.ModelicaDEVS.UsersGuide.Introduction

Information

The goal of this thesis is to implement a new Dymola/Modelica library, consisting of a number of blocks that enable simulation according to the DEVS formalism. The ulterior motive is to provide Dymola with an additional integration method based on the DEVS methodology.

Dymola/Modelica primarily deals with continuous physical problems, usually described by differential equations. Integration is therefore an important subject and justifies the attempt to improve/enhance Dymola's current possibilities regarding integration methods.

It may be a bit surprising at a first glance why a methodology such as DEVS, originally designed for discrete systems, should be useful for the simulation of continuous systems.
Toward the end of the nineties however, a new approach for numerical integration has been developed by Zeigler et al. [Zeigler98]: given the fact that all computer-based simulations have to undergo a discretisation in one way or another - as digital machines are not able to process raw continuous signals - the basic idea of the new integration approach was to replace the discretisation of time by a discretisation of state, such that the system is not supposed to advance from time step to time step anymore, but rather from state to state. While conventionally the time axis was subdivided into intervals of equal length, the time instants when the system executes the next simulation step are now distributed irregularly because of their dependence on the time instants when the system enters a new state which is not necessarily at equidistant time instants.
The DEVS formalism turned out to be particularly suited to implement such a state quantisation approach given that it is not limited to a finite number of system states, in contrast to other discrete-event simulation techniques.
The Quantised State Systems introduced by Kofman [Kofman01] in 2001 improved the original quantised state approach of Zeigler, and hence gave rise to efficient DEVS simulation of large and complex systems.

The simulation of a continuous system by a (discrete) DEVS model comes with several benefits:

• Usually, the classic methods use a discretisation of time, which however has the drawback that the variables have to be updated contemporarily. Thus, the time steps have to be chosen according to the variable that changes the fastest, otherwise a change in that variable could be missed. In a large system where probably very slow but also very fast variables are present (many slow and a few fast variables, in the worst case), this is critical to computation time, since the slow variables have to be updated way too often.
  Note that the need for updating variables contemporarily does not hold for methods with dense output. However, today's integration methods make rarely use of dense output, hence the above statement is true for the majority of used integration methods.
• The DEVS formalism however allows for asynchronous variable updates, whereby the computational costs can be reduced significantly: every variable updates at its own speed; there is no need anymore for an adaptation to the fastest one in order not to miss important developments between time steps.
  This property could be extremely useful in stiff systems that exhibit widely spread eigenvalues, i.e., that feature mixed slow and fast variables.
• The DEVS formalism is very well suited for problems with frequent switching operations such as electrical power systems. Given that the problem of iteration at discontinuities does not apply anymore, it even allows for real-time simulation.
• For hybrid systems with continuous-time, discrete-time and discrete-events parts, a discrete-event method provides a "unified simulation framework": discrete-time methods can be seen as a particular case of discrete-events methods [Kofman01] and continuous-time parts can be transformed straightforwardly to discrete-time/discrete-events systems.
• When using the Quantised State Systems approach of Kofman in order to transform a continuous system into a discrete system, there exists a closed formula for the global error bound [Cellier05], which allows a mathematical analysis of the simulation.