Continuous compliance compensation of position-dependent flexible structures

The implementation of lightweight high-performance motion systems in lithography and other applications imposes lower requirements on actuators, amplifiers, and cooling. However, the decreased stiffness of lightweight designs increases the effect of structural flexibilities especially when the point of interest is not at a fixed location. This is for example occurring when exposing a silicon wafer. The present work addresses the problem of compliance compensation in flexible structures, when the performance location is time-varying. The compliance function is derived using the frequency domain representation of the solution of the partial differential equation (PDE) describing the structure. The method is validated by simulation results.