State feedback control of switching server flowline with setups

Abstract

We consider the control of flowlines consisting of switching servers, through which different types of jobs flow. Switching from one job type to an other takes time. Examples of such flowlines can be found in manufacturing industry, food processing industry, communication networks, and traffic flow. The optimal process cycle with respect to work in process levels for a single switching server with two job types is known from previous work. This optimal work in process value is an absolute lower bound on average work in process levels for larger flowlines. In this study we derive conditions for workstations in a flowline that have to be met in order to achieve this minimal work in process level for the whole flowline. Based on these conditions, the class of flowlines is characterized that can behave as if it were a single switching server. A state feedback controller is proposed that steers a trajectory to the desired trajectories for all servers in the flowline, from any arbitrary start point. Convergence to the desired process cycles is proven mathematically. Although the analysis is performed with a hybrid fluid model, the controller has successfully been implemented in a discrete event case study.