New design and simulation of the GDEVS abstraction of an integrator

ABSTRACT

In this paper we present our recent work on generalized discrete event modelling. In the general framework of modelling and simulation of linear systems under time-continuous - or not - signals, the description of the integrator operator becomes fundamental as well as the description the time delay operator and the concept of output feedback. Therefore, this paper shall present the description of an integrator under piecewise linear input trajectories in a first step, then under trajectories described by a sequence of general order polynomials, ensuring a user given accuracy. Moreover, its remarkable behaviour in case of input discontinuities strongly contrast with the rather poor one of classical numerical solvers. Furthermore a thorough comparison with discrete-time simulation techniques, like the classical Euler one, allows the assessment of an important computational gain using the techniques proposed here. Finally, the complete treatment of an hybrid system example not only illustrates the relevance of this approach, but underlines the interest of its application in the more general context of mixed-mode simulation and distributed simulation.

REFERENCES

• 1: Praehofer, H. "'System theoretic formalisms for combined discrete-continuous system simulation'", Int. Journal of General Systems, 19:219--240, 1991.
• 2: Bernard P. Zeigler, Multifacetted modelling and discrete event simulation, Academic Press Professional, Inc., San Diego, CA, 1984
• 3: Bernard P. Zeigler , Tag Gon Kim , Herbert Praehofer, Theory of Modeling and Simulation, Academic Press, Inc., Orlando, FL, 2000
• 4: Norbert Giambiasi , Bruno Escude , Sumit Ghosh, GDEVS: A generalized discrete event specification for accurate modeling of dynamic systems, Transactions of the Society for Computer Simulation International, v.17 n.3, p.120-134, Sept. 2000
• 5: Naamane A., and I. Simeonov. "hybrid mathematical dealing and control of the anaerobic waste waters treatment processes", In Proceedings of Int. Conf. AIS, april 2002, Lisboa, Portugal.
• 6: Jean Claude Carmona , Norbert Giambiasi , Aziz Naamane, Generalized Discrete Event Abstraction of Continuous Systems: Application to an Integrator, Journal of Intelligent and Robotic Systems, v.41 n.1, p.37-64, September 2004 [doi>10.1023/B:JINT.0000049167.10212.48]
• 7: N. Giambiasi and J. C. Carmona, "Generalized Discrete Event Abstration of Continuous Systems: GDEVS formalism", Simulation Modelling Practice and Theory, Elsevier, vol. 14, pp. 47--70, jan. 2006.
• 8: Giambiasi N., A. Naamane, and A. Damiba Simulation, SCSI, vol. 77(1--2):4--22 July-August 2001.
• 9: Damiba, A. "Modélisation et simulation à évènements discrets de Bond Graph", PhD thesis, Université Aix-Marseille 3, France, Oct. 2000.
• 10: David Clark, Handhelds Drive Mixed-Signal Chip Development, Computer, v.33 n.11, p.12-15, November 2000 [doi>10.1109/MC.2000.881690]
• 11: Otter M., H. Elmquist, and S. Mattson, "Hybrid modeling in Modelica based on the synchronous data flow principle", in CASCD'99, August 22--26, 1999, Hawaï, USA.
• 12: Ghosh S., and N. Giambiasi, "Breakthrough in modle-ing and simulation of mixed-signal electronic designs in n VHDL", Modeling and Simulation, May 2001.

INDEX TERMS

Keywords:
G-DEVS, discrete event model: DEVS, discrete systems, hybrid continuous systems, piecewise linear trajectory