High-Speed AFM Imaging of Nanopositioning Stages Using H$_{\infty }$ and Iterative Learning Control

This paper presents a method that combines a robust controller ( $H_\infty$ ) and an iterative learning controller (ILC) to control a low mechanical bandwidth nanopositioning stage for high-speed atomic force microscopy (AFM) imaging. In conventional scanning configurations, the imaging speed of a low-resonance frequency scanner is limited to a few Hz. However, the images obtained using the proposed method have no obvious anamorphosis with a scan speed of up to 80 Hz. This method uses a sinusoidal scanning mode in the fast-scan axis, which effectively reduces the mechanical vibration of the XY-scanner and improves the imaging bandwidth. In addition, a compact high-bandwidth Z-scanner configured with a symmetrical dual-actuator was developed to replace the Z-axis of the nanopositioning stage for high-speed tracking of the sample topography. To further improve the imaging performance, an ILC was designed to suppress the nonlinear behavior of piezoelectric and reduce the tracking error. In addition, a model-based $H_\infty$ was designed to reduce the measurement error and enhance the image quality. All algorithms and real-time control are implemented with a field-programmable gate array (FPGA) platform. The experimental results demonstrated that these configurations exhibit significant performance improvements by comparison with conventional scanning modes.