基于阈值优化的压电微动平台迟滞模型

The Hysteresis Model of Piezoelectric Micro-positioning Stage Based on Threshold Optimization

为减少PI迟滞模型的无效算子数,进而提高模型的运算速度,采用阈值优化法来改进PI迟滞模型。采用PI迟滞模型拟合被描述对象的实测曲线时,实测曲线在各阈值点处的斜率可用该点处迟滞算子的权重和来表达,该权重和越接近该点曲线的斜率,PI迟滞模型的精度就越高。这样便可在保证模型精度满足要求并使其在各阈值点处相同的情况下,对模型的阈值进行优化,进而减少模型的算子数。根据测得的最大实测升程曲线,基于阈值优化法,建立了压电微动平台的迟滞模型。实验结果表明,所建模型算子数仅为7个,且不含无效算子;在0~15.94μm的位移范围内,所建模型的误差变化范围为0.23~0.40μm,即1.4%~2.5%。所建模型可较好地描述压电微动平台的迟滞非线性。

In order to reduce the number of invalid operators of PI hysteresis model,and to improve the operation speed of the model,the threshold optimization method is adopted to improve the PI model.When PI hysteresis model is used to fit the measured curves of an object,the slope of the measured curve can be expressed by the weight sum of the operator at each threshold point,the smaller difference between the weight sum and the curve slope,the higher accuracy of the PI hysteresis model.In this way,the threshold of PI hysteresis model can be optimized,and the operator number can be reduced,when the model accuracy meets the requirements and the accuracy is same at each threshold.According to the maximum measured lifting curve,the hysteresis model of a piezoelectric micro-positioning stage is established based on the threshold optimization method.The experimental results show that the numbers of the model operators are only 7,and they do not contain the invalid operators;within the displacement range of 0~15.94μm,the error range of the model is 0.23~0.40μm,that is 1.4%~2.5%.The model can better describe the hysteresis nonlinearity of the piezoelectric micro-positioning stage.