Schedule stabilization and robust timing control for time-constrained cluster tools

Stable schedules that repeat identical timing patterns for each work cycle have been important implication for cyclic manufacturing systems such as cluster tools for semiconductor manufacturing or flexible manufacturing systems. While it has been claimed that stable schedules have advantages including steady operation, predictable behavior, minimum cycle times, less work-in-progress inventory, recently stable schedules also play essential roles for meeting critical time window constraints on the operations such as wafer residency time constraints in a cluster tool or track equipment for some chemical vapor deposition processes or wet cleaning processes. However, when the process times or robot task times are subject to random variation or abrupt random disturbances, the stable schedule is disturbed and the perturbed wafer residency times may violate time window constraints. We prove that a cluster tool with dual arms, after any schedule disturbance, can be stabilized to the stable schedule. We characterize the condition for stabilization based on the event graph theory. We also present a control strategy that guarantees such stabilization and reduces the stabilization time.