压电陶瓷执行器迟滞特性的广义非线性Preisach模型及其数值实现

Generalized nonlinear Preisach model for hysteresis nonlinearity of piezoceramic actuator and its numerical implementation

压电陶瓷执行器的迟滞非线性不具有经典Preisach模型的次环一致特性,直接利用该模型对压电陶瓷执行器的迟滞特性建模会产生较大误差。为了提高压电陶瓷执行器的迟滞特性建模精度,在非线性Preisach模型的基础上推导得到适用于压电陶瓷迟滞特性的广义非线性Preisach模型,并给出简化分类计算公式。广义非线性Preisach模型将经典Preisach模型表示定理中的次环一致特性修改为次环等弦长特性,放宽了对描述对象的限制要求。实验数据表明,与经典Preisach模型相比,广义非线性Preisach模型预测位移的误差绝对值的最大值降低了0.22μm,均方根误差降低了0.11μm,能够更精确地描述压电陶瓷的迟滞特性。

The hysteresis nonlinearity of the piezoceramic actuator can not satisty the congruency property of the classical Preisach model so that the modeling error is large when applying the classical Preisach model to the piezoceramic actuator. In order to improve the accuracy in hysteresis modeling of the piezoceramic actuator, the generalized nonlinear Preisach model and its new numerical implementation based on the nonlinear Preisach model with some modifications are presented. The new model has equal vertical chord property of minor loops to relax the congruency property of the classical Preisach model. Experimental results show that the maximum of the absolute error predicted by the generalized nonlinearity Preisach model reduces 0.22 μm and the root mean square error reduces 0.11 μm compared to the classical Preisach model. The generalized nonlinear Preisach model can describe the hysteresis of the piezoceramic actuator more accurately.