A current cycle feedback iterative learning control approach for AFM imaging

In this paper, we proposed a novel current cycle feedback (CCF) iterative learning control (ILC) approach to achieve high-speed imaging on atomic force microscope (AFM). AFM imaging requires precision positioning of the AFM probe relative to the sample in 3-D ($x$ $y$$ z$). It has been demonstrated that, with advanced control techniques such as the inversion-based iterative control (IIC), precision positioning of the AFM probe in the lateral ($x$ $y$) scanning can be successfully achieved. Precision positioning of the probe in the vertical $z$-axis direction, however, is still challenging because the issues such as the sample topography are unknown, in general; the probesample interaction is complicated, and the probesample position is sensitive to the probesample interaction. The main contribution of this paper is the development of the CCF-ILC approach for the AFM $z$-axis control, which decouples the robustness of the feedback control from the precision tracking of the feedforward control. Particularly, the proposed CCF-ILC controller design utilizes the recently developed robust inversion technique to minimize the model uncertainty effect on the feedforward control and to remove the causality constraints in other CCF-ILC approaches. It is shown that the iterative law converges and attains a bounded tracking error upon noise and disturbances. The proposed method is illustrated through experimental implementation, and the experimental results show an increase of eight times faster imaging speed for contact-mode imaging.