Compensating nonlinearities in high-speed atomic force microscopy using data-driven feedforward controller design

Piezoelectric actuators are widely used in nano-positioning stage of atomic force microscopes (AFM). The nonlinear dynamics of these actuators adversely affect the AFM image quality unless they are compensated with a controller. We propose a feedforward controller design method which adjusts the scan waveforms with the aim of minimizing the hysteresis distortions in the lateral direction of motion. The data-driven design approach requires a pair of forward and backward stripes of images of the sample to detect the hysteresis mappings through solving a nonlinear optimization problem with a genetic algorithm. The parameters of the optimization are then used to shape the scan waveforms to compensate for the effects of hysteresis. The quick and straightforward design makes the proposed feedforward controller a good solution for lateral scanners in high-speed AFM where implementation of feedback control is often hindered by the physical constraints and latency of the system. We show that the design procedure can be successfully applied on AFM instruments regardless of the imaging mode, scan speed, or the sample under study.