  In this paper, a practical fractional-order variable-gain super-twisting
algorithm (PFVSTA) is proposed to improve the tracking performance of wafer
stages for semiconductor manufacturing. Based on the sliding mode control
(SMC), the proposed PFVSTA enhances the tracking performance from three
aspects: 1) alleviating the chattering phenomenon via super-twisting algorithm
and a novel fractional-order sliding surface~(FSS) design, 2) improving the
dynamics of states on the sliding surface with fast response and small
overshoots via the designed novel FSS and 3) compensating for disturbances via
variable-gain control law. Based on practical conditions, this paper analyzes
the stability of the controller and illustrates the theoretical principle to
compensate for the uncertainties caused by accelerations. Moreover, numerical
simulations prove the effectiveness of the proposed sliding surface and control
scheme, and they are in agreement with the theoretical analysis. Finally,
practice-based comparative experiments are conducted. The results show that the
proposed PFVSTA can achieve much better tracking performance than the
conventional methods from various perspectives.
