Article,
Monitor design with multiple self-loops for maximally permissive supervisors
ISA Transactions, (March 2016)
DOI: 10.1016/j.isatra.2015.12.016
Abstract
We design a maximally permissive Petri net supervisor with a small number of control places for flexible manufacturing systems. Self-loops are allowed in the obtained supervisor sine they have more control ability than pure (self-loop-free) Petri nets. The proposed method can lead to simpler supervisory structure than the previous work. The propose approach is a non-iterative deadlock control strategy since we can compute all control places by solving an integer linear program. The proposed work can find optimal Petri net supervisors for the net models that cannot be optimally controlled by pure Petri net supervisors. In this paper, we improve the previous work by considering that a control place can have multiple self-loops. Then, two integer linear programming problems (ILPPs) are formulated. Based on the first ILPP, an iterative deadlock control policy is developed, where a control place is computed at each iteration to implement as many marking/transition separation instances (MTSIs) as possible. The second ILPP can find a set of control places to implement all MTSIs and the objective function is used to minimize the number of control places. It is a non-iterative deadlock control strategy since we need to solve the ILPP only once. Both ILPPs can make all legal markings reachable in the controlled system, i.e., the obtained supervisor is behaviorally optimal. Finally, we provide examples to illustrate the proposed approaches.
