Métodos de controle de fluxo de entrada para sistemas modelados por grafos de eventos temporizados

Abstract

This thesis deals with the control of systems modeled by timed events graphs (TEG) and the max-plus algebra, such systems are subject to synchronization phenomena and time delay. The main focus for application are manufacturing systems, however it is not limited to only these. Currently, the problems of control systems modeled by TEG are approached in two different ways: (a) based on dioid the formal power series, and (b) based on dioid of daters. The main feature of the first approach, lies in the fact that this is based on techniques of transfer functions. The second approach, based on dioid of daters, allows to deal directly with the fulfillment of the system. The main types of control that use transfer functions are the methods by reference control. The goal of the model reference control refers to the imposition of a desired behavior for a given system, which in turn is dictated by the use of a feedback controller. Therefore this method seeks to determine the best controller possible to fulfill this goal. In the context of TEG, this minimizes the amount of controller token on TEG and delays as much as possible the entry of raw materials in the system. For a given model reference control, the problem faced consists of finding the biggest controller, in case it exists. These control issues to TEG are usually proposed in the just-in-time (JIT) management policy, in which the goal is to deliver the raw material at the exact moment of need of jobs, without forming unnecessary stocks within the manufacturing plant, but given the specifications of production demand. Generally speaking, the proposals of control are based on the open loop control, using pre-compensation, and closed loop, using the feedback. The algebraic form of dealing with the problem through a formal power series, is by far a more complex approach , which doesnt guarantee the best criterion of JIT optimization. The goal of this thesis is to propose two control methods based on dioid of daters. The first method propose the calculation of parameters of a feedback controller that delays the entry of raw materials in the system modeled by TEG, also it calculates the number of tokens in the feedback system, limiting the most tokens in the modeled system. These parameters obtained from the controlling law imposed on the modeled system, showing up, this way the results achieved by the method of control, are superior to results presented by the model reference control approach with simple feedback. The second method, control method II, proposes the firing synchronization of several internal transitions in a system modeled by TEG. This control is achieved by delaying the entry of raw materials in the system and, in most cases, by modifying the production rate of the system. Two general equations are proposed for the calculation of the parameters of the controller which synchronizes the firing of these various transitions. An equation calculates the delay times on the feeding input, the other equation calculates the production rate that the system must operate to perform the desired synchronization. The calculation of the number of tokens of feedback is obtained in the same way as in the method I. This type of control is important because synchronizing transitions allow to define the exact time that an event or activity can begin or end, in a sequence of defined activities. The results of this method are presented in synchronization of two, three and four transitions. Where results are expected, the proposed methods reduce the complexity for the calculation of the controllers for these two types of control, which would lead to a reduction in the computational load, providing a stabilizing effect of the system, avoiding stocks overflow, using as parameter the JIT management policy.