Multivariable feedback control in stage synchronization

Synchronization in lithographic wafer scanners involves a wafer-to-reticle stage controller. However, in view of the increasing wafer stage bandwidths the need for an additional reticle-to-wafer stage controller becomes more evident, i.e. a cross-coupling controller. By itself, this has severe implications for the stability and control design of the synchronized system, which becomes multivariable. In this work, an ℋ∞ controller is synthesized that can effectively deal with the synchronization problem while guaranteeing robust closed-loop stability. An application of the ℋ∞ design will be given through measurement results obtained from an industrial wafer scanner.