Data-Driven Feedforward Hysteresis Compensation with Genetic Algorithm for Atomic Force Microscope*

Nonlinear dynamics of piezo actuators such as hysteresis, distort the Atomic Force Microscopy (AFM) images as they adversely affect the accuracy of the nano-positioning setup. To compensate for the effects of hysteresis on lateral scanner actuators of AFM, a data-driven feedforward controller design algorithm is proposed. The pair of forward and backward images of a sample are used to extract a mapping between the trace and retrace motion of the actuator. A model corresponding to the input-output mapping of the actuator is defined with a set of unknown parameters. The values of these parameters, which shape the hysteresis curves of the actuator, are optimized through defining and solving an optimization problem. A genetic algorithm is utilized as a tool to look for the optimal values. The hysteresis mapping model is then implemented in the form of an inversion-based feedforward controller to correct the scan waveforms and get matching forward and backward images of the sample. The proposed sensor-less data-driven method is easy to implement as it does not depend on the instrument, the sample under study, or the imaging properties.