Switching models and control of Petri Nets with shared resources under marking constraints

Abstract

ABSTRACT Nowadays multi-option phenomena can generate potential problems related to industrial manufacturing systems. For instance, time and money loss are both expensive costs that should be paid when failing to make the right control choice decision, especially given the existence of various constraints. Therefore, the shared resource allocation between several processes can be transformed into a switching control problem that can be modeled using (Min, +) algebra. Due to the finite number of states and ergo of the application of this type of system, they are defined under the class of Discrete Event Systems. Accordingly, while taking into consideration modes of representation, this paper seeks to discuss a new modelling approach for competitive Timed Events Graphs under capacity constraints. The deduced switching models are then examined to solve the control problem issue of an industrial manufacturing process composed of cells of pick and place robots. To deduce the adequate control laws, an original solution based on the use of linear equations described by (Min, +) linear algebra is provided.