A manufacturing machine processing two product types arriving at constant rate and setup times involved is considered in this study. An optimal process cycle is derived with respect to minimal weighted time averaged work in process (wip) level. In addition, a feedback law is proposed that steers the system to this optimal process cycle from arbitrary start point. The analysis has been done for both unbounded and bounded buffer capacity. Although the analysis is done for continuous models, the feedback law has been implemented successfully in a discrete event simulation.

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Manufacturing systems are event driven systems and are therefore often considered from an event domain perspective. Notions from control system theory are all characterized in a time domain setting. In this paper the coupling between both domains is investigated. Also the relevance of this interconnection if control is applied to manufacturing systems is shown.

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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.