Balanceamento just-in-time de sistemas max-plus lineares com restrições: aplicação à linha de montagem

Abstract

Discrete Events Systems Timed subjected to synchronization and delay phenomena can be modeled by a subclass of Petri nets named Timed Event Graphs, whose dynamics can be described linearly by Max-Plus algebra. This dissertation deals with the state feedback control of such systems. To this end, two control methodologies are developed based on algebraic properties of the modeled systems. The first one proposes the synthesis of controllers that respect the restrictions imposed on the systems, besides not allowing the formation of stocks inside the plant. It is also addressed how to find deterministically, by a equation, a controller that allows the maximum delay of part entries in the system. In order to solve control problems, some concepts of Max-Plus algebra, such as Residual Theory and Semimodule Theory are used. The second methodology proposes the controllers design that must respect the constraints imposed on the system and allow the system to function in a just-in-time management context, with maximum production rate, remembering that the just-in-time policy is a control policy, that aims not to build up inventories in the systems. This is done by delaying system entry dates as much as possible without changing their production rate. This methodology is based on the Alter- nating Algorithm, Semimodule Theory and spectral matrix concepts such as eigenvalue and λ-super-eigenvector. The computational package Scicoslab is used for extracting information from systems, such as the maximum production rate and the production time of a particular piece. Also, it allows the systems simulation, providing the synthesis of controllers. The proposed methods are used in numerical examples to demonstrate their effectiveness.