压电驱动器迟滞特性的类Hammerstein模型

Hammerstein-likeModel for Hysteresis Characteristics of Piezoelectric Actuators

压电驱动器中迟滞特性会影响微操作系统的定位精度。为了消除迟滞对系统的不良影响,该文提出了类Hammerstein模型来描述压电驱动器的迟滞特性。首先,提出了改进迟滞算子(MDHO),在算子中增加偏置、死区宽度、斜率调整滞环的高度和宽度,体现迟滞的非对称性和速率相关性;然后,利用改进迟滞算子加权叠加表示静态非线性部分,迟滞算子的参数和权重可以在线调整来适应外界条件的变化,利用输入自回归模型表示动态线性部分,建立了可以描述压电驱动器速率相关迟滞特性的类Hammerstein模型;最后,依次通过最小二乘法、矩阵扩围、矩阵奇异值分解对模型中的参数进行辨识,并证明了所辨识的参数是无偏估计。研究结果表明所提出的建模方法是有效的。

The hysteresis characteristics of piezoelectric actuators will affect the positioning accuracy of the micro-operating system.A Hammerstein-like model is proposed to describe the hysteresis characteristics of piezoelectric actuators.Firstly,a modified dynamic hysteresis operator(MDHO)is proposed.By adding the offset,dead zone width and slope in the operator,the height and width of the hysteresis can be adjusted to reflect the asymmetry and rate correlation of hysteresis.Then the modified hysteresis operator is used to represent the static nonlinear part.The parameters and weights of the hysteresis operator can be adjusted online to adapt to changes in external conditions.The input autoregressive model is used to represent the dynamic linear part;a Hammerstein-like model that can describe the rate dependent hysteresis characteristics of piezoelectric actuators is established.Finally,the parameters in the model are identified by the least squares method,matrix expansion,and matrix singular value decomposition in turn and the identified parameters were proved to be unbiased estimates.The effectiveness of the proposed modeling method is verified by experiments.