Modeling and Identification of Piezoelectric-Actuated Stages Cascading Hysteresis Nonlinearity With Linear Dynamics

Abstract

In this paper, we propose a new modeling and identification approach for piezoelectric-actuated stages cascading hysteresis nonlinearity with linear dynamics, which is described as a Hammerstein-like structure. In the proposed approach, the hysteresis and linear dynamics together with the delay time and higher order dynamic behaviors are obtained with three data-driven identification steps under designed input signals. In the first step, the step input signal is applied to estimate the delay time of the piezoelectric-actuated stages. In the second step, the autoregression with exogenous signal identification algorithm is adopted to identify the linear dynamics using a small-amplitude band-limited white noise input signal. In the third step, with the identified linear dynamics model, the parameters of the rate-independent Prandtl–Ishlinskii hysteresis model are identified by the particle swarm optimization algorithm using a simple low-frequency triangle input signal with different amplitudes. Finally, the experimental results on a piezoelectric-actuated stage show that both the hysteresis and dynamic behaviors of the piezoelectric-actuated stage are well predicted by the proposed modeling method. In addition, we provide the analysis of quantitative prediction errors of the identified model with comparison to experimental data, which clearly demonstrate the effectiveness of the proposed approach.