Learning Piezoelectric Actuator Dynamics Using a Hybrid Model Based on Maxwell-Slip and Gaussian Processes

Piezoelectric actuators (PEAs) are increasingly applied to the field of ultraprecision positioning; however, unwanted nonlinearities, such as hysteresis, degrade their performance. This article integrates a Gaussian process (GP) with a Maxwell-slip (MS) model to capture nonlinearities in PEAs. The GP predicts the output of a PEA or the error of the MS model by using the current and historical applied input voltages, as well as the measured historical output displacements, as input. The measured output is replaced by the output of the MS model in the case that a displacement sensor is unavailable. The experimental results show that by properly selecting system order, the proposed approach achieves a precise result and provides the boundary of the prediction error in terms of variance. If the output displacement is available and the GP predicts the output of a PEA directly, the normalized root-mean-square error (NRMSE) is as low as 0.29%. The NRMSE is reduced further to 0.14% if the dataset used for prediction is updated online.