Application of adaptive inverse compensation feedforward—MPC feedback control to AFM piezoelectric micro-positioning platform

As the integral constituent of atomic force microscope (AFM), piezoelectric micro-positioning platform (PMP) plays an pivotal role in AFM working accuracy. However, the PMP platform has hysteretic nonlinear characteristics, which bring challenges to high-precision positioning applications, especially in large travel applications. In this paper, the nonlinear Prandtl–Ishlinskii (P–I) model and the linear auto-regressive with extra inputs dynamic model are cascaded to form the Hammerstein model to characterize the dynamic characteristics of PMP, and the mixed algorithm of the beetle antennae search-differential evolution is designed to identify the parameters of the established model. In order to eliminate the hysteresis effect, a compound controller based on adaptive inverse compensation is proposed, which is composed of feedforward controller of P–I inverse model and model prediction controller feedback controller. As the compound controller depends on modeling accuracy, the tracking error caused by model mismatch is improved by adaptive mechanism. The experimental tracking results of sinusoidal signals and triangular signals of different frequencies show that the proposed method can improve the tracking performance of PMP and verify its effectiveness.