Liveness and resource usage ratio-enforcing supervisor for a class of generalized Petri nets

In order to circumvent the state explosion problem involved in the analysis of a reachability graph, the structure theory is widely adopted when dealing with deadlock control and liveness-enforcing problems of flexible manufacturing systems modeled by Petri nets. Siphons, as a kind of significant structural objects, are extensively used for the deadlock prevention. However, since a siphon is defined as a set of places and does not contain any weight information, the siphon-based methods encounter a series of problems when dealing with generalized Petri nets whose arc weights are equal to or greater than one. As a concept different from siphons, augmented weighted simple directed circuits are proposed in our previous work to investigate a kind of intrinsically live structures in general systems of simple sequential processes with resources allocation (GS³PR). The work extends the concept of resource usage ratios (RU-ratios) to GS³PR to explore such intrinsically live structures. On the ground of RU-ratios, a kind of liveness and ratio-enforcing supervisors is applied to control GS³PR models. The monitors in such a supervisor are simply and intuitively connected to a plant net model and can be reused by adjusting their parameters when the configuration of the plant is changed, which resembles the working style of a programming logic controller. Several examples are used to illustrate the proposed method.