Just-in-Time Balancing of Feedback Assembly Lines Via Constrained-Linear Tropical Model

Abstract

Abstract Discrete Events Systems are systems that are subject to synchronization and delay phenomena. They can be modeled by a subclass of Petri nets named Timed Event Graphs whose dynamics can described by Tropical algebra (Max or Min plus Algebra). The aim of this article is to present a methodology to project controllers that respect the restrictions imposed to the system operation ensuring the just-in-time policy. This is a control policy that proposes the use of the biggest possible delay of the system input dates without changing production rates, keeping the system demands. To this end, the controller synthesis methodology is developed based on Residuation Theory and on the concept of super-eigenvector. Sufficient conditions to get the controller is presented with an example to illustrate the applicability of the results.