Linear Supervisors Of Petri Nets Based On Reachability Graph Analysis Under Java Platform

As a powerful mathematical modeling tool,Petri nets has been widely used in the modeling,analysis,control and simulation of flexible manufacturing systems(FMSs).However,the analysis of complex Petri nets relies on the Petri net simulation softwares.Therefore devel-opment of Petri net simulation softwares is one of the keys to solving practical problems.Deadlock is an inevitable problem in the design process of FMS.Based on the reachability graph,it can definitely find a maximally permissive liveness-enforcing supervisor if such a supervisor exists.Based on the theory of regions,the reachability graph be divided into two parts:live zone and dead zone.The method of vector coverage effectively reduces the number of markings to be considered,including the first-met bad markings and the legal markings.However,before using the vector coverage method,it is necessary to calculate the reachability graph of the Petri nets.For a complex Petri net,the reachability graph is very large and there even may has a state explosion problem.This paper has carried out research on the above two aspects,mainly completed the follow-ing work:1.This paper combines the simplified rules of Petri nets and the vector coverage method.When simplifying the Petri nets,this paper supplements the simplified rules based on the simplified six principles.This paper introduces a T-invariant simplified rule of Petri nets for FMSs.Given a Petri net for FMS,firstly simplify the Petri net according to the T-invariant simplified rules and the simplified six principles,and then calculate the markings to be considered by using the vector coverage method.Finally,the supervisors is designed to Petri nets of simplification,thus implementing the deadlock control of the original Petri net.Combination of simplification method of Petri nets and vector coverage method,not only effectively reduces the reachable states that needs to be calculated,but also reduces the number of markings obtained by using the vector coverage method,thereby improving the design efficiency of the supervisors.2.For a complex Petri net,the reachability graph of the simplified Petri net is still very large.In this case,the concept of a single holder resource place is introduced for the S~3PR(System of Simple Sequential Processes with Resources),and the simplified rule of the single holder resource place are given.Combining the simplified rule of the single holder resource place,the T-invariant simplified rule and the simplified six principles to design the supervisors,the number of the reachable states that need to be calculated is further reduced,thereby further improving the design efficiency of the supervisors.3.This paper has optimized and improved the Petri net simulation software V1.0.Firstly,problems of the software are fixed,modifying the core architecture of the software to make the software hierarchy more distinct.Solved the problem of interface.Redundant codes is deleted.Secondly,the simplified module and deadlock control module are added,and the function of interacting with the software and PIPE software through XML files is added.Finally,a comprehensive functional test of the optimized Petri net simulation software V1.0is carried out.The results show that the software is stable and reliable,the modeling and simulation is convenient and fast,and the analysis results are accurate.