Structural Simplification Of Petri Net Controllers Via Disjunctive Generalized Mutual Exclusion Constraints

In the era of rapid development of industrialization,there is a complexity in engineering.In order for the systems to be constructed according to industrial demands,it is necessary to design an excellent supervisor,which not only prevents the system from deadlocks,but also improves the production efficiency of the systems with limited production cost.As a modeling tool in discrete event systems,Petri nets can describe and analyze complex manufacturing systems and intuitively explain many system characteristics in the manufacturing processes.Supervisory control theory of Petri net is an important research field.Among them,Generalized Mutual Exclusive Constraints(GMECs)are an important kind of control requirements specification in the supervisory control theory of discrete event systems.It was proposed by Giua et al in 1992,mainly focusing on the supervision of system states.In the scenario of Petri nets,the supervision is mainly based on the Generalized Mutual Exclusive Constraints.This specification mainly contains two types,i.e.,the conjunctive constraints and the disjunctive constraints.The former is a conjunction of GMECs,so it called the conjunctive constraints.The latter consists of a disjunction of GMECs.Previous work has mainly shown that how to simplify the supervisor structure which designed by conjunctive constraints.There is a lack of research on the structure simplification of supervisors designed by disjunctive constraints.Therefore,a simplified method for Petri net supervisors based on disjunctive constraints is presented.In this thesis,the simplified algorithm is mainly analyzed from the aspects of constraint norm inequalities and the logical relations.The main contributions are shown as follows:1.Through the analysis of the composition of a finite number of disjunctive constraint inequalities,we discuss with the simplification principle of the logical function of the four-variable Karnaugh map.Then all the possible simplified results of the Karnaugh map within four variables are summed up.It is mapped to the process of constraint specification simplification,which simplifies the disjunctive constraints by reducing the number of inequality constraints or improving the connection form of constraints.Finally,we establish a simplified algorithm of low dimensional logic function based on Karnaugh map.2.On the basis of low dimensional simplification,we further analyze the case consisting of inequalities,the number greater than four in disjunctive inequality constraints is analyzed.The region is divided according to the consistency of the place,Moreover,the constraint space composed of inequality specifications is compared to simplify the high-dimensional inequality constraints,then we establish the simplification algorithm for the high-dimensional partition.This algorithm presents the design process of disjunctive constraint specification controller,so that the supervisory control strategy can be implemented more effectively.Finally,a case study is carried out to analyze the simplification of the supervisory controller designed by the control specification before and after the implementation of the algorithm,from the aspects of the connection form of the constraint inequality,the number of connection arcs and the number of variables in the library.In this thesis,a simplified method is proposed based on the behaviors of the place through the in-depth study of the GMECs.It provides a new way to analyze the disjunctive constraints.In practice,a simpler controller structure is used to achieve the desired control strategy,simplify system implementation complexity and save system resources.