Design Of Maximally Permissive Petri Net Supervisor By Set Inhibitor Arcs

Flexible manufacturing systems(FMSs)is a typical automatic control system,which have the advantages of high efficiency and high flexibility.However,if the resources in an FMS have not been properly allocated,it may cause deadlocks.As a modeling tool,Petri net has great advantages in modeling FMS and deadlocks control.The deadlock control methods by Petri nets can be divided into two categories: structural analysis and reachability graph analysis.Structural analysis is based on the special structural characteristics of the net model.Reachability graph analysis is the study of the association between various markings.Reachability graph analysis can generally design an optimal supervisor.This thesis focuses on the analysis of reachability graphs.Control places are designed to prevent all Markings/transition separation instances(MTSIs).An MTSI is a pair of a marking and a transition.Once the transition fires at the paired marking,the system reaches some illegal markings.An MTSI is said to be prevented if the transition is disabled at the marking.Once all MTSIs are prevented,the system cannot reach any illegal markings.The main contributions are presented as follows:1.This thesis proposes a new Petri net structure,set inhibitor arc,and firing rules.A set inhibitor arc is an arc from a place to a transition labeled by a set of integer intervals.At marking ,if the token number in the place is within a certain integer interval of the set inhibitor arc,the transition is disabled.If the token number in the place is not belong to any interval of set inhibitor arc,the transition is enabled.2.A control strategy is proposed by using the firing rules of set inhibitor arcs.First,legal markings in the original net must be reachable,to satisfy the maximally permissiveness of the controlled system.To reduce computational complexity,the vector covering method is used to reduce the legal markings that need to be considered.By analyzing the reachability graph,we can obtain all critical transitions.For each critical transition ,we can compute the set of -dangerous markings and the set of -enabled good markings.At a -dangerous marking,if the token number in the control place is within an integer interval of the set inhibitor arcs,the critical transition is disabled.At the same time,it is also necessary to ensure that critical transition is enabled on all -enabled good markings.If the token number of the control place at any -enabled good marking does not belong to any interval of the set inhibitor arcs,critical transition is enabled.Finally,we formulate an integer linear programming problem(ILPP),and solve it to design the control place.3.The thesis analyzes the advantages of new Petri net structure.It is of minimal supervisor structure and efficient computation.Compared with the control strategy by data inhibitor arcs,the number of constraints and variables of the designed ILPP can be greatly reduced.In this way,the computational complexity is reduced.Thus,control strategy by set inhibitor arcs is more efficient to lager scale Petri net models.Finally,multiple examples are used to demonstrate the control strategy of the set inhibitor arcs.