Optimal Supervisory Control of Flexible Manufacturing Systems by Petri Nets: A Set Classification Approach

TLDR

Supervisory control typically regulates controllable events in a system, but Petri net models with nonconvex reachability spaces cannot be optimally controlled by linear constraints. This study proposes to classify legal markings of flexible manufacturing system Petri nets into subsets to facilitate control. Each subset is linked to a linear constraint that blocks first‑met bad markings, and an integer linear programming model minimizes the number of such constraints while a supervisory structure implements their disjunctions to achieve liveness and maximal permissiveness. Because nonconvex reachability spaces cannot be optimally controlled by conjunctions of linear constraints, the disjunctions of the derived constraints make all legal markings reachable and forbid first‑met bad markings, resulting in a live and maximally permissive controlled net.

Abstract

Supervisory control is usually considered as an external control mechanism to a system by controlling the occurrences of its controllable events. There exist Petri net models whose legal reachability spaces are nonconvex. In this case, they cannot be optimally controlled by the conjunctions of linear constraints. For Petri net models of flexible manufacturing systems, this work proposes a method to classify the legal markings into several subsets. Each subset is associated with a linear constraint that can forbid all first-met bad markings. Then, the disjunctions of the obtained constraints can make all legal markings reachable and forbid all first-met bad markings, i.e., the controlled net is live and maximally permissive. An integer linear programming model is formulated to minimize the number of the constraints. A supervisory structure is also proposed to implement the disjunctions of the constraints. Finally, examples are provided to illustrate the proposed method.