Optimal actuator shape design with input and state constraints for a wafer heating application

Thermal actuation can reduce deterioration of the imaging quality due to wafer heating. Because the placement of thermal actuators is critical for the performance of the resulting control system, a method to aid the design of an actuator layout is developed. Optimal actuator shapes are computed as the solution of an optimization problem that involves input and state constraints. The resulting actuator shapes have a clear physical interpretation for the next-generation wafer scanners and numerical results seem to indicate that the designed actuator shapes might be unique.