Abstract:In order to accurately describe the complex nonlinear characteristics of piezoelectric actuated positioning platform, a nonlinear mathematical model combining hysteresis, dynamics and creep was proposed based on the classical Hammerstein structure model and fractional operator model in series. The creep and hysteresis nonlinear characteristics of the model are described by fractional operator and PI model respectively, and the mechanical dynamic characteristics are expressed by second-order discrete transfer function. In addition, the parameter identification of the coupling model is considered, and the proposed coupling model is verified by the piezoelectric-actuated positioning stage. Under the action of 1-100Hz sinusoidal input voltage signal, compared with the Hammerstein structure model without considering creep characteristics, the root mean square error index of the coupling model proposed in this paper is reduced by more than 27%, and the relative error index is reduced by about 50%. The experimental results fully show the effectiveness of the coupling model proposed in this paper. Finally, based on the establishment of the model, the inverse creep and hysteresis models are designed to compensate the system, and the PID control algorithm is used to adjust the performance of the system. The simulation results show that the compound control scheme has a good tracking effect under low frequency and mixed frequency input signals.
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