On the choice of basis functions in FIR feed-forward design for wafer stages

In view of the increasing demands on scanning resolution and wafer throughput, control perfor- mance in the presence of disturbances is considered important for lithograpic systems. These sys- tems consist of various positioning modules that need to be synchronized at nano-scale accuracy while being exposed to large acceleration forces. The goal of this project was to establish this nano- scale accuracy by optimizing the coefficients in a Finite Impulse Response (FIR) filter feed-forward structure. The gradients used in the optimization are reconstructed via basis functions. Two types of basis functions are compared throughout this report, namely time delay and time derivative ba- sis functions. The time delay function is a more steady function gives a reasonable estimation of the gradient of the error at a low number of coefficients, but also at a high number of coefficients. Contrarily, the time derivative function, which is not constant over the considered interval of co- efficients, gives a better result at a low number of coefficients, but a worse result at a high number of coefficients. The choice therefore is dependent on the number of coefficients. This is one of the main conclusions of this work.