Rate-dependent hysteresis modeling and compensation of piezoelectric actuators using Gaussian process

Rate-dependent hysteresis nonlinearity of the piezoelectric actuators (PEAs) deteriorates the positioning accuracy of the nano-positioning stage. To deal with it, the Gaussian Process (GP) is applied in this work to model the PEAs and also to compensate for it. The proposed GP-based model is capable of describing the nonlinear memorability as well as rate-dependence of hysteresis by introducing both the voltage value and its changing rate to the model input. The usage of the kernel function makes the model flexible and accurate without specifying a function form and the parameters. The kernel function contains only three hyperparameters, which can be determined by combining the differential evolution algorithm and Bayesian inference framework. An inverse hysteresis model is then obtained by interchanging the input and output variables of the GP-based hysteresis model to serve as a feedforward compensator. Based on this feedforward compensator, open-loop and closed-loop controllers are developed and tested. The comparative experimental studies are carried out on a PEA stage and the results demonstrate the effectiveness and superiority of the GP-based hysteresis model and compensator.