Modelling and simulation of hybrid systems with an extension of Coloured Petri Nets

Gebhard Decknatel

Address

Abstract

We consider railway systems as continuous-discrete (hybrid) systems, where the continuous train motion is controlled by discrete train control systems. Modern train control algorithms no longer divide the track into discrete sections which can only be occupied by one train, but instead consider the precise position and speed of the trains. This can improve the performance of the system, for instance by making it possible to let the trains drive in absolute or relative braking distance.

There are different ways to combine discrete and continuous aspects in one simulation model. One possibility is to use separate discrete and continuous models and connect them with an interface. We chose an integrated approach instead, which includes both aspects in one formalism and allows the construction of hybrid models without imposing a division into discrete and continuous parts. Considering the current forms of railway modelling, we decided to use Petri nets a representative of the discrete formalisms and to extend them with a means to describe continuous processes.

Hybrid Petri nets are often defined on the basis of nets with anonymous tokens. This approach is particularly useful to model the continuous change of variables such as temperatures, concentrations or fluid levels in tanks. On the other hand, these nets cannot describe individual objects, which we consider important in our context since we want to model individual trains on different parts of the railway network as well as different instances of the train control systems.

We therefore decided to use high-level nets as a starting point. These nets may possess tokens with real-valued attributes, which is already relatively close to modelling continuous processes. The only step missing is to be able to change the values of these attributes continuously. As the most basic form of continuous processes, we therefore defined integrating continuous transitions, which can change those attribute values with a rate given by another token. To complement this, we also added algebraic continuous transitions, which can maintain certain algebraic relationships between continuously changing attribute values. These two simple types of new transitions allow a flexible modelling of continuous processes without elaborate annotations.

The formal definition of these hybrid nets is based on the definitions of Coloured Petri Nets taken from the literature. A prototypical implementation was built using the tool Design/CPN.