Feedback control design for cluster tools with wafer residency time constraints

Cluster tools for semiconductor manufacturing have been studied widely in terms of transportation robot scheduling. Cluster tool systems are discrete event systems, and usually modeled in timed Petri nets and timed event graphs. Many efficient robot operation sequences such as the backward sequence and the swap sequence have been developed, but they do not guarantee efficiency under consideration of wafer residency time constraints for some process modules. In this paper, we propose a way to control cluster tools with wafer residency time constraints using the max-plus algebra and timed event graphs. Conditions to meet time constraints are developed, and we introduce a methodology to add feedback control arcs to timed event graph models of single-armed cluster tools with the backward sequence, and dual-armed cluster tools with the swap sequence. Bounded variation on processing times also considered as well as time constraints.