The Simplification Of Cascade Petri Net And Its Application For Controller Design

Petri net is a powerful tool of simulation and analyzing system . Recently ,it is widely applied to the field of discrete event system (DES).Petri net can not only portray the system framework, but also can depict the dynamic behavior. A discrete event system is the dynamical system that evolves according to the abrupt occurrence of events, at possibly unknown irregular intervals. Substantially, DES is a manmade system. Anactual DES may enter into some forbidden states. The avoidance of forbidden states is to design a controller for an event-driven controlled DES such that its closed-loop behaviors satisfying a desirable specification.The principal research results and contents are composed by two parts, namely, the cascade Petri net simplification part and the supervisory control part:The cascade Petri net simplification part: Firstly, the character of strongly connected state machine and workflow net with their simplification methods are studied based on the definition of simplified net system.Then, the simplification technique of cascade Petri net is proposed, It can simplify the subnets of strongly connected state machine and workflow net which are in the cascade Petri net. The research results about the cascade Petri net simplification will be used for designing controller directly.The supervisory control part: A controller design method is proposed based on simplified controlled Petri net. It is applied to the net whose maximal uncontrollable subnet is cascade Petri net and every cascade subnet with loops is strongly connected state machine or workflow net.This net can be simplified into a loop-free subnet based on simplified controlled Petri net, hence, the linear integer program (LIP) method can be applied for maximally permissive control. It extends the LIP method and solves the controller design problem for a class of uncontrollable subnet with loops.