Inverse Control of Piezoelectric Motion Systems with Hysteresis Modeling and Parameter Optimization

This paper presents an enhanced Prandtl-Ishlinskii (EPI) model with a hybrid differential evolution optimization algorithm for the asymmetric and rate-dependent hysteresis description of a piezoelectric motion system. Considering the fact that the classic PI model can only describe symmetric hysteresis nonlinearities. To characterize the asymmetric and rate-dependent feature of the hysteresis non-linearities, both the radial basis function (RBF) neural networks and the polynomial function are introduced to construct the enhanced Prandtl-Ishlinskii (EPI) model, where the system input voltage and the derivative of the system input voltage are used as the input of the RBF neural networks. With the combination of the JAYA algorithm and the traditional differential evolution (DE) algorithm, an adaptive hybrid DE algorithm is developed to identify the coefficients of the polynomial and the weights of both the RBF neural network and the classic PI model. Compared with the traditional DE, the convergence speed is improved. Based on the inverse of the classic PI model, a feed-forward controller with the enhanced PI model is designed to achieve trajectory tracking. The effectiveness of both the presented hysteresis model and the proposed inverse control scheme is verified by the simulation and experimental results, which demonstrate excellent modeling accuracy and the satisfactory tracking performance.