MODELING BY HYBRID PETRI NETS Hassane ALLA Professeur

MODELING BY HYBRID PETRI NETS Hassane ALLA Professeur à l'UJF In collaboration with René DAVID Directeur de recherche émérite CNRS 1

Discrete Event Systems état de la vanne en fermeture g ouverte en ouverture b d a fermée temps t 1 t 2 t 3 t 4 2

Motivation Objective : Systems Dynamic Analysis 3

Motivation (cont’d) Large numbers: continuous approximation may be convenient t t 4

Outline DISCRETE, CONTINUOUS and HYBRID PETRI NETS TIMING IN DISCRETE & CONTINUOUS PETRI NETS AUTONOMOUS and TIMED HYBRID PETRI NETS APPLICATION EXAMPLES CONCLUSION 5

DISCRETE PETRI NETS CONTINUOUS PETRI NETS HYBRID PETRI NETS 6

Discrete PN P 1 T 2 T 3 P 2 P 4 T 1 P 3 T 4 P 1 T 2 Firing of T 1 T 3 P 2 P 4 T 1 P 3 T 4 7

Continuous PN 8

Hybrid PN m 2 T 1 1 T 2 4 T 3 0 0 1 2 m 1 T 2 9

TIMING IN DISCRETE PETRI NETS & CONTINUOUS PETRI NETS 10

Timing in a Discrete PN Machine M 1 Buffer 1 Machine M 2 Buffer 2 P 1 P 3 1 2 T 1 P 2 P 4 1 3 T 2 11

Timing in a Continuous PN Tank 1 V 2 = 2 liter/sec V 1 = 3 liter/sec Pump Tank 2 12

Discrete System : Approximation P 1 P 3 d 1= 1 2 P 1 T 1 P 2 P 4 1 d 2= 3 V 1= 2 T 1 P 2 75 T 2 Discrete model V 2 = 3 T 2 Continuous model 13

Continuous System : Approximation m 1 m 2 P 1 m 1(t) = (3 -2) t = t V 1=2 T 1 75 m 2(t)=75 -t P 2 75 V 2=3 T 2 0 t 0 v 1 (t ) =V 1 = 2 ü ï ý pour t < 75 v 2 (t ) =V 2 = 3ïþ 75 v 1 (t ) =V 1 = 2 ü ï ý pour t ³ 75 v 2 (t ) =V 1 = 2ïþ 14

Continuous System : exact model 15

Maximum Firing Speeds Depending on Time 16

Generalization The basic rules related to an autonomous continuous PN are verified The instantaneous firing speeds may be defined in various ways First example Second example 17

AUTONOMOUS HYBRID PETRI NETS 18

Influence of the Discrete Part on the Continuous Part 19

Influence of the Continuous Part on the Discrete Part 20

Transformation of Continuous Marking into Discrete Marking 21

Transformation of Discrete Marking into Continuous Marking 22

General Case 23

TIMED HYBRID PETRI NETS 24

Example of Hybrid PN Tank 1 V 4=2 liter/sec Valve L V 3 = 3 liter/sec Pump Tank 2 25

APPLICATION EXAMPLES 26

Performance evaluation of a production System Electronic components assembly-test workshop (diodes and transistors) (Motorola in Toulouse – France) Wafer 400 -5000 Chips Chip 27

Performance evaluation of a production System (cont’d) Electronic components assembly-test workshop (diodes and transistors) (Motorola in Toulouse – France) Wafer Cutting Molding Furnace Test 28

Production System 29

Water Supply System 30

Water Supply System 31

Transfer Line 32

Controlled system via Communication Networks q Use of the communication networks to carry out tasks of control Actuators System Communication Networks Controller q Sensors E Not deformed reception of informations: (delays, flows capacities, losses) E Real time System : Temporal accuracy Network Control System NECS Project 33

Controlled system via Communication Netwo -Motivations q Open loop control Communication networks Control device Process q Modeling of the networks Messages: Continuous flows Decisions of routing or emission: Discrete events Networks communications can be represented by hybrid tools of modeling : hybrid Petri Nets 34

Modeling Tools E Water supply system: Natural sources valve Emitter 1 Emitter 2 valve buffer Tank valve Communication network valve Receiver 1 Receiver 2 Consumptions 35

An analogy V 1 V 2 Flow of messages Natural source 2 Natural source 1 T 2 V 1 Transmitting sources Tank buffer T 3 T 4 V 3 Consumption 1 V 4 Consumption 2 V 3 V 4 t Receiving sources t 36

Communication Network: Network architectures Backbone of US Backbone of Europe Regional network Network IP bus National network Network IP ring Network IP bus Internet = Set of interconnected sub-network Selected reference model: TCP/IP 37

Networks architecture Network capacity? E 1 Rt 1 E 2 Rt 4 R Rt 3 E 3 Congested network 38

Congestion control Algorithms of TCP: Slow start Congestion Avoidance cwnd = 1 acq Tempo cwnd = 2 acq Tempo acq congestion window (Ko) Tempo cwnd = 4 Expiration of Tempo Losses of data R E 22 16 11 8 4 2 1 Thres 2 Congestion Avoidance Slow start Number of transmission Resume of slow start 39

A transmission line Case of transmission line merged in Internet environment E 1 0+ V 1 T’ 1 Cnl 1 V 1 Rt T 1 V 2 T 2 V 1 T ” 1 0+ Cnl 2 V 2 R T’ 2 C V T 3 40

Related Models 41

Conclusion Continuous systems have been studied for a long time Modeling, analysis and control of DES have undergone major developments in recent decades In recent years a need has emerged to consider systems which are partially continuous and partially discrete CONTINUOUS Petri nets and HYBRID Petri nets can be used for modeling these systems 42

Bibliography SURVEY REFERENCES H. Alla, R. David, Continuous and Hybrid Petri Nets, Journal of Circuits, Systems and Computers, Special Issue on Petri Nets, Vol 8 No 1, 1998 pp. 159 -188. R. David, H. Alla, On Hybrid Petri Nets, Discrete Event Dynamic Systems, Theory and Applications, Kluwer Academic Publishers, 11, 9 -40, 2001. R. David and H. Alla, Discrete, Continuous, and Hybrid Petri Nets, in preparation, to be published by Springer, Heidelberg, 2004. BIBLIOGRAPHY ON HYBRID PETRI NETS www. diee. unica. it/~aldo/bibliohpn. html by Alessandro Giua & Aldo Piccaluga, Dip. di Ingegneria Elettrica ed Elettronica, Università di Cagliari, Italy. 43