Acceleration-snap feedforward scheme for a motion system with viscoelastic tuned-mass-damper

Bandwidth-limiting flexible modes in motion systems like the stage systems of a wafer scanner can effectively be damped by incorporating a viscoelastic tuned-mass-damper. This allows for an increase of bandwidth. The viscoelastic properties however pose a challenge on the feedforward design and thereby limit the achievable tracking performance. This is because the viscoelastic properties, which cannot be described by the simple addition of an elastic and a viscous element, induce a relaxation effect that prolongs well beyond the moment that inertial forces induced by the setpoint are being applied to the system. To cope with this problem, a tenth-order model fit from measured frequency response data that sufficiently captures the viscoelastic properties is combined with a data-based optimization approach needed to fine-tune a limited set of acceleration-snap feedforward gains. Experimental results from an industrial wafer stage system demonstrate the applicability of the approach.