D.J. Murray-Smith. Department of Electronics and Electrical Engineering University of Glasgow Glasgow UK SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

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1 CONTINUOUS SYSTEM SIMULATION

2 Continuous System Simulation D.J. Murray-Smith Department of Electronics and Electrical Engineering University of Glasgow Glasgow UK SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

3 First edition D.J. Murray-Smith Originally published by Chapman & Hall in 1995 Typeset by EXPO Holdings, Malaysia ISBN DOI / ISBN (ebook) Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the UK Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored, or transmitted, in any form or by any means, without the prior permission in writing of the publishers, or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of licences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to the publishers at the London address printed on this page. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. A catalogue record for this book is available from the British Library Library of Congress Catalog Card Number: (bb) Printed on permanent acid-free text paper, manufactured in accordance with ANSI/NISO Z and ANSI/NISO Z

4 CONTENTS Preface xi 1 The principles of modeling Objectives in the modeling of systems Continuous-variable and discrete-event models Types of continuous-variable model Modeling and simulation procedures for continuous-variable models 4 References 11 2 An introduction to simulation methods The need for simulation Methods of simulation Techniques based on special-purpose simulation hardware Techniques based on general-purpose computer hardware A review of simulation applications 18 References 21 3 Problem organization for continuous system simulation Introduction Descriptions for continuous-variable models: reduced and state-variable forms Conversion from reduced form to state-variable form Transfer function descriptions Bond graph representations One-port components Causality in bond graph representations Junctions in bond graphs Coupling between physical domains Signals in bond graphs Simulation program development from bond graph models Block diagram and signal flow graph representations Block diagram and signal flow graph methods for transfer function simulation The direct construction approach The parallel construction approach The iterative construction approach An example of block diagram construction from a transfer function 37

5 vi Contents 3.8 Modeling of distributed parameter elements Introduction Pure time delay Distributed time delay Simulation models involving pure and distributed delay elements Parameter sensitivity analysis methods in system modeling and simulation Methods for sensitivity co-system simulation Mathematical models of systems having both discrete and continuous elements 47 References 49 4 The principles of numerical modeling An introduction to numerical integration methods Fixed-step integration algorithms: one-step methods Introduction Taylor series descriptions Errors in fixed-step integration methods Explicit Runge-Kutta methods Trapezoidal integration Fixed-step integration algorithms: multistep methods Problems of integration step-size selection and numerical instability Variable-step integration algorithms Problems of 'stiff' models Discontinuities and their effects Numerical methods for discontinuous problems Problems of implicit loop structures 66 References 66 5 Sampled-data models and operator methods Introduction Approximations based on sampled-data theory Modeling of linear systems using sampled-data approximations Cascaded elements Closed-loop systems Modeling of nonlinear systems using sampled-data approximations Cascaded elements Closed-loop models Sampled-data description for a continuous state-space model Linear time-invariant models Operational methods for difference equation models Integration operators Simulation using operational methods Simulation of a single transfer function Simulation of cascaded transfer functions Simulation of linear closed-loop systems Simulation of time-varying and nonlinear models by operator methods Assessment of simulation performance by frequency response methods 83

6 Contents vii Frequency response of discrete integrators 83 References 84 6 The principles of equation-oriented simulation software Introduction Simulation programming using general-purpose high-level languages Simulation programming using matrix packages Simulation packages Simulation programming using simulation languages Introduction The Simulation Councils' 1967 recommendations (CSSL'67) The general structure of simulation programs using CSSL'67-type languages SLIM - a simple continuous system simulation language The main features of the language The syntax of the SLIM language Output facilities and graphics An example of a simulation program in the SLIM language Examples of other simulation languages CSSL IV ACSL DESIRE Comparisons of SLIM with widely used simulation languages 105 References The principles of block diagram-oriented simulation tools Graphical man-machine interfaces for simulation The block-based approach to the description of dynamic systems Examples of block-oriented simulation environments with a graphical user interface A simple simulation example using graphical block-oriented tools 113 References Simple examples using common simulation tools Introduction A coupled-tuned electrical circuit simulation A control system simulation: speed control of a water turbine Simulation of a neural encoder model A constrained pendulum simulation Simulation of a simple digital control system 131 References Internal verification and external validation The need for testing Terminology and definitions Internal verification 142

7 viii Contents Static checks Dynamic checks External validation Theoretical validity Empirical validity Measured response information for empirical validation System identification and parameter estimation methods in the empirical validation process Robustness issues in external validation Possible outcomes of the external validation process Documentation of the validation process 150 References Case study I - a two-tank liquid level control system Introduction Modeling of a pair of interconnected tanks A nonlinear mathematical model Linearization of the model Programs for simulation of the nonlinear coupled-tank system Internal verification of the simulation program External validation of the simulation model Discussion 162 Reference Case study II - an aircraft automatic landing system Introduction Modeling and simulation of an aircraft directional-control system Modeling and simulation of a lateral beam guidance system Discussion 173 References Case study III - respiratory gas-exchange process simulation Introduction and background physiology Modeling of pulmonary gas-exchange processes The computer simulation Discussion 182 References Case study IV - a simulation model of active skeletal muscle Introduction Models of active muscle Simulation of active muscle for constant length conditions Models of active muscle for constant tension conditions and simulation of the after-loaded isotonic twitch Parameter sensitivity analysis 196

8 13.4 Simulation of the complete twitch response and repetitive stimulation 13.5 Discussion References 14 Real-time simulation 14.1 An introduction to real-time applications 14.2 Hardware and software aspects of real-time simulation 14.3 Analog simulation techniques The operational amplifier The summing unit The integrator unit The coefficient unit Multipliers and other nonlinear units Scaling of variables Operating modes 14.4 Digital techniques Real-time integration algorithms Choice of communication interval Error analysis in real-time simulation Multirate methods 14.5 Special-purpose hardware for real-time digital simulation Introduction Array processors and multiprocessor systems Transputer-based parallel systems 14.6 Hardware-in-the-Ioop simulation and partial-system testing 14.7 Applications in training and education Introduction Simulators for operator training Real-time simulation in teaching References 15 Current trends in continuous system simulation 15.1 Developments in simulation languages 15.2 Improvements in the man-machine interface 15.3 Developments involving parallel processor systems Hardware developments in parallel processing for simulation Simulation software for parallel processor systems 15.4 Artificial intelligence and simulation Knowledge-based systems in modeling and simulation Knowledge representation using frames and inheritance Qualitative modeling and qualitative simulation References Appendix A The Laplace transform A.l Introduction A.2 Linearity theorem Contents ix

9 x Contents A3 Differentiation theorem A4 Final value theorem A5 Example Reference Appendix B The transfer function Reference Appendix C Block diagrams and signal flow graphs C1 Introduction C2 Block diagrams C3 Signal flow graphs Reference Appendix D Discrete-time models and sampled-data theory D.1 Introduction D.2 Discrete-time models D.3 Discretization of a continuous-time model D.4 The sampling process References Appendix E SLIM software instructions E.1 Introduction E.2 Hardware requirements E.3 Software installation E.4 Starting and exiting SLIM E.5 Useful hints for using SLIM E.6 Starting and exiting SLIMPLOT E.7 Useful hints for using SLIMPLOT Index

10 computer. This language, which is fully described in Chapter 6, provides a basis for some preliminary work on equation-oriented methods and can be used by the reader to gain practical experience before considering more complex examples involving use of more comprehensive simulation languages, such as ACSL. Although the software provided on the diskette is limited in terms of the size of problems that can be tackled and in the range of facilities provided, it is hoped that it may enhance the text considerably for those having access to a personal computer. The limitations of the language are fully described and comparisons are made, in terms of its facilities and performance, with commercially supported languages. However, it must be emphasized that this software is intended only as an aid to understanding simulation methods and is not a substitute for established and supported modem simulation languages which have many features not included within SLIM. The case studies in Chapters 10, 11, 12 and 13 have been chosen to be of interest to readers with a background principally in engineering, physics or applied mathematics. However, both here and in other sections of the book, some use is also made of bioengineering examples to emphasize the importance of simulation in biomedical fields and to highlight some of the problems that can arise in the modeling and simulation of such systems. In every example background information is provided which is intended to provide readers not active in the field with sufficient information to allow them to understand the problem, the associated mathematical model and the particular simulation issues raised. Care has been taken to ensure that objectives for the simulation work are stated clearly in the case studies presented. Other topics covered in later chapters include real-time simulation techniques, which are of great importance for many types of engineering and laboratory applications, and a brief review of current trends in simula- xii Preface as much as it is of any other computer application area. Recognizing the fact that information inherent in the underlying model is at fault can present serious problems even for experienced users of simulation techniques. Careful consideration must be given to methods of testing and validation. Without this the potential advantages of a simulation approach are nullified. The first chapter of the book sets the scene in this respect with a review of the objectives of modeling and simulation and an account of systematic procedures which help to ensure that these objectives are satisfied. More detailed discussion of the verification and validation of simulation models is presented in later sections, especially in Chapter 9 and in the case study of Chapter 10. The book is intended mainly for readers with little or no previous experience of computer simulation methods but having a reasonably numerate background. An elementary understanding of ordinary differential equations and some knowledge concerning their use in the mathematical modeling of physical systems is necessary. Large sections of the book should also be of value to those already working in the field of computer simulation and modeling. The objective has been to cover the general principles of continuous system simulation methods in a thorough fashion and, through appropriate examples and case studies, to illustrate the application of these principles using modem simulation packages. Both equation-oriented languages and block diagram-based packages are considered. Separate chapters are included which cover the questions of problem description and organization at a mathematical level and the principles of numerical modeling before any attempt is made to discuss specific problem-oriented languages. A simple continuous system simulation language called SLIM (Simulation Language for Introductory Modeling) is provided with the book on a diskette which can be used on any DOS-based IBM-compatible personal

11 PREFACE Computer simulation of dynamic systems is a topic which is growing steadily in importance in the physical sciences, engineering, biology and medicine. The reasons for this trend relate not only to the steadily increasing power of computers and the rapidly falling costs of hardware, but also to the availability of appropriate software tools in the form of simulation languages. Problem-oriented languages of this kind assist those who are not specialists in computational methods to translate a mathematical description into a simulation program in a simple and straightforward fashion. They can also provide useful diagnostic information when difficulties are encountered. Therefore, a simulation language provides, in comparison with languages such as Fortran, Basic, Pascal or C, the same type of advantages for simulation which those standard high-level languages provide over an assembly language for other computer applications. Simulation involves experimentation with models of real systems. The reasons for using a simulation approach to problem solving depend, to some extent, on the field of application. In engineering, simulation techniques can often allow valuable insight to be gained at an early stage in a design, when it would otherwise be unobtainable until a prototype system or scale model was constructed. In some engineering applications, such as the development of aircraft flight-control systems, simulation may be the only feasible and safe approach for initial investigations. Even at much later stages of system development, a simulation-based approach may still be useful, since the required results may often be obtained by simulation more quickly, effectively and cheaply than by experimentation and testing of the real system. System performance can also be investigated using simulation for a much wider range of conditions than can be contemplated for the real system because of operating constraints or safety requirements. Similar factors can apply in other fields, such as biomedical systems engineering. System simulation, using digital computers, can relate either to models based on continuous variables or to discrete-event descriptions. Continuous system simulation techniques are applied to systems described by sets of differential equations and algebraic equations. Such descriptions of dynamic properties are applicable to many types of engineering system, to a wide range of problems in the physical sciences and to certain types of biological system. Discrete-event simulation is also concerned with systems which are dynamic in nature, but in this case events and the times at which they occur are of primary importance. Examples of applications for which discrete-event simulation is important are in air and road traffic control, in manufacturing systems and in the optimization of computer systems or communications networks. This book is concerned primarily with continuous system simulation and includes discussion of di~crete-event techniques only in the context of mixed models which include some discrete elements together with continuous system descriptions. The proper use of simulation techniques cannot be separated from the intelligent use of mathematical models. The concept of 'garbage in, garbage out' is true of simulation

12 tion. Topics covered under this latter heading include the effects of new developments in conventional computer hardware and software, the influence of parallel architectures on simulation methods, and links which are being established between the fields of artificial intelligence and simulation. In preparing a book intended for engineers and scientists in a number of different disciplines it has been recognized that readers may not all be fully familiar with the relevant mathematical techniques. A number of appendices have therefore been included to cover relevant topics such as the Laplace transform, transfer function descriptions and block diagram notation. The graphical routines included in the accompanying software are part of the NAG Graphics Library. This product contains a collection of over 100 carefully designed routines which provides Fortran and C programmers with a convenient and versatile means of producing a graphical representation of numerical and statistical results. It is used worldwide in commerce, financial modeling, industry, academic research and many other areas, and is available for a wide spectrum of machines. Interfaces are also supplied to the most commonly used plotting packages. NAG also provide a wide range of other products such as mathematical and statistical routines in Fortran, C, Pascal and Ada; Fortran 90 compilers and tools; symbolic solvers; data visualization software; linear programming software and a gateway generator which automatically generates MATLAB gateway. For further information, a quotation or details of your local distributor please contact: Preface xiii Sales Department NAG Ltd Wilkinson House Jordan Hill Road Oxford OX2 9BX United Kingdom Many people have contributed to the preparation of this text and the accompanying software. First of all, I wish to thank many students in the Department of Electronics and Electrical Engineering at the University of Glasgow who have assisted in the development of some of the material through their project work, by pointing out errors in sections which have been used to support courses at undergraduate and post-graduate level, and by helping with the development and testing of the SLIM software. In particular, I wish to mention the contribution made by Fran<;ois Gaudaire, who developed many of the XANALOG simulation diagrams used in the examples and case studies of Chapters 8, 10, 11, 12 and 13. I also wish to thank Mingrui Gong for her assistance with some of the model validation results included in Chapter 10. I have also had very helpful feedback from experienced engineers on postgraduate short courses, most recently at one organized by PROPESA at the Centro Tecnico Aeroespacial, Sao Jose dos Campos, Brazil. To all the many individuals who have provided assistance, of one kind or another, I wish to express my sincere appreciation. Finally, I must acknowledge the support, encouragement and patience of my wife, Effie, who has helped to make this book possible. David Murray-Smith Glasgow 1994

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