Abstract

Nanopositioning stages are widely used in high-precision positioning applications. However, they suffer from an intrinsic hysteretic behavior, which deteriorates their tracking performance. This study proposes an adaptive conditional servocompensator (ACS) to compensate the effect of the hysteresis when tracking periodic references. The nanopositioning system is modeled as a linear system cascaded with hysteresis at the input side. The hysteresis is modeled with a modified Prandtl–Ishlinskii (MPI) operator. With an approximate inverse MPI operator placed before the system hysteresis operator, the resulting system takes a semi-affine form. The design of the ACS consists of two stages: first, we design a continuously implemented sliding mode control (SMC) law. The hysteresis inversion error is treated as a matched disturbance, and an analytical bound on the inversion error is used to minimize the conservativeness of the SMC design. The second part of the controller is the ACS. Under mild assumptions, we establish the well-posedness and periodic stability of the closed-loop system. In particular, the solution of the closed-loop error system will converge exponentially to a unique periodic solution in the neighborhood of zero. The efficacy of the proposed controller is verified experimentally on a commercial nanopositioning device under different types of periodic reference inputs, via comparison with multiple inversion-based and inversion-free approaches.

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