Modeling and Control of a Manufacturing Flow Line Using Partial Differential Equations

This brief deals with a control framework for manufacturing flow lines. For this framework, a continuous approximation model of the manufacturing system is required, which is computationally feasible and able to accurately describe the dynamics of the system (both throughput and flow time). Often used models, such as discrete-event models and flow models, fail to meet these specifications: the use of discrete-event models may lead to intractably large control problems, while flow models do not accurately describe the system dynamics. Therefore, we consider here a relatively new class of models for the description of manufacturing flow lines, namely partial differential equation (PDE)-models, which seems to meet the required specifications. However, for the few ldquomanufacturingrdquo PDE-models that have been introduced in literature so far, the accuracy has not been validated yet. In this brief, we, therefore, present a validation study on three of these PDE-models available from literature, which shows that there is a need for more accurate PDE-models. Furthermore, we propose to use one of these PDE-models for the design of a model predictive controller (MPC-controller), which is to be applied in closed loop with a discrete-event manufacturing flow line. For two considered tracking problems, the resulting MPC-controller is shown to outperform a classical push strategy.