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.