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MODELING

In collaboration with René DAVID. Directeur de recherche émérite CNRS. Hassane ALLA. Professeur à l'UJF. MODELING. BY HYBRID PETRI NETS. état de la vanne. en fermeture. g. ouverte. b. d. en ouverture. a. fermée. temps. t1. t2. t3. t4. Discrete Event Systems. Motivation.

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MODELING

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

  2. état de la vanne en fermeture g ouverte b d en ouverture a fermée temps t1 t2 t3 t4 Discrete Event Systems

  3. Motivation Objective : Systems DynamicAnalysis

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

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

  6. DISCRETE PETRI NETS CONTINUOUS PETRI NETS HYBRID PETRI NETS

  7. P 1 T 3 P P 2 4 T 2 T 1 P 3 T 4 Firing of T1 P 1 T 3 P P 2 4 T 2 T 1 P 3 T 4 Discrete PN

  8. Continuous PN

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

  10. TIMING IN DISCRETE PETRI NETS & CONTINUOUS PETRI NETS

  11. Machine M1 Machine M2 Buffer 1 Buffer 2 P1 1 T1 P3 2 P2 T2 P4 1 3 Timing in a Discrete PN

  12. Tank 1 V2 = 2 liter/sec V1 = 3 liter/sec Pump Tank 2 Timing in a Continuous PN

  13. 1 1 Discrete System : Approximation P1 P1 T1 P3 d1= T1 2 V1= 2 P2 P2 75 T2 P4 d2= T2 V2=3 3 Continuous model Discrete model

  14. P1 T1 V1=2 P2 75 T2 V2=3 = = ü v ( t ) V 2 1 1 ï pour t < 75 ý ï = = v ( t ) V 3 þ 2 2 = = ü v ( t ) V 2 1 1 ï pour t ³ 75 ý ï = = v ( t ) V 2 þ 2 1 Continuous System : Approximation m1 m2 m1(t)=(3-2)t=t 75 m2(t)=75-t t 0 0 75

  15. Continuous System : exact model

  16. Maximum Firing Speeds Depending on Time

  17. 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

  18. AUTONOMOUS HYBRID PETRI NETS

  19. Influence of the Discrete Part on the Continuous Part

  20. Influence of the Continuous Part on the Discrete Part

  21. Transformation of Continuous Marking into Discrete Marking

  22. Transformation of Discrete Marking into Continuous Marking

  23. General Case

  24. TIMED HYBRID PETRI NETS

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

  26. APPLICATION EXAMPLES

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

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

  29. Production System

  30. Water Supply System

  31. Water Supply System

  32. Transfer Line

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

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

  35. Natural sources Emitter1 Emitter2 Communication network valve valve buffer • Tank valve valve Receiver1 Receiver2 • Consumptions Modeling Tools • Water supply system:

  36. V1 V2 Flow of messages V4 V4 Natural source 2 • Natural source 1 • t • t • T1 • T2 V1 V2 V2 V1 V3 V3 Transmittingsources • Tank • t • t buffer • T4 V4 V4 • T3 V3 V3 Receivingsources • Consumption 1 • Consumption 2 An analogy

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

  38. E1 Rt4 Rt1 R E2 Rt3 Rt2 E3 Congested network Networks architecture Network capacity?

  39. Expiration of Tempo • Losses of data Tempo E R congestion window (Ko) cwnd = 1 Congestion Avoidance 22 acq Tempo Thres1 16 cwnd = 2 Thres2 Tempo acq 11 Slow start 8 cwnd = 4 4 acq 2 1 Number of transmission Resume of slow start Congestion control Algorithms of TCP: Slow start Congestion Avoidance

  40. 0+ 0+ V1 V2 V2 V1 R E1 Rt Cnl 1 Cnl 2 T’1 T1 T2 T’2 V1 T ”1 V T3 C A transmission line Case of transmission line merged in Internet environment

  41. Related Models

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

  43. 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 .

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