Using D-elementary hybrid Petri nets and linear hybrid automata for modelling manufacturing systems

Hybrid Petri nets are known to be a powerful tool for modeling positive hybrid dynamic systems; and hybrid automata to have a great analysis power. Many authors have used these two models in a coupled manner to combine their advantages and translation algorithms from hybrid Petri nets to hybrid automata exist in the literature. Here we investigate a subclass of hybrid Petri nets called D-elementary hybrid Petri net. We present a structural algorithm allowing the translation of the D-elementary hybrid Petri nets out of linear hybrid automata. The resulting automaton has particular characteristics. The translation algorithm preserves the behavioral semantics; we prove hereafter the timed bisimilarity of the D-elementary hybrid Petri net and the linear hybrid automaton obtained by the translation algorithm. A manufacturing system will be used as an illustrative example.