关键词: 迟滞非线性, Rayleigh模型, 反向传播（BP）神经网络, 前馈控制

Abstract: Aiming at the hysteresis nonlinearity of the piezoelectric driven systems for tunable external cavity diode lasers, a modelling and control method was proposed herein based on Rayleigh-BP model. Firstly, a Rayleigh-BP rate-dependent hysteresis model was developed by spatial expansion method, which achieved an accurate prediction of rate-dependent hysteresis nonlinearity of piezoelectric driven systems. Secondly, the inverse model of Rayleigh model was solved by an inverse algorithm, and the model was combined with a BP neural network to design a feedforward controller to compensate the systems. Finally, the feedforward control method was validated by simulation and experiments. The results show that the Rayleigh-BP model developed has high accuracy, the root mean square error is only as 0.0469 μm at 10 Hz. The feedforward control method may significantly improve the linearity of the system outputs, the root mean square error of the simulation results is as 0.0274 μm and the linear correlation coefficient R2 is as 0.999 92 at 40 Hz. The experimental results show a root mean square error of 0.0506 μm and a linear correlation coefficient R2 of 0.999 55 at 30 Hz, which greatly reduces the hysteresis phenomenon.

Key words: hysteresis nonlinearity, Rayleigh model, back propagation(BP) neural network, feedforward control