Coupling event domain and time domain models of manufacturing systems

Abstract

Abstract-Manufacturing systems are often characterized as discrete event systems (DES) and consequently, these systems are modeled with discrete event models. For certain discrete event modeling paradigms, control theory/techniques have been developed in event domain. However, from a control or performance perspective, a lot of notions are time related, like stability, settling time, transient behavior, throughput, flow time, efficiency, etc. Moreover, if we also consider market/customer requirements, almost all requirements are within time perspective: due dates, deliverability, earliness, tardiness, etc. Therefore, it is also useful to have time driven models of manufacturing systems. To combine the insights in modeling and control obtained in both time and event domain, it is useful to create a coupling between those two domains. This paper describes modeling techniques in both time domain and event domain for a class of manufacturing systems and establishes a generic coupling between two model descriptions. The coupling exists of two maps between the models' states, enabling real-time control of manufacturing systems.

Backward Reachability of Autonomous Max-Plus-Linear Systems

“…Section 2). These models are widely employed in the analysis and scheduling of infrastructure networks, such as communication and railway systems (Heidergott et al, 2006), production and manufacturing lines (Roset et al, 2005;van Eekelen et al, 2006), as well as in biological systems (Brackley et al, 2012). They cannot model concurrency and are related to a subclass of timed Petri nets, namely timed-event graphs (Baccelli et al, 1992).…”

Finite Abstractions of Stochastic Max-Plus-Linear Systems

“…In some cases, it is possible to obtain a smaller value for H ij by substituting the density function directly into the inequality in (5). Furthermore H ij may be independent of the size of the safe set.…”

“…MPL systems are predisposed to describe the timing synchronisation between interleaved processes, under the assumption that timing events are dependent linearly (within the max-plus algebra) on previous event occurrences. MPL systems are widely employed in the analysis and scheduling of infrastructure networks, such as communication and railway systems [3], production and manufacturing lines [4,5], or biological systems [6].…”

Fundamentals of the statistical theory of the construction of continuum models of production lines

“…7) является модельное представление процесса взаимодействия предметов труда с технологическим оборудованием и между собой. x ,x ,x ,x -определяющее соответственно количество изделий в буфере, количество изделий в технологической обработке, время до окончания обработки и количество обработанных изделий [27] S , -стоимость затрат технологических ресурсов перенесен-ных на предмет труда за общее время обработки предмета труда [26,28] (рис. 14).…”