Optimal Supervisory Control of Flexible Manufacturing Systems by Petri Nets: a Set Classification Approach
Résumé
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 non-convex. 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.