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Modelling of hybrid systems based on extended coloured Petri nets

  • Y. Y. Yang
  • D. A. Linkens
  • S. P. Banks
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 999)

Abstract

In this paper the modelling of hybrid systems, which are composed of both discrete event subsystems and continuous subsystems, is addressed. A general system structure for the hybrid system modelling is proposed along with their formulations. Based on these concepts, an extended coloured Petri net (ECPN) is proposed in order to implement the hybrid system modelling. Key ideas introduced in extended coloured Petri nets are dynamic colours, dynamic transitions, and dynamic places, which make ECPNs capable to model both variables governed by continuous dynamics and the ordinary Petri net tokens for discrete events. Thus, two aspects of hybrid system, continuous variables and discrete events, are unified in ECPNs by the number of tokens and the value of the tokens (defined as the colour state in this paper). A formal definition of ECPNs is also given. Finally, an illustrative example is given which shows how to use the developed approach for hybrid system modelling.

Keyward

Hybrid systems coloured Prtri net modelling and simulation 

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References

  1. 1.
    Fahrland, D. A., Combined discrete event continuous system simulation, Simulation, 1970, Feb., 61–72.Google Scholar
  2. 2.
    Pantelides, C. C., and Barton, P. I., Equation-oriented dynamic simulation: current status and future perspectives, Computers and Chemical Engineering, 1992 17, 263–285.Google Scholar
  3. 3.
    Pantelides, C. C., Gritsis, D., Morison, K. R., and Sargent, R. W. H., The mathematical modelling of transient systems using differential-algebraic equations, Computers and Chemical Engineering, 1988, 12, 449–454.Google Scholar
  4. 4.
    Nerode, A., and Kohn, W., Models for hybrid systems: automata, topologies, controllability, observability, Hybrid Systems, Lecture Notes in Computer Science 736, Springer-Verlag, 1993, 317–346.Google Scholar
  5. 5.
    Antsaklis, P. J., Stiver, J. A., and Lemmon, M., Hybrid system modelling and autonomous control, Hybrid Systems, Lecture Notes in Computer Science 736, Springer-Verlag, 1993, 366–392.Google Scholar
  6. 6.
    Lemmon, M., Stiver, J. A., and Antsaklis, P. J., Event identification and intelligent hybrid control, Hybrid Systems, Lecture Notes in Computer Science 736, Springer-Verlag, 1993, 268–296.Google Scholar
  7. 7.
    Alur, R., Courcoubetis, C., Henzinger, T. A., and Ho, P. H., Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems, Hybrid Systems, Lecture Notes in Computer Science 736, Springer-Verlag, 1993, 209–229.Google Scholar
  8. 8.
    Henzinger, T. A., Manna, Z., Pnueli, A., Towards refining temporal specifications into hybrid systems, Hybrid Systems, Lecture Notes in Computer Science 736, Springer-Verlag, 1993, 60–76.Google Scholar
  9. 9.
    Peterson, J. L., Petri Nets, Computer Surveys, 1977, 9(3), 223–253.Google Scholar
  10. 10.
    Yang, Y. Y., Linkens, D. A., and Banks, S. P., An unified approach for modelling of hybrid systems, Proceedings of the European Simulation Multiconference, Barcelona, Spain, 1–3 June, 1994, 240–244.Google Scholar
  11. 11.
    Deshpande, A. R., Control of Hybrid System, PhD Thesis, University of California, Berkeley, USA, 1994.Google Scholar
  12. 12.
    Ho, Y. C. (Ed.), Discrete Event Dynamic Systems-Analysing Complexity and Performance in Modern World, IEEE Press, 1992.Google Scholar
  13. 13.
    Barton, P. I., and Pantelides, C. C., The modelling and simulation of combined discrete/continuous processes, The 1991 ICHEME Event, 1991, 115–118.Google Scholar
  14. 14.
    David, R. and Alla, H., Petri Nets and Grafcet: tools for modelling discrete event systems, Printice Hall, 1992.Google Scholar
  15. 15.
    Murata, T., Petri nets: Properties, analysis and applications, Proceedings of IEEE, 1989, 77 (4), 541–580.Google Scholar
  16. 16.
    Zuberek, W. M., Timed Petri nets: definition, properties and applications, Microelectron. Reliab., 1991, 31(4).Google Scholar
  17. 17.
    Jensen, K., Coloured Petri Nets: Basic Concepts, Analysis Methods, and Practical Use, Vol. 1, Springer-Verlag, 1992.Google Scholar
  18. 18.
    Christensen, S., and Petrucci, L., Towards a modular analysis of coloured Petri nets, in Jensen, K. (Ed.), Application and Theory of Petri Nets 199S, Lecture Notes in Computer Science 616, Springer-Verlag, 1992, 113–133.Google Scholar
  19. 19.
    Chiola, G., Ajmone, M., Balbo, G., and Conte, G.(1993), Generalized stochastic Petri nets: A definition at the net level and its implementations, IEEE Trans. on Software Eng., 19(2), 89–107.Google Scholar
  20. 20.
    Hatono, I., Yamagata, K., and Tamura, H., Modelling and online scheduling of flexible manufacturing system using stochastic petri nets, IEEE Trans. on Software Engineering, 1991, 17(2).Google Scholar
  21. 21.
    Dubois, D., and Stecke, K. E., Dynamic analysis of repetitive decision-free discreteevent process: the algebra of timed marked graphs and algorithmic issues, Annuls. of Operations Research, 1990, 26, 151–193.Google Scholar
  22. 22.
    Dubois, E., and Alla, H., Hybrid Petri nets with a stochastic discrete part, Proc. of European Control Conference 93, Netherlands, June 1993, 144–149.Google Scholar
  23. 23.
    Yang, Y. Y., Linkens, D. A., and Mort, N., Modelling of a soaking pit/rolling mill process based on extended coloured Petri nets, Proceedings of the IFAC/IFORS/IMACS Symposium of Large Scale Systems Theory and Applications, London, UK, July 11–13, 1995.Google Scholar
  24. 24.
    Lu, Y. Z., and Williams, T. J., Modelling, Estimation and Control of Soaking Pits, ISA Publisher, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Y. Y. Yang
    • 1
  • D. A. Linkens
    • 1
  • S. P. Banks
    • 1
  1. 1.Department of Automatic Control and Syetems EgnineeringUniversity of SheffieldSheffieldUK

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