Modeling and Identification of Rate Dependent Hysteresis in Piezoelectric Actuated Nano-Stage: A Gray Box Neural Network Based Approach

Abstract

A modeling and parameter identification method for rate dependent hysteresis of piezoelectric actuated nano-stage is presented in this work. A system level quasi-static hysteresis model is employed to construct a neural network. To better describe the rate dependent behavior of hysteresis in piezoelectric actuated stage, a Nonlinear AutoRegressive Moving Average with eXogenous input (NARMAX) based dynamic model is incorporated with the quasi-static hysteresis model, where the weights of specifically designed neural network corresponds to the model parameters. To handle the multivalued problem of hysteresis, generalized input gradient is proposed to convert multivalued mapping of hysteresis into one-to-one mapping. The parameters of the nonlinear rate dependent hysteresis in piezoelectric actuated stage is identified by neural network training, taking advantage of their universal function approximation capabilities. The proposed scheme is also compared with conventional black box and particle swarm optimization identification based methods, simulation and experimental results demonstrate significant performance improvement with an error of 20.77nm for proposed method whereas 96.56nm and 31.46nm for black box and particle swarm optimization respectively.