where they help us gain a better understanding of the functioning of our physical world. They are also important to the design of new engineering systems where they enable us to predict the behavior of a system before it is actually built. Model ing and simulation are the only techniques available that allow us to analyze arbitrarily nonlinear systems accurately and under varying experimental conditions. The two books, Continuous System Modeling and Continuous Sys tem Simulation, introduce the student to an important subclass of these techniques. They deal with the analysis of systems described through a set of ordinary or partial differential equations or through a set of difference equations. These books do not describe the tech niques of discrete-event modeling and simulation since those are quite distinct from the techniques that are at the heart of our dis cussion, and since excellent texts can be found on the book market that deal with discrete-event modeling and simulation explicitly and exclusively. However, this does not mean that the systems which can be tackled by either of the two classes of modeling and simulation techniques are necessarily different. One and the same system can often be modeled either through differential equations or through discrete events, depending on the granularity level of the desired model. Yet, as the reader may have already noticed, my two books are quite bulky as they are, and adding the concepts of discrete event modeling and simulation to the text would have meant adding several hundred pages more. I felt that this was not justified. This book introduces the concepts of modeling, i.e., it describes the transition from the physical system itself down to an abstract description of that system in the form of a set of differential and/or difference equations. This text has a flavor of the mathematical dis cipline of dynamical systems, and is strongly oriented towards the Newtonian physical sciences. The concepts of mass and energy con servation, and the laws of thermodynamics are at the heart of the ix x Preface discussion. Various modeling techniques such as bond graphs and System Dynamics are introduced, and various specialized software tools such as DYMOLA and STELLA are presented, techniques and tools which support the process of modeling. While some chapters introduce new modeling techniques, others exercise previously intro duced concepts by means of virtually hundreds of practical examples. I believe strongly in the idea of "learning through practice." While the basic modeling concepts are introduced in methodology chap ters, many of the tricks -the blows and whistles of modeling- are presented in the flow of discussing examples. The companion book, Continuous System Simulation, introduces the concepts of simulation, i.e., it describes the transition from the mathematical model to the trajectory behavior. This text has a fla vor of the mathematical discipline of applied numerical analysis. It introduces some ofthe techniques currently available for the numeri cal integration of differential equations, it talks about the generation of random numbers and the design of statistical experiments, and it introduces parameter estimation techniques. Finally, the basic principles behind the design of simulation software and simulation hardware are presented from a computer engineering point of view. Here at the University of Arizona, the material is taught in two consecutive courses which are open to both graduating seniors and graduate students, and this is the ideal setting for use of these books in a classroom environment. The texts are organized in such a man ner that they contain only a few cross references between them. Con sequently, it is feasible to study the material described in the com panion book prior to the material contained in this book, although I recommend starting with this book. The material is perfectly un derstandable to juniors as well (no junior level prerequisites for these courses exist), but the teacher will have to keep a fairly rapid pace in order to make it through an entire volume in one semester, and he or she must rely on home reading. This pace may be too stiff for most juniors. That is, when teaching these topics at junior level, the teacher will probably have to restrict himself or herself to covering the first few chapters of each text only, and for that purpose, better textbooks are on the market, books which cover these introductory topics in broader depth. The two texts have been written by an engineer for engineers. They teach the essence of engineering design. Engineering intuition is often preferred over mathematical rigor in the derivation of for mulae and algorithms. My home department is the Department of Electrical and Computer Engineering. However, the two courses are Preface xi cross-listed in the Computer Science Department, and they are reg ularly attended by graduate students from the Aeronautical and Me chanical Engineering Department, the Systems and Industrial Engi neering Department, and the Applied Mathematics Program. These students perform equally well in the classes as our own students, which reflects the fact that the applications covered in these courses stem from a wide variety of different topic areas. Due to the interdisciplinary nature of the subject matter, each chapter has been organized as a separate entity with a "front matter" and a "back matter" of its own. Thus, each chapter is in fact a minibook. The front matter consists of a Preview section which tells the student what she or he can expect from the chapter. The bulk of the chapter contains a number of subsections. It often starts with an Introduction, and it always ends with a Summary. The back matter starts with the Reference section, often followed by a Bibliography section which is not meant to be exhaustive, but which can provide the student with a selected set of pointers for further reading. Following the bibliography, all chapters offer a Homework Problems section. More difficult homeworks are marked with an asterisk. Most homeworks can be solved within a few hours. Most chapters also have a Projects section which is meant to provide the student with ideas for senior projects and/or masters' theses. This section shows to the student that the topics mastered can be directly applied to larger and more serious problems. Finally, many chapters end with a Research section in which open research problems are presented which might be tackled by M.S. or Ph.D. students in their theses and/ or dissertations. The projects and research sections are meant to enhance the student's motivation since they show that the topics learned can be used in serious research. These sections are not meant to be discussed in class, but are recommended for home reading. Studying science is fun, and understanding science by means of mathematical models is even more fun. I experience the development of these textbooks as an extremely creative and rewarding endeavor which provides me with much satisfaction. I hope that my own fascination with the subject matter is reflected in my books and will prove to be highly contagious. Fran~ois E. Cellier Tucson, Arizona, October 1990 About This Book This text introduces concepts of modeling physical systems through a set of differential and/o r difference equations. The purpose of this endeavor is twofold: it enhances the scientific understanding of our physical world by codifying (organizing) knowledge about this world, and it supports engineering design by allowing us to assess the consequences of a particular design alternative before it is physically built. The text contains 15 chapters which only partially depend on each other. A flowchart of the chapter dependencies is shown below. Chapter 1 introduces the basic terminology and provides the student with a motivation for the class. xiii xiv About This Book Chapter 2 introduces the primary concepts behind the user inter face of state-of-the-art simulation software. At the end of Chapter 2, the student should be able to use continuous-system simulation languages such as DARE-P, DESIRE, and ACSL, and she or he should be able to formulate simple differential equation models in terms of these software systems. Chapters 3 and 4 introduce basic modeling concepts used in elec trical engineering (Kirchhoff's laws applied to RLC circuits) and in mechanical engineering (Newton's law applied to spring-damper mass systems). These concepts are very basic, and every engineer can be expected to master these concepts irrespective of his or her home department. I usually defer the last few pages of Chapter 4 (the Euler equation, the Lagrangian, and the Hamiltonian) to home reading and do not request this material in any tests. Chapter 5 deals with the concepts of modular and hierarchical modeling. It is shown how hierarchical models can be implemented in current simulation languages using macros, and the shortcom ings of this approach are demonstrated. The modeling language DYMOLA is introduced as an alternative, which provides for true modular modeling. Chapter 6 is the first of a series of more specialized chapters. It deals with advanced concepts of electronic circuit modeling. It intro duces SPICE, the most common among today's circuit simulators, and it shows how DYMOLA might be used as an alternative. DY MOLA provides much more insight into the internal structure of sub models than SPICE does. When I teach this course, I skip over the details of the bipolar transistor model and refer this to home reading not requested on any test. This chapter can be easily skipped ex cept for the section "How DYMOLA Works," which should be read in preparation for the next chapter. Chapter 7 is an important methodological chapter. It introduces the concept of bond graph modeling which provides the student with a tool essential to the understanding of the functioning of physical systems in general. The chapter contains a short survey of bond graph modeling software and discusses in greater detail how DY MOLA can be used for bond graph modeling. Chapter 8 applies the freshly mastered methodological tool of the bond graph to phenomena of thermodynamics, namely, conduction, convection, and radiation. This chapter sheds light on the mecha nisms of power flow and energy conservation in general. Mastering the knowledge provided in this chapter can be expected of all en-
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