MODELS FOR CONTINOUS AND HYBRID SYSTEM SIMULATION Mariana C. D’Abreu Computer Science Department Universidad de Buenos Aires Planta Baja, Pabellón I, Ciudad Universitaria (1428) Buenos Aires, ARGENTINA Gabriel A. Wainer Dept. of Systems and Computer Engineering Carleton University1125 Colonel By Drive. 4456 Mackenzie Bldg. Ottawa, ON, K1S 5B6, CANADA
ABSTRACT The DEVS formalism was defined as a method for modeling and discrete event systems. DEVS theory evolved and it was recently upgraded in order to permit modeling of continuous and hybrid systems. Here, we present a first experience on the use of two of the existing methods for defining continuous variable DEVS models(namely, the QDEVS and the GDEVS formalisms), to develop continuous and hybrid systems simulations. We show how to model these dynamic systems under the discrete event abstraction. Examples of model simulations with their execution results are included. An experimental analysis on quantization methods within models is also presented. 1 INTRODUCTION
Complex systems analysis has usually beentackled using different mathematical formalisms, Partial Differential Equations (PDE) being one of the preferred tools of choice (Taylor, 1996). In most complex systems, solutions to these equations are very difficult or impossible to find. A variety of numerical methods find approximate solutions to these equations, being successful in studying many different phenomena. The appearance of digitalcomputers allowed enhancing previously existing numerical methods. Simulation-based approaches succeeded in providing a means of analyzing particular problems (instead of the general solutions obtained by solving PDEs). Simulation of continuous systems on digital computers requires discretization. Classical methods as Euler, RungeKutta, Adams, etc., are based on discretization of time resulting in adiscrete time simulation model (Press et al. 1986). Instead, methods like DEVS (Discrete EVent Specification) formalism (Zeigler et al. 2000) were built in order to allow the specification of discrete event models. The DEVS formalism was defined as a method for modeling and discrete event systems. DEVS provides means to handle explicit time, and to define complex models in a hierarchical modularfashion.
DEVS theory evolved and it was recently upgraded in order to permit modeling of continuous and hybrid systems. GDEVS (Generalized Discrete EVent Specification) (Giambiasi et al. 2000) is a generalization of constant input-output trajectories beyond DEVS abstraction; under this formalism, trajectories are organized through piecewise polynomial segments. This presents some advantages,including greater accuracy in modeling continuous systems and the ability to develop a uniform approach to model hybrid systems, i.e. composed of both continuous and discrete components. Another approach to solve these problems under the DEVS formalism is based on state variable quantization (Zeigler et al. 1998). The idea beyond this method is to provide quantization of the state variables obtaininga discrete event approximation of the continuous system. This formalism is known as Q-DEVS and quantization is done using a piecewise constant function. In the long term, we want to attack the development of hybrid systems based on the DEVS formalism and its extensions, building libraries to make easy to use components developed on top of DEVS modeling tools. In this article we show our firstresults in this sense. We present the implementation of a library of Bond Graphs (Cellier 1991) based on GDEVS. Likewise, we present other components often used in continuous systems using QDEVS. One of the benefits is that for a given accuracy, the number of transitions can be reduced, decreasing the execution time of simulations. Discrete time models can be simulated under discrete event...