Ingeniero electronico

Keynote Address, Proc. ESS'93, European Simulation Symposium, Delft, The Netherlands, Oct. 25.-28., 1993, pp. xxxi-xli.

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OBJECT{ORIENTED MODELING OF HYBRID SYSTEMS
Hilding Elmqvist DynaSim AB Research Park Ideon S{223 70 Lund Sweden Elmqvist@Gemini.LDC.LU.SE Francois E. Cellier Dept. of Electr. & Comp. Engr. The University of Arizona Tucson, Arizona 85721 U.S.A. Cellier@ECE.Arizona.EduMartin Otter Inst. fur Robotik & Systemdynamik DLR Oberpfa enhofen D{82230 Wessling Germany DF43@Master.DF.OP.DLR.DE

ABSTRACT
A new methodology for the object{oriented description of models consisting of a mixture of continuous and discrete components is presented. The object{oriented paradigm enables the user to describe such models in a modular fashion that permits the reuse of these modelsindependently of the environment in which they are to be embedded. The paper explains the basic mechanisms needed for object{oriented modeling of hybrid systems by means of language constructs available in the object{oriented modeling language Dymola. It then addresses more advanced concepts such as variable structure models containing e.g. ideal electrical switches, ideal diodes and dry friction.INTRODUCTION
Hybrid models contain both continuous and discrete parts. In simulation programs, the continuous parts are described by sets of di erential equations and algebraic equations in either explicit form (ODE) or implicit form (DAE). Traditionally, the discrete parts are expressed with event descriptions. A numerically sound methodology for simulating hybrid models was developed about 15years ago (Cellier 1979). Unfortunately, this methodology requires a compact description of all di erential equations in a single monolithic continuous block, and a description of the accompanying events in one or several separate discrete blocks. This model structure does not support the reuse of models. Object{oriented programming has evolved to support the independent development and reuse ofsoftware components. This programming paradigm was rst developed in the context of discrete{event simulation (Birthwistle et al. 1973) and carried over to continuous system modeling about 15 years ago. Dymola, an object{oriented modeling language for continuous systems was designed by Elmqvist for this purpose, and a prototypical implementation of Dymola

was made available (Elmqvist 1978).Dymola represented an important step forward towards the reuse of continuous system models in a truly environment{ independent fashion. Recently, Dymola has been upgraded from a mere university prototype to a fully{ supported commercial software tool (Elmqvist 1993). A continuous system modeling methodology that does not allow for descriptions of discontinuities is not generally useful, at least notin the context of engineering applications. All but the most trivial engineering models of dynamic systems contain some sorts of discontinuities. This paper discusses a recent extension of the Dymola language de nition to allow descriptions of models of dynamic systems with discontinuous behavior in a truly reusable object{oriented fashion. Several novel high{level constructs are introduced thatare much easier to use, closer to the physical system description, and less error prone than corresponding constructs in today's simulation languages such as ACSL (Mitchell & Gauthier 1991). A di erent approach to objectoriented hybrid system modeling is described in (Andersson 1992), in which facilities for discrete event modeling in the object-oriented modeling language Omola (Andersson 1990) arediscussed. Event handling in Omola supports the (explicit) de nition of events and corresponding actions. Contrary, in Dymola the (explicit) de nition of events is replaced by higher{level constructs. Generators have been developed that automatically translate Dymola models into either an ACSL (Mitchell & Gauthier 1991) program or a DSblock (Otter 1992) Fortran subroutine. While Dymola also...