Practical Fractional-Order Variable-Gain Super-Twisting Control with Application to Wafer Stages of Photolithography Systems.

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.