该文提出了一种与速率相关的Prandtl-Ishlinskii(P-I)模型来表征压电驱动器的速率相关迟滞非线性。该模型基于双边Play算子的经典P-I模型, 引入多项式修正其中心对称性。在此基础上将驱动电压升降速率引入模型参数中, 用以描述其率相关性。测试压电驱动器的率相关迟滞特性, 采用最小二乘算法对模型参数进行辨识。结果表明, 在速率为0.12~6 V/ms内最大误差为0.076~0.190 μm, 均方根误差为0.044~0.077 μm, 相对误差为1.2%~3.2%, 验证了所建模型的准确性。

A rate dependent Prandtl-Ishlinskii(P-I) model is proposed to characterize the rate dependent hysteresis nonlinearity of piezoelectric actuators. Based on the classical P-I model of bilateral Play operator, the polynomial is introduced to modify its central symmetry. On this basis, the rise and fall rate of the driving voltage is introduced into the model parameters to describe its rate correlation. The rate dependent hysteresis characteristics of piezoelectric actuator are tested; the least square algorithm is used to identify the model parameters. The results show that the maximum error range is 0.076~0.190 μm, the root mean square error range is 0.044~0.077 μm, and the relative error is 1.2%~3.2% in the rate range of 0.12~6 V/ms, which verifies the accuracy of the model.