Hybrid industrial dynamical system supervision via hybrid continuous causal Petri Nets (HC2PNs)

A continuous time system representation, using a causal directed graph and asynchronous piece-wise linear approximation for variables, is given first. Then, an equivalent timed continuous Petri net is obtained : places represent continuous time variables ; place marking represents the corresponding variable evolution ; transitions represent dynamic causal links among variables ; the firing speed of a transition is defined depending on the parameters of the continuous system and the marking of the input place. This leads to the definition of a Continuous Causal Petri Net (C 2 PN). Then a hybrid dynamical system is considered : the continuous part is represented by a C 2 PN, and the discrete part by a classical PN, interfaced by a very simple classical PN. The integrated three PNs constitute a single homogeneous HDS modeling tool named Hybrid Continuous Causal Petri Net (HC 2 PN). Simulation results on a simple example are given for evaluating the proposed approach.