Concise Encyclopedia of Modelling & Simulation

680 Pages·1992·27.141 MB·English

by  D.P. Atherton and P. Borne (Eds.)

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CONCISE ENCYCLOPEDIA OF
MODELLING & SIMULATION
Editors
DEREK Ρ ATHERTON
University of Sussex, Brighton, UK
PIERRE BORNE
Institut Industriel du Nord, Villeneuve d'Ascq, France
Series Editor-in-Chief
MAD AN G SINGH
UMIST, Manchester, UK
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First edition 1992
Library of Congress Cataloging in Publication Data
Concise encyclopedia of modelling & simulation / editors,
Derek P. Atherton, Pierre Borne. — 1st ed.
p. cm. — (Advances in systems, control, and information
engineering)
Includes bibliographical references and index.
1. Computer simulation—Encyclopedias. 2. Mathematical
models—Encyclopedias. I. Atherton, Derek P. II. Borne,
Pierre. III. Title: Concise encyclopedia of modelling and
simulation. IV. Series.
QA76.9.C65C657 1992
003* .3—dc20 91-33278
British Library Cataloguing in Publication Data
Atherton, Derek P.
Concise encyclopedia of modelling & simulation.—
(Advances in systems, control & information engineering)
I. Title II. Borne, Pierre III. Series
620.00724
ISBN 0-08-036201-X
©™ The paper used in this publication meets the minimum requirements of the
American National Standard for Information Sciences—Permanence of Paper for Printed
Library Materials, ANSI Z39.48-1984.
Printed and bound in Great Britain by BPCC Wheatons Ltd, Exeter
HONORARY EDITORIAL ADVISORY BOARD
Chairman
John F Coales CBE, FRS
Cambridge, UK
Editor-in-Chief
Madan G Singh
UMIST, Manchester, UK
D Aspinall J Lesourne G Schmidt
UMIST, Manchester, UK Conservatoire National Technische Universität München
des Arts et Métiers, Germany
Κ J Aström Paris, France
Lund Institute of Technology
Sweden Β Tamm
Ρ A Payne Tallinn Technical University
UMIST, Manchester, UK Estonia
A Bensoussan
INRIA, Le Chesnay, France
A Ρ Sage M Thoma
George Mason University Universität Hannover
Ρ Borne
Fairfax, VA, USA Germany
Institut Industriel du Nord
Villeneuve DAscq, France
A W Goldsworthy OBE Y Sawaragi R Vichnevetsky
Jennings Industries Ltd Japan Institute for Systems Rutgers University
Victoria, Australia Research, Kyoto, Japan New Brunswick, NJ, USA
vi
FOREWORD
With the publication of the eight-volume Systems & Control Encyclopedia in September 1987,
Pergamon Press was very keen to ensure that the scholarship embodied in the Encyclopedia
was both kept up to date and was disseminated to as wide an audience as possible. For these
purposes, an Honorary Editorial Advisory Board was set up under the chairmanship of
Professor John F. Coales FRS, and I was invited to continue as Editor-in-Chief. The new work
embarked upon comprised a series of Supplementary Volumes to the Main Encyclopedia and
a series of Concise Encyclopedias under the title of the Advances in Systems, Control and
Information Engineering Series. This task involved me personally editing the series of
Supplementary Volumes with the aim of updating and expanding the original Encyclopedia
and arranging for the editing of a series of subject-based Concise Encyclopedias being
developed from the Main Encyclopedia. The Honorary Editorial Advisory Board helped to
select subject areas which were perceived to be appropriate for the publication of Concise
Encyclopedias and to choose the most distinguished experts in those areas to edit them. The
Concise Encyclopedias were intended to contain the best of the articles from the Main
Encyclopedia, updated or revised as appropriate to reflect the latest developments in their
fields, and many totally new articles covering recent advances in the subject and expanding on
the scope of the original Encyclopedia.
Professor Derek Atherton and Professor Pierre Borne contributed a number of articles for the
Simulation Techniques and Model Simplification subject area in the Systems Ü Control
Encyclopedia and both are well known and respected figures in the field of modelling and
simulation. They have gathered together as contributors to the Encyclopedia most of the
leading experts within the field to provide a comprehensive and well balanced collection of
articles covering all aspects of the subject.
Modelling and simulation has roots that can be traced back to the Newtonian era, but it is now
emerging as a discipline in its own right largely due to the great advances that have been made
in line with advances in computing technology. It is a discipline that has applications in all
areas of engineering and the physical sciences, but its boundaries are not yet well defined and
the two main approaches—from physical sciences and from operations research—are still in
the process of unification. As the field matures, emphasis is switching from simulation to
modelling. This volume reflects the changing emphasis within the area and covers all recent
advances in modelling and simulation. It will prove valuable to engineers, physical scientists,
control scientists and all those with an interest in the design, modelling and simulation of
theoretical and physical systems.
Madan G Singh
Series Editor-in-Chief
vii
PREFACE
Modelling is a key aspect of any study or investigation. We can often only discuss sensibly a
topic for which we have a model in mind, whether it be some aspect of economic behavior, the
effects of a drug on a person, the performance of a transportation system or the behavior of a
physical process. In this Concise Encyclopedia we are primarily concerned with the last of
these; other topics are addressed in detail in other Concise Encyclopedias in the Advances in
Systems, Control and Information Engineering series. There are many types of physical
processes of interest to the engineer and scientist and many representations that may be used
for modelling them. The form of model used for a particular process may depend on various
factors, such as the purpose for which the model is being used, the ease with which the
representation yields relevant information and the accuracy of data expected from the model.
Many forms of models are available: knowledge-based, data-based, linguistics-based,
graphical or mathematical. All these model types are discussed in this volume but the main
emphasis is placed on mathematical models and their various forms. Although simulation and
other computational techniques can be used to study and evaluate the behavior of mathematical
models many algorithmic techniques are only applicable to linear mathematical models. These
models, if described continuously in time, can be either distributed or lumped parameter, the
former leading to partial differential equations and the latter leading to differential equations.
A common representation for the latter is a state-space description and several articles describe
various aspects and transformations of state-space representations. An important area covered
is that of model reduction, a procedure for reducing the order of a state-space representation,
which, for example, may lead to a simplification in the analysis of a system containing the
model. Some physical processes may have inputs and outputs which are known only at discrete
points in time, in which case they can be described by difference equations or discrete state-
space representations. Much of the theory of discrete systems parallels that of continuous
systems, for example the ^-transform replaces the Laplace transform: both of these topics are
subjects of articles in the Encyclopedia.
There are two main approaches to obtaining mathematical models of physical processes,
namely by using known physical relationships for the elements involved or by means of an
identification experiment, where a model is obtained from records of its input-output data. The
first approach requires knowledge of the behavior of system elements and is to some extent the
domain of the specialist in, for example, mechanical systems, electrical systems or thermal
plant; topics which are covered together with many others in various articles. Identification too
has many facets: whether it is done off line, in which case the modeller may be able to choose
the input signal; on line, where the available signals provided by the process operation have to
be used; the choice of model order; and the form of model representation. Several articles
address these and other aspects of identification.
As indicated earlier, nonlinear models, as distinct from linear models, may present difficulties
for the analyst who wishes to use them to obtain additional information. Simulation therefore
plays an extremely important role in analyzing nonlinear models as computational methods
provide the only general means for analyzing nonlinear systems. Articles describing various
aspects of simulation and other computational approaches such as the finite-difference and
finite-element methods provide coverage of these powerful techniques. Before use a model
must be validated to check that its behavior is satisfactory for the proposed use and procedures
for achieving this are discussed in several articles.
This Concise Encyclopedia contains articles giving a broad coverage of the field of
modelling and simulation which should be of value to the practising engineer, researcher or
postgraduate student.
The Editors would like to thank Professor Madan Singh for the opportunity to prepare an
Encyclopedia covering this important field. Of course, this project would not have been
possible without the valuable contributions of the authors of the articles, and our thanks is
extended to them. The administrative load in preparing a work of this kind is enormous and the
help of our secretarial staff during the course of the project has been much appreciated. Finally,
we are grateful for the support and cooperation of Mr Peter Frank and the editorial staff at
Pergamon Press and for their efforts in preparing the volume for publication.
D Ρ Atherton and Ρ Borne
Editors
ix
GUIDE TO USE OF THE ENCYCLOPEDIA
This Concise Encyclopedia is a comprehensive reference The nature of an encyclopedia demands a higher
work covering all aspects of modelling and simulation. degree of uniformity in terminology and notation than
Information is presented in a series of alphabetically many other scientific works. The widespread use of
arranged articles which deal concisely with individual the International System of Units has determined that
topics in a self-contained manner. This guide outlines such units be used in this Encyclopedia. It has been
the main features and organization of the Encyclopedia, recognized, however, that in some fields Imperial
and is intended to help the reader to locate the maximum units are more generally used. Where this is the case,
amount of information on a given topic. Imperial units are given with their SI equivalent quantity
Accessibility of material is of vital importance in a and unit following in parentheses. Where possible,
reference work of this kind and article titles have the symbols defined in Quantities, Units, and Symbols
therefore been selected not only on the basis of article published by the Royal Society of London have been
content, but also with the most probable needs of the used.
reader in mind. An alphabetical list of all the articles Most of the articles in the Encyclopedia include a
contained in this Encyclopedia is to be found on pp. bibliography giving sources of further information.
xiii and xiv. Each bibliography consists of general items for further
Articles are linked by an extensive cross-referencing reading and/or references which cover specific aspects
system. Cross-references to other articles in the of the text. Where appropriate, authors are cited in
Encyclopedia are of two types: in-text and end-of- the text using a name/date system as follows:
text. Those in the body of the text are designed to
refer the reader to articles that present in greater detail ...as was recently reported (Smith 1990).
material on the specific topic under discussion. They
generally take one of the following forms: Jones (1988) describes...
...as fully described in the article Simulation The contributors' names and the organizations to
Modelling Formalism: Bond Graphs. which they are affiliated appear at the end of all the
articles. All contributors can be found in the alphabetical
...or on simulation (see Identification: Maximum List of Contributors, along with their full postal address
Likelihood Method). and the titles of the articles of which they are authors
or coauthors.
The cross-references listed at the end of an article The most important information source for locating
serve to identify broad background reading and to a particular topic in the Encyclopedia is the multilevel
direct the reader to articles that cover different aspects Subject Index, which has been made as complete and
of the same topic. fully self-consistent as possible.
xi
ALPHABETICAL LIST OF ARTICLES
Abstract Realization Theory Finite-Element Method
Aeronautics and Space Systems Flexible Manufacturing Systems
Aggregation Flexible Spacecraft Dynamics
Aggregation, Chained Fluid Flow Control
Aggregation: Model Reduction Forecasts
Aircraft Dynamics: State Equations Fuzzy Models
Algorithms Heating, Ventilation and Cooling Systems: Digital
Approximate Realization Theory: Comparison of Simulation
Optimal Methods Hybrid Analog-Digital Computers
Automatic Modelling of Three-Dimensional Objects Hypotheses
Balanced Realization of Linear Stationary Dynamic Identification
Systems Identification: Basic Problem
Bayes' Rule Identification: Correlation Methods
Biological and Biomedical Systems Identification: Experiment Design
Causality Identification: Frequency-Domain Methods
Chaotic Behavior Identification: Least-Squares Method
Chemical Engineering Simulation Identification: Maximum Likelihood Method
Chemical Reactor Modelling Identification: Model Structure Determination
Closed-Loop Systems Identification: Practical Aspects
Closed Systems Identification: Pseudorandom Signal Method
Cognition Identification: Recursive Methods
Combined Discrete and Continuous Models: Firmware Identification: Time-Domain Methods
Comparison Systems Identification: Transient- and Frequency-Response
Composite Systems Methods
Constraints Information Processing
Controls Inputs
Correlation Integrodifferential Systems
Coupling Interactive Simulation Model and Program Generation
Data International Association for Mathematics and
Databases Computers in Simulation
Decomposition International Federation of Automatic Control
Deterministic Systems Iteration
Difference Equations, Ordinary Kaiman Filters
Differential Equations Knowledge Bases
Digraphs Laplace Transforms
Discrete Variables Laplace Transforms and Bode Diagrams
Distillation Columns: Bilinear Models Large Stochastic Systems
Distributed Model Simulation Software Linear Systems
Distributed Parameter Systems Linear Systems: Kronecker Canonical Forms and
Distributed Parameter Systems: Space and Time Invariants
Decomposition Linearization
Dynamic Systems Markov Processes
Dynamic Systems Modelling: Basic Principles of Matrix Triangularization: Givens Transformations
Lumped Parameter Systems Matrix Triangularization: Householder
Dynamic Systems Modelling: Distributed Parameter Transformations
Models and Discretization Mechanical Systems Simulation
Effective Systems Methodology
Emulation and Microprogramming Model-Based Fault Diagnosis
Entropy Model Simplification: Frequency-Domain Approach
Estimation Modelling of Industrial Robots
Events Models
Exogenous Variables Multibond Graphs
Extrapolation Multidimensional Systems Modelling
Feedback Loops Multitimescale Systems
Finite-Difference Method Multitimescale Systems: Dynamical Location
xiii
Alphabetical List of Articles
Multivariable Systems Similarity
Nonlinear Effects and Their Modelling Simulation Languages
Nonlinear Systems Simulation Modelling Formalism: Bond Graphs
Nonlinear Systems: Approximation by Simple State- Simulation Modelling Formalism: Ordinary Differential
Space Models Equations
Nuclear Reactor Modelling Simulation Modelling Formalism: Partial Differential
Object-Oriented Simulation Equations
Observability Singular Perturbations: Boundary Layer Problem
Observers Singular Perturbations: Discrete Version
Open-Loop Systems Singular Systems
Ordinary Differential Equation Models: Numerical Smith-McMillan Canonical Forms for Rational
Integration of Initial-Value Problems Matrices
Ordinary Differential Equation Models: Symbolic Spectral Methods
Manipulation Stability
Ordinary Differential Equations State-Space Modelling and Transformations
Outputs State-Space Modelling: Square Root Algorithms
Parameters State Variables
Partial Differential Equation Models: Numerical Stochastic Processes
Solution Structural Analysis
Partition Structural Analysis: Graph Representation
Perturbations Structure and Parameter Identification by Simulation
Petri Nets Experimentation
Petri Nets for the Design of Control of Discrete Systems
Production Systems Taxonomy
Polynomial Matrices in Systems Theory Time Horizons
Power Electronics Systems: Petri-Net Modelling Traffic and Transportation Systems
Power Plants: Modelling Transfer Functions
Power Plants: Nonlinear Modelling Transients
Power System Component Identification: Transport Equations
Pseudorandom Signal Method Truncation
Power Systems: Steady-State Power Flow Modelling Validation
Processes Validation of Identified Models
Project Management: Network Models Validation of Simulation Models: General Approach
Random Variables Validation of Simulation Models: Statistical Approach
Reliability Variables
Robustness Verification
Robustness in Model-Based Fault Diagnosis Vibrations and Vehicle Dynamics
Sampled Data Systems Water Distribution Systems: Steady-State Analysis
Samples Wave Propagation in Periodic Structures
Servovalves, Electrohydraulic Workshop Dynamic Modelling
Ship Dynamics Identification and Modelling z-Transform Method
xiv
A
Abstract Realization Theory Given initial state x(0) (resp. jt ), it is easy to write
n
the solution of Eqns. (1):
There is always a trade-off in systems theory between
the generality and scope of the model under consider-
ation, and the number of properties that can be derived y(t) = HeF'x(0)+ Γ He'('-r)Gw(r) dr, t^O (2a)
J
from it. Inherited from classical mechanics and from 0
electrical network theory, the linear constant multivari- k
able dynamical system seems to strike a happy medium; ^ H F ^O + ^HF^-'GH/, k^O (2b)
it can often reasonably be used as an exact model or a /=i
first-order approximation, and has been very exten-
The contribution of the input function u to the output
sively studied so that a wealth of results are known
function y is thus given by the convolution of u with
about it. the kernel function HeF'G (resp. {HF*_G, }), known
The purpose of this article is to relate the external
as the impulse response of the system (it is the output of
behavior of such a system (i.e., the way it transforms
the system corresponding to zero initial conditions and
input functions of time into output functions of time)
the unit pulse input
and its internal structure (i.e., the way it can be built
from physical components). It will lead to existence ό(0 ο 0
theorems for linear systems having a prescribed exter- ο o(o 0
nal behavior, as well as to some of their fundamental
properties. 0 <H0J
" 1 0
0 0
7. Introduction resp. {u = , υ. = 0, k*0}
0
Lo
1J
We shall first define more precisely the object of our
study. of dimension m).
DEFINITION 1. An m-input, p-output, n-dimensional The terms of the kernel sequence {HF*"'G} or the
linear constant dynamical system is a triplet of matrices successive derivatives at zero of the analytic kernel
Σ = (F, G, H) where F is an nx η matrix (the transition function HeF'G are enough to specify the input-output
map), G is nxm (the input map) and H is pxn (the correspondence defined by the system. These terms,
output map).
A* = HF*-'G (3)
For the purpose of this article, the coefficients of
these matrices belong to a field Κ (essentially the real are called the Markov parameters of the system.
or complex numbers or finite fields), and we can inter- Other representations can be given of this input-
pret Σ either as a continuous time system output correspondence. If we call *(z), w(z), y(z) the
Laplace transforms of x(0, u(t), y (ή (resp. the ζ trans-
x(t) = Fx(t) + Gu(t) forms of {xk}, {uk}, {yk}), then Eqn. (la) transforms into
y(t) = Hx(t) (la) zx(z) = Fx(z) + Gu(z)+x(0)
y(z) = Hx(z) (4)
or as a discrete time system
Hence, assuming JC(0) = 0,
x+i = Fx + Gu
k k k y(z) = H(zl-F)-lGu(z) (5)
(lb)
(exactly the same results are obtained from Eqn. (lb)
where ueK'" (the input space), xeX=K" (the state by replacing JC(0) by x). This function, Z =
{)
space) and y e Kp (the output space). The dimension of H(zl — F)~'G, is called the transfer function of the
the state space η is called the dimension of the system. system. It is the Laplace transform (resp. ζ transform)
Other interpretations of this model are possible of the impulse response.
(e.g., as a linear delay-differential system, a two- This transfer function is a rational matrix, which
dimensional filter or a discrete time system with dis- represents a linear mapping from functions of ζ (trans-
cretized coefficients) by taking matrices F, G and H forms of the input) into functions of ζ (transforms of
over a ring. the output).
1