Globally smooth lemniscate trajectory with adaptive integral terminal sliding mode control and inversion-based hysteresis compensation for pi ezoelectric stage precise tracking

Abstract

High-precision measurement systems use an xy-axis piezoelectric scanner following a pre-determined trajectory to achieve three-dimensional scanning at micro/nano-scales. Most systems employ a raster scanning trajectory due to ease of implementation; however, raster scanning generates infinite odd harmonics, which can induce mechanical resonance leading to image distortion. Moreover, the nonlinear response characteristics of piezoelectric materials frequently result in unexpected displacements. This paper presents a novel sequential scanning trajectory that eliminates the need for a step function and minimizes the risk of mapping errors. An advanced controller combining an inverse hysteresis model with adaptive integral terminal sliding mode control (AITSMC) was developed and first applied in the piezoelectric scanner through theoretical derivation and stability analysis to prove its feasibility. In simulations and experiments, the proposed controller significantly mitigated the effects of hysteresis during trajectory tracking and achieved superior tracking accuracy and lower RMSE compared to existing sliding mode controllers.