Table Of ContentEngineering Applications of MATLAB® 5.3
and SIMULINK® 3
Springer
London
Berlin
Heidelberg
New York
Barcelona
Hong Kong
Milan
Paris
Singapore
Tokyo
Mohand Mokhtari and Michel Marie
Engineering Applications
of MATLAB® 5.3 and
SIMULINK® 3
Translated from the French by Mohand Mokhtari, Michel Marie,
Cecile Davy and Martine Neveu
, Springer
Mohand Mokhtari, PhD
Valeo THERMIQUE HABITACLE, 8 rue Louis Lormand, BP 13, 78321
La Verriere Cedex, France
Michel Marie, PhD
Institut Lemonnier, BP269, rue d'Herouville 14031, Caen, France
ISBN 978-1-85233-214-3 Springer-Verlag London Berlin Heidelberg
British Library Cataloguing in Publication Data
Mokhtari, Mohand
Engineering applications of MA TLAB 5.3 and SIMULINK 3
1.MATLAB (Computer file) 2.SIMULINK (Computer file)
3.Engineering -Computer simulation 4.Engineering
mathematics -Data processing
I. Title II.Marie, Michel
620.00285'5369
ISBN 978-1-85233-214-3
Library of Congress Cataloging-in-Publication Data
Mokhtari, Mohand, 1954-
Engineering applications of MAT LAB 5.3 and SIMULINK31 Mohand Mokhtari and
Michel Marie.
p.cm.
Includes bibliographical references and index.
ISBN 978-1-85233-214-3 (alk. paper)
1. Engineering mathematics--Data processing. 2. MATLAB. 3. SIMULINK. I. Marie
Michel, 1964-II. Title.
TA345 .M57 2000
620'.001'SI--dc21 99-089481
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publishers.
e-ISBN-13:978-1-4471-0741-5
DOl: 10 .1 007/978-1-4471-0741-5
© Springer-Verlag London Limited 2000
MA TLAB® and SIMULINK® are registered trademarks of The Math Works Inc.,
http://www.mathworks.com
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a
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Typesetting: Camera ready by author
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Foreword
In recent years MATLAB®, together with SIMULINK® and the many associated toolboxes,
has became a standard in the fields of engineering, simulation and numerical calculation.
A veritable programming environment in themselves, MATLAB® and SIMULINK® bring
unequalled possibilities of resolution and simulation in the fields of numerical calculation and
the study of dynamic systems to students and professionals alike. These features are enhanced
by excellent graphic visualisation in 2D and 3D.
The originality of this book is to intelligently marry theory and practice. The theory is
exposed in the first half of the work, the second part of the work being devoted to the study of
real applications of control process and signal processing.
This approach allows the reader, at any stage, to see the importance of the theory worked out
in practical examples and follow the examples with their theoretical structure presented in a
clear and concise way.
The presentation of these applications begins with an initial mathematical study of the
physical processes leading to the discrete modelling stage.
In each of these case studies, the authors demonstrate the power of MA TLAB® and
SIMULINK® tools as well as the power of the toolboxes dedicated to the control of processes,
fuzzy logic, neuronal networks and signal processing.
This enlightening approach gives the reader (novice or specialist) a clear and thorough
understanding of these tools.
The authors do not limit themselves to the traditional framework of commands and the
representation of states but also approach the fields of fuzzy logic and neural networks. Their
many years of teaching associated with their many research projects in these areas ensure us
of the objective importance of these, alas little known, techniques.
Two appendices are given over to the study of concrete examples of two significant features
of SIMULINK®; encapsulation of sets of blocks and the modelling of S-Functions.
Encapsulation or masking facilitates the presentation of clear and concise hierarchical models
and the S-Functions allow the reader to extend the library of SIMULINK® by the addition of
supplementary blocks specific to its field of application.
Aided by the many screenshots and graphs, the reader can easily appreciate the precision of
these tools.
vi Foreword
Already acknowledged as a reference for technicians, engineers and academics, the latest
enhancements of MA TLAB® and SIMULINK® strengthen the quality of these tools. This
book extensively explores each of their facets and so, in itself, becomes an invaluable new
toolbox.
Joel Courtois
Doctor in Computer Science
Manager of EPITA
(Ecole Pour l'Informatique et les Techniques Avancees)
School of Computer Engineering, Paris
Preface
MATLAB® is a high-level computing language. It is widely used in industry, universities and
engineering schools. It has become a necessary tool in engineering and scientific research,
thanks to its simplicity of use and its great power in calculation and visualisation.
In addition, many toolboxes exist which are dedicated to a specific scientific field.
The additional SIMULINK® tool makes possible the modelling and simulation of analogue
dynamic systems whether analogical, discrete or hybrid, using a graphic blocks representation
Since the release of its 5th version, new functionalities such as multidimensional arrays,
object-oriented programming, structures and cells, have enabled MATLAB®, to become a real
programming language.
This book is divided into two parts. The first one refers to the notions and theoretical bases
necessary for a good understanding of the techniques used in the second part, which deals
with process control and numerical signal processing.
Each application is dealt with using several techniques, including classical methods of
automatic control, and both deterministic and random discrete signal processing, as well as
fuzzy logic and neural networks.
The preliminary mathematical study of the modelling of physical processes starts by
producing the equations that link their inputs/outputs to the editing of their analogical or
discrete models.
In the use of M-files, the focus is placed on SIMULINK® and the S-functions for which an
appendix has been created.
The encapsulation (masking) of a set of SIMULINK® blocks, the creation of personalised
libraries -which is one of the main functionalities in SIMULINK® is studied in the appendix.
We have used the functions and blocks of SIMULINK® of the "Control System TOOLBOX",
"Signal Processing TOOLBOX", "Neural Network TOOLBOX" and "Fuzzy Logic
TOOLBOX".
This book is dedicated to any technician, engineer, university or industrial researcher who
will find in it the necessary mathematical tools, as well as the means offered by MA TLAB®
Toolboxes and SIMULINK® to solve any modelling or numerical computing problems in a
quick and efficient way.
viii Preface
Teachers, students and engineers will find this book an effective aid to the study and control
of dynamic systems.
The M-files and SIMULINK® models developed in this book are collected on a CD ROM to
enable the reader to carry out these programs easily.
Contents
Chapter 1: Analog and digital control ................................................................ 1
1. The principle ......................................................................................................................... 1
2. Presentation of main types of corrector.. ............................................................................... 2
2.1. Proportionnal corrector .............................................................................................. 2
2.2. Integral control ........................................................................................................... 3
2.3. Derivative corrector .................................................................................................... 3
2.4. Derivative return corrector ......................................................................................... 4
2.5. Phase lead corrector ................................................................................................... 5
2.6. Phase lag corrector ..................................................................................................... 7
2.7. PID controller. ............................................................................................................ 9
2.8. Predictive action corrector ....................................................................................... 13
2.9. PIR corrector, pure delay system .............................................................................. 14
3. Analog correctors discretisation .......................................................................................... 15
4. Corrected systems stability .................................................................................................. 16
4.1. General conditions of stability ................................................................................. 16
4.2. Nyquist criterion ....................................................................................................... 17
4.3. Discrete systems stability ......................................................................................... 17
5. Examples ............................................................................................................................. 18
5.1. Using some MATLAB® functions ............................................................................ 18
5.2. Using a PIR corrector ............................................................................................... 24
6. LQ, LQI, quadratic linear control... ..................................................................................... 27
6.1. LQI control of a monovariable process .................................................................... 27
6.1.1. Model without integrator. .............................................................................. 27
6.1.2. Model with integrator .................................................................................... 28
6.2. LQI control of a multi variable process ..................................................................... 28
6.2.1. LQ multi variable control ............................................................................... 29
6.2.2. LQI multi variable control .............................................................................. 30
6.3. Application example ................................................................................................ 30
6.3.1. LQI control of a monovariable aerothermal system ...................................... 31
6.3.2. LQI control of a multivariable system ........................................................... 36
7. RST control ......................................................................................................................... 38
7.1. Monovariable system ............................................................................................... 38
7.2. Multi variable system ................................................................................................ 40
7.3. Application example ................................................................................................ 40
7.3.1. RST monovariable control of the temperature ............................................. .41
7.3.2. RST multivariable control of the aerothermal process ................................. .43
x Contents
Chapter 2: State representation of continuous and discrete
systems .................................................................................................... 47
1. State representation of continuous systems ......................................................................... 47
1.1. Heuristic approach ................................................................................................... 47
1.2. State representation generalization ........................................................................... 49
2. State representation of discrete systems ........... '" ................................................................ 50
2.1. Heuristic approach ................................................................................................... 50
2.2. Application ............................................................................................................... 52
3. Controllability and observability ......................................................................................... 53
3.1. Controllability .......................................................................................................... 53
3.2. Observability ............................................................................................................ 53
4. State reconstruction of a discrete dynamic system .............................................................. 54
4.1. Closed-loop estimation of a deterministic process ................................................... 54
5. State return control .............................................................................................................. 56
6. Examples ............................................................................................................................. 57
6.1. State return control system of a process including an integration ........................... 57
6.2. State return control system of a process not including an integration ...................... 65
6.3. Control system by poles placing of a discrete system ............................................... 74
7. Kalman filter ....................................................................................................................... 78
8. Discrete stochastic Kalman predictor .................................................................................. 89
Chapter 3: Fuzzy logic control ............................................................................. 95
1. The fundamental principle .................................................................................................. 95
2. Stages of implementation of a fuzzy regulator .................................................................... 96
2.1. Fuzzification stage .................................................................................................... 96
2.2. Inference stage .......................................................................................................... 97
2.3. Defuzzification stage .............................................................................................. 100
3. Graphical interface of the" Fuzzy Logic TOOLBOX" ..................................................... 104
4. Creation of a fuzzy system using the toolbox commands .................................................. 109
4.1. Input and output variables fuzzification ................................................................. 11 0
4.2. Fuzzy Rules Editor ................................................................................................. 113
4.3. Defuzzification ....................................................................................................... 119
4.4. Using the regulator in a control law ....................................................................... 120
5. Fuzzy regulator use in SIMULINK® ................................................................................. 127
6. Sugeno's method ............................................................................................................... 131
6.1. Realisation of the fuzzy regulator using the graphic interface ................................ 131
6.2. Realisation of the fuzzy regulator using the TOOLBOX commands ..................... 139
Chapter 4: Neural networks ................................................................................ 149
1. Introduction ....................................................................................................................... 149
2. Linear adaptive neural networks ....................................................................................... 150
2.1. Architecture ............................................................................................................ 150
