Nonpure Petri Net Supervisors for Optimal Deadlock Control of Flexible Manufacturing Systems

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.