基于Maxwell模型的压电驱动系统前馈控制方法

Feed-forward control method of piezoelectric drive system basedon Maxwell model

为了提高外腔可调谐半导体激光器的测量精度,基于Maxwell模型提出了用于消除其压电驱动系统迟滞非线性的前馈控制方法.基于经典Maxwell力学模型,建立了描述非凸、非对称迟滞环的静态迟滞模型;根据频率与位移幅值的关系建立了率相关系数矩阵,与静态迟滞模型耦合得到率相关迟滞模型,实现了不同频率下压电驱动系统迟滞非线性的精准预测;构建了迟滞逆模型,对压电驱动系统进行前馈补偿控制.实验结果表明,率相关迟滞模型具有较高的精度,1 Hz下模型均方根误差为0.049μm, 50 Hz下模型均方根误差为0.252μm.基于迟滞逆模型的前馈控制方法能够明显提高系统输出位移的线性度,增大线性度范围,线性相关系数R2由0.971 58提高到了0.999 77.

In order to improve the measurement accuracy of external cavity tunable semiconductor lasers,a feed-forward control method for eliminating hysteretic nonlinearity of piezoelectric drive systems is proposed based on Maxwell model.A static hysteresis model that can describe non-convex and asy mmetric hysteresis loops was established based on the classical Maxwell mechanical model.The rate-dependent coefficient matrix was established,which was coupled with the static hysteresis model to obtain the rate-dependent hysteresis model,which realized the accurate prediction of hysteresis nonlinearity of piezoelectric drive system at different frequencies.A hysteresis inverse model was constructed to control the feed-forward compensation of the piezoelectric drive system.The experimental results show that the rate-dependent hysteresis model established in this paper has high accuracy,with a root mean square error of 0.049μm at 1 Hz and 0.252μm at 50 Hz.The feed-forward control method based on hysteresis inverse model can significantly improve the linearity of the output displacement of the system,increase the linearity range,and increase the linear correlation coefficient R 2 from 0.97158 to 0.99977.