基于GMEC转换算法的Petri网结构控制器综合方法

针对含不可控变迁Petri网系统禁止状态控制器设计问题，提出了一种基于矩阵变换和整数线性规划的结构控制器综合方法。该方法的关键是对代表系统合法状态的广义互斥约束(generalized mutual exclusion constraint, GMEC)进行转换。首先，根据Petri网系统的关联矩阵，将库所集分为无关库所集、不可控库所集和补足库所集。其次，通过对非允许GMEC中补足库所的权值和不可控库所的权值进行处理，并运用整数线性规划将非允许GMEC转换为允许GMEC。在允许GMEC的基础上，根据库所不变量原理设计出Petri网系统的结构控制器。最后，以某零件加工系统为例验证了所提方法的泛用性和高效性，为实际智能制造系统的监督控制器设计提供有效参考方案。

Synthesis of Petri net structural controller based on GMEC transformation algorithm

This paper proposed a controller synthesis method based on matrix transformation and integer linear programming to address the problem of forbidden state controller design for Petri net systems with uncontrollable transitions. The key idea behind this method involved transforming GMEC that represent the legal states of a Petri net system. Based on the incidence matrix of a Petri net, it divided the set of places into irrelevant places, uncontrollable places, and complementary places. By modifying the weights of complementary places and uncontrollable places in the given GMEC, it then converted the given GMEC into an allowable one by solving integer linear programming problems. Using the allowable GMEC, this paper designed a structural controller for Petri nets based on the principle of place invariants. Finally, it took a part processing system as an example to show that the application is versatile and efficient, offering an effective solution for the controller design of intelligent manufacturing systems.