The Relationship Between The Number Of Control Places Of S~3PR Linear Controller And The Initial Marking

In the actual operation process of automated production system,there may be misallocation of resources,leading the system to a deadlock state.And then the system cannot run nor-mally.In severe cases,it will cause major economic losses or even disasters.Therefore,the deadlocks must be considered and solved at the beginning of the design of automated production systems.As a modeling tool,Petri nets have been widely used in the model-ing,analysis and other aspects of automated production systems.In the aspect of deadlock analysis and control,deadlock control methods based on Petri nets can be divided into two categories:analysis methods based on reachability graphs and those based on structures.Based on reachability graph and structure-based analyses,this paper discusses the relation-ship between the number of control places needed by the two methods and the initial marking when the initial marking of S~3PR network is changed and a linear controller is added to the network system to ensure maximum permissive behavior.The main tasks completed are as follows:1.When S~3PR nets do not contain ? resource,the relationship between the maximum permissive behavior controllers and the initial marking is introduced.That is,the maximum permissive behavior controllers will not exceed the number of strict minimal siphons,regardless of whether based on structure or on reachability graph.2.Based on the ? resource,the concept of double element ? resource is proposed,and it is proved that the maximum permissive behavior controller can be obtained by controlling the strict minimum siphons of S~3PR nets when only double element ? resource is contained.This means that no matter which control method is used,the maximum permissive behavior controllers will not exceed the number of strict minimum siphons.3.By further expanding the concept of ? resource,the definition of single element ? resource is given,and it is proved that when S~3PR nets do not contain single element ? resource,the maximum permissive behavior controller can be obtained by controlling its strict minimum siphon being not emptied.Then a special case with single element ? resource is introduced;that is,for S~3PR nets whose legal marking set is non-convex,maximum permissive behavior cannot be obtained by adding linear controllers.