Nonpure Petri Net Supervisors for Optimal Deadlock Control of Flexible Manufacturing Systems
Résumé
This paper illustrates that Petri nets with self-loops are more
powerful than pure nets in modeling and control of flexible
manufacturing systems. A self-loop in a Petri net cannot be
mathematically represented by its incidence matrix. This paper
presents a mathematical method to design a maximally permissive
Petri net supervisor that is expressed by a set of control places
with self-loops. A control place with a self-loop can be represented
by a constraint and a self-loop associated with a transition whose
firing may lead to an illegal marking. The constraint is designed to
ensure that all legal markings are reachable and the self-loop is
used to prevent the system from reaching illegal markings by
disabling the transition at a specific marking. A marking reduction
approach is developed in order to cut down the considered markings,
which can greatly decrease the computational overhead of the
proposed method. An integer linear programming model is developed to
compress the number of control places, aiming to reduce the
structural complexity of the resulting supervisors. Finally,
illustrative examples are used to validate the proposed method and
to demonstrate that it can obtain an optimal supervisor for some
cases that cannot be optimally controlled by pure net supervisors.