Table Of ContentContinuous 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-
