Abstract
In this paper, a nonlinear coupling model with hysteresis, dynamics, and creep is proposed to describe accurately the complex characteristics of piezoelectric-actuated positioning stage, where a classic Hammerstein model in series with a fractional-order model is given. The fractional-order model is presented to express the nonlinear creep characteristics. Firstly, the Hammerstein structure model is composed of two blocks, where the former block is the classical PI model to describe the static hysteresis effects, and the latter block is the second-order discrete transfer function model to characterize the dynamic characteristics. In addition, the parameters of the coupling model are identified. Secondly, based on the built model, the inverse of fractional-order model and the inverse of PI model are implemented as the feedforward compensations, and an adaptive control is designed to adjust the tracking performance of the whole system. Finally, the effectiveness of the proposed coupling model and controllers are verified by the piezoelectric-actuated positioning experiment stage. Experimental results show that the established coupling model can accurately characterize the hysteresis, dynamics, and creep properties of the stage. Also, the results show that the tracking error is less than 0.8% at low frequency and mixed frequency.
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