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Advanced Textbooks in Control and Signal Processing
Series Editor
Professor Michael J. Grimble, Professor of Industrial Systems and Director
Professor Michael A. Johnson, Professor Emeritus of Control Systems and Deputy Director
Industrial Control Centre, Department of Electronic and Electrical Engineering,
University of Strathclyde, Graham Hills Building, 50 George Street, Glasgow G1 1QE, UK
Other titles published in this series:
Genetic Algorithms
K.F. Man, K.S. Tang and S. Kwong
Neural Networks for Modelling and Control of Dynamic Systems
M. Nørgaard, O. Ravn, L.K. Hansen and N.K. Poulsen
Fault Detection and Diagnosis in Industrial Systems
L.H. Chiang, E.L. Russell and R.D. Braatz
Soft Computing
L. Fortuna, G. Rizzotto, M. Lavorgna, G. Nunnari, M.G. Xibilia and R. Caponetto
Statistical Signal Processing
T. Chonavel
Discrete-time Stochastic Processes (2nd Edition)
T. Söderström
Parallel Computing for Real-time Signal Processing and Control
M.O. Tokhi, M.A. Hossain and M.H. Shaheed
Multivariable Control Systems
P. Albertos and A. Sala
Control Systems with Input and Output Constraints
A.H. Glattfelder and W. Schaufelberger
Analysis and Control of Non-linear Process Systems
K. Hangos, J. Bokor and G. Szederkényi
Model Predictive Control (2nd Edition)
E.F. Camacho and C. Bordons
Digital Self-tuning Controllers
V. Bobál, J. Böhm, J. Fessl and J. Macháček
Principles of Adaptive Filters and Self-learning Systems
A. Zaknich
Control of Robot Manipulators in Joint Space
R. Kelly, V. Santibáñez and A. Loría
Robust Control Design with MATLAB®
D.-W. Gu, P.H. Petkov and M.M. Konstantinov
Control of Dead-time Processes
J.E. Normey-Rico and E.F. Camacho
Robotics
B. Siciliano and L. Sciavicco
Publication due October 2007
B. Hrúz and M.C. Zhou
Modeling and Control
of Discrete-event
Dynamic Systems
with Petri Nets and Other Tool
123
Branislav Hrúz, PhD MengChu Zhou, PhD
Department of Automatic Control Systems Department of Electrical
Faculty of Electrical Engineering and Computer Engineering
and Information Technology New Jersey Institute of Technology
Slovak University of Technology Newark, NJ 07102
812 19 Bratislava 1 USA
Slovak Republic
British Library Cataloguing in Publication Data
Hruz, B. (Branislav)
Modeling and control of discrete-event dynamical systems :
with Petri nets and other tools. - (Advanced textbooks in
control and signal processing)
1. Discrete-time systems - Mathematical models 2. Automatic
control - Mathematical models 3. Petri nets
I. Title II. Zhou, MengChu
003.8
ISBN-13: 9781846288722
Library of Congress Control Number: 2007929991
Advanced Textbooks in Control and Signal Processing ISSN 1439-2232
ISBN-13: 978-1-84628-872-2 e-ISBN-13: 978-1-84628-877-7
Printed on acid-free paper
© Springer-Verlag London Limited 2007
MATLAB® is a registered trademark of The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760-
2098, USA. http://www.mathworks.com
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reprodu-
ced, stored or transmitted, in any form or by any means, with the prior permission in writing of the
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sent to the publishers.
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of
a specific statement, that such names are exempt from the relevant laws and regulations and therefore
free for general use.
The publisher makes no representation, express or implied, with regard to the accuracy of the infor-
mation contained in this book and cannot accept any legal responsibility or liability for any errors or
omissions that may be made.
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Springer Science+Business Media
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To our wives Mira and Fang Chen
Series Editors’ Foreword
The topics of control engineering and signal processing continue to flourish and
develop. In common with general scientific investigation, new ideas, concepts and
interpretations emerge quite spontaneously and these are then discussed, used,
discarded or subsumed into the prevailing subject paradigm. Sometimes these
innovative concepts coalesce into a new sub-discipline within the broad subject
tapestry of control and signal processing. This preliminary battle between old and
new usually takes place at conferences, through the Internet and in the journals of
the discipline. After a little more maturity has been acquired by the new concepts
then archival publication as a scientific or engineering monograph may occur.
A new concept in control and signal processing is known to have arrived when
sufficient material has evolved for the topic to be taught as a specialised tutorial
workshop or as a course to undergraduate, graduate or industrial engineers.
Advanced Textbooks in Control and Signal Processing are designed as a vehicle
for the systematic presentation of course material for both popular and innovative
topics in the discipline. It is hoped that prospective authors will welcome the
opportunity to publish a structured and systematic presentation of some of the
newer emerging control and signal processing technologies in the textbook series.
In society today, much of the modern technological infrastructure is event
driven where the system outcome is often dependent on a benign sequence of
desirable actions taking place. In industry, the action sequence may be highly
structured and deterministic but, elsewhere in the community, the action sequence
may be fuzzy or even stochastic, making the constraint of a safe system control
sequence a much more difficult task. Many of the sequential event-driven systems
found today, may be modelled as discrete-event dynamic systems (DEDS). The
characterising features of DEDS are discrete states that capture the status to change
value at discrete time points. In DEDS, the (logical) conditions that lead to
individual or sets of events being activated to generate a sequence of changing
system states is an important part of the system and its mathematical model. This
viewpoint contrasts with much of the standard control literature which is often
dominated by the exhaustive treatment of systems described by linear or nonlinear
ordinary differential equations systems or even, occasionally, spatially-dependent
partial differential equation systems.
As the references in this book show, the tools to describe DEDS, analyse their
performance and generate control algorithms have been under development since
viii Series Editors’ Foreword
the late 1970s. However, it appears that around 1990 there was a flurry of
publications as Petri nets and other techniques began to receive serious
consideration. Now, in 2007, sufficient development has taken place for this course
textbook on the Modeling and Control of Discrete-event Dynamic Systems to enter
the Advanced Textbooks in Control and Signal Processing series. Professors
Branislav Hrúz and MengChu Zhou have had many years of experience of teaching
courses in the methods of DEDS and we are pleased to welcome their new volume
into the series.
This textbook is comprised of three groups of chapters. The first group,
Chapters 1–5, is concerned with establishing the basis mathematical tools for the
modelling and control of DEDS. This includes chapters on the application of
mathematical graph theory, the ideas of formal language concepts and finite
automata. The concepts and structure of control for DEDS appears in Chapter 5.
Graphical techniques for DEDS then dominate the second group of chapters, 6–
11. These techniques start with flow diagram methods in Chapter 6. This short
chapter is followed by four key chapters, 7–10, on Petri nets. These chapters detail
the basics (Chapter 7), and the properties (Chapter 8) of Petri nets, and then move
on to Grafcet in Chapter 9 and the timed, colored, fuzzy and adaptive varieties of
Petri nets in Chapter 10. A brief look at statecharts and their link to Petri nets in
Chapter 11 closes this second group of chapters.
The final grouping of three chapters looks at what might be termed DEDS
tasks. Chapter 12 has a strong implementation focus with a useful section on ladder
logic diagrams and comments on how Petri nets might contribute to this
widespread programmable-logic-controller programming paradigm. The problems
of supervisory control and job scheduling are considered in the last two chapters of
this final group.
The practitioner will be interested to see the applicability of the DEDS
techniques illustrated by the wide range of systems used as examples in the
textbook. There is a large group of examples based on the problems of flexible
manufacturing systems (FMS). These are based on different cell structures using
components like ‘pick and place’ robots, milling units, conveyor belt systems,
storage units or bins, and workpiece sorting units. Fortunately, all these
components are easily understood by the non-manufacturing specialist and so
provide good accessible introductory examples. Manufacturing industry
transportation systems based on automatic guided vehicles (AGVs) are also used in
examples. Real system complexity is soon experienced by the reader when FMS
and AGV systems are interlinked.
Other examples used in the textbook include crane-based loading systems,
tank-filling systems, distributed computer systems, motor- and motion-control
systems. The discussion of a two-tank-filling system (given in Chapter 8) provides
an alternative view of a control problem often treated in classical control
engineering textbooks. The problem of modelling the operation of a pedestrian
crossing and the human resources problem of when three participants will make it
to a meeting give a fascinating illustration of the potential of DEDS techniques to
model and analyse problems in fields far removed from manufacturing.
Industrial Control Centre M.J. Grimble
Glasgow, Scotland, U.K. M.A. Johnson
December 2006
Preface
For whatsoever doth make manifest is light
Ephesians 5.13
This book presents results of research achieved in friendly collaboration across
borders and moreover between continents and emphasizes a belief in engineering
science being for the benefit of mankind the world over. This aspect of the book’s
ethos is epitomized by the authors’ profiles, one being from Central Europe and
one from the USA.
Motivation
A number of years ago research work on a woodworking process control raised our
interest in discrete event dynamic systems (DEDS). We remembered that the
process was an automatic production of laminar parquetry precasts. Work-piece
preparation and composition included many discrete events and concurrent
processes. Since then, we have started a systematic study of DEDS. Each school
year since 1993, we have given lecture courses on DEDS within the Master
program at the Department of Automatic Control Systems, Faculty of Electrical
Engineering and Information Technology of the Slovak University of Technology
in Bratislava, and undergraduate and graduate programs in the Department of
Electrical and Computer Engineering, New Jersey Institute of Technology, Newark,
NJ 07102, USA, respectively.
The presented textbook contains most of the lecture material gradually
elaborated in the courses of the past ten years. Our teaching activities have been
accompanied by significant research and student projects in the field of DEDS,
mainly on various topics concerning Petri nets used for modeling, analysis,
performance evaluation, discrete-event control, supervisory control, and job
scheduling of manufacturing processes, automatic guided vehicles in flexible
manufacturing, assembly/disassembly processes, computer networking, and
workflow management. Other discrete event models and their applications under
our study include statecharts, ladder logic diagrams, finite state machines, digraphs,
and Grafcet.
While performing the teaching and research activities, we have felt a strong
need for a textbook that systematically and comprehensively introduces the
x Preface
mathematical background and various modeling tools for the purpose of DEDS
analysis, performance evaluation, control, and scheduling. Thus students and
researchers of various background can easily learn and grasp the essence of DEDS
that is of growing importance. Their demand and the needs arising from our
teaching, research and development activities motivate us to write this present
book.
Contents
The mentioned lectures and this book particularly concentrate on Petri nets and
their use in the modelling and control design for DEDS. They serve as a basis for
extending to other tools and approaches such as Grafcet, statecharts, supervisory
control theory and job scheduling. The textbook contains the necessary
mathematics and computer science material. It includes discrete mathematics,
formal languages, and finite automata. They are essential for non-computer
science/engineering students to master the subjects of DEDS. Such material helps
one describe and understand the nature of DEDS as well as the methods to describe
and govern them. Standard and reactive flow diagrams are then introduced. The
substance and properties of Petri nets and other tools useful for the modeling of
DEDS have been built up systematically. Advanced Petri net tools include timed,
stochastic, colored, fuzzy, and adaptive Petri nets. Petri net-related tools include
Grafcet (also terms Sequential Function Charts), and statecharts. Various aspects
concerning control design methods are followed consistently throughout the
textbook. Theoretical aspects are illustrated and explained using numerous
problem-solving examples dealing with various computer-integrated systems. We
summarize the contents of all fourteen chapters as follows.
Chapter 1 introduces the concept of systems and states, continuous, discrete-
time, and discrete-event systems, the definition and properties of DEDS, and some
system examples. Basic transition systems are described in detail as the most
fundamental representation of DEDS.
Chapter 2 presents directed graphs, subgraphs, and directed paths and circuits
in them. Examples are given to illustrate these concepts.
Chapter 3 introduces the concept of formal languages and their classification.
They form the basis for many theoretical developments in both computer science
and supervisory control theory of DEDS.
Chapter 4 discusses DEDS control system including specifications and control
functions.
Chapter 5 introduces the concept of finite automata or state machines. It
discusses through examples how they can be used to describe a real system and
how control specification can be described with their help. Non-deterministic finite
automata are also presented.
Chapter 6 discusses the standard flow diagrams used in software development
and reactive flow diagrams for DEDS.
Chapter 7 introduces the idea of Petri nets, their basic definition, matrix
representation, and various classes. It also discusses how they can be interpreted
for control purposes.
Preface xi
Chapter 8 presents the important properties of Petri nets and their implications
in modelled systems. Analysis methods based on reachability trees are elaborated.
Examples are given. The structural properties of Petri nets are also discussed.
Chapter 9 presents Grafcet (also named sequential function chart) – its presence
in industry is significant, especially among automatic control and automation
equipment companies. Its comparison with Petri nets is given.
Chapter 10 introduces the advanced concepts resulting from the study of Petri
nets and industrial needs in exploring their utility. They include deterministic and
stochastic timed Petri nets for performance evaluation purposes. Colored Petri nets
are used to specify complex systems with many similar subsystems, components or
specifications. Fuzzy Petri nets combine fuzzy set theory and Petri nets to describe
uncertainty embedded in many practical applications. Adaptive Petri nets further
embed learning capability into Fuzzy Petri nets.
Chapter 11 presents the idea of statecharts and their applications to complex
system design.
Chapter 12 introduces modeling methodology, conflict resolution, ladder logic
diagrams, and control program design for DEDS.
Chapter 13 presents the essential concepts of supervisory control theory based
on automata and Petri nets. Several fundamental approaches are presented.
Chapter 14 discusses the job scheduling problems and the use of Petri nets for
such purposes. The solution method based on max-plus algebra is also introduced.
Aim and Use of this Textbook
This book aims to introduce to students, engineers and researchers the
fundamentals of various discrete event modelling tools, as well as applications.
The discrete mathematics and related background material are included. It is
suitable for class use and can be easily tailored to meet the different needs from
senior undergraduate and graduate students. In an introductory course to DEDS for
engineering students, the following contents are suggested:
Chapters 1–8, and 11
For a more advanced course in DEDS and for students with required
mathematics and entry-level knowledge of DEDS, the following contents should
be offered:
Chapters 1, 2, 4, 7–14.
For computer science and engineering students, such materials as discrete
mathematics, formal language, and automata can be skipped or only their brief
review is needed.
Acknowledgements
We would like to express our deep gratitude to all who helped us and supported
our effort in writing this book, especially our wives, children and parents. We
would acknowledge the professionalism demonstrated by the staff members of
