On the transformation from automata into Petri Nets in FMS

Automata and Petri nets are both used in research of discrete event systems (DES). Based on supervisory control theory, this paper provides an algorithm to convert automata into Petri nets in flexible manufacturing systems (FMS). The automaton to be transformed should satisfy three conditions: (1) it contains no self-loop, (2) its initial state is also the marker state, and (3) it is nonblocking. The automaton is first divided into several sub-automata by projecting it onto some groups of events. Second the redundant automata are deleted. Then the sub-automata remained are changed separately into places with transitions and arcs in Petri nets formalism. In Petri nets formalism of FMS, places are distinguished by idle, operation, and resource places. We set the initial tokens of idle and resource places to be n - 1 (n is the number of states corresponding to the automaton) and set the initial tokens of the operation places to be zero. Then the places and transitions are connected together to form a complete Petri net.