An Dong, Li Haodong, Xu Ying, Zhang Lixiu
College of Mechanical Engineering, Shenyang Jianzhu University, Hunnan East Road No.9, Hunnan New District, Shenyang 110168, China.
Micromachines (Basel). 2018 Jan 26;9(2):44. doi: 10.3390/mi9020044.
Piezoelectric ceramic actuators have been widely used in nanopositioning applications owing to their fast response, high stiffness, and ability to generate large forces. However, the existence of nonlinearities such as hysteresis can greatly deteriorate the accuracy of the manipulation, even causing instability of the whole system. In this article, we have explained the causes of hysteresis based on the micropolarization theory and proposed a piezoelectric ceramic deformation speed law. For this, we analyzed the piezoelectric ceramic actuator deformation speed law based on the domain wall theory. Based on this analysis, a three-stage Prandtl⁻Ishlinskii (PI) model (hereafter referred to as tripartite PI model) was designed and implemented. According to the piezoelectric ceramic deformation speed law, this model makes separate local PI models in different parts of piezoelectric ceramics' hysteresis curve. The weighting values and threshold values of the tripartite PI model were obtained through a quadratic programming optimization algorithm. Compared to the classical PI model, the tripartite PI model can describe the asymmetry of hysteresis curves more accurately. A tripartite PI inverse controller, PI inverse controller, and Preisach inverse controller were used to compensate for the piezoelectric ceramic actuator in the experiment. The experimental results show that the inclusion of the PI inverse controller and the Preisach inverse controller improved the tracking performance of the tripartite PI inverse model by more than 80%.
压电陶瓷致动器因其响应速度快、刚度高以及能够产生大力而被广泛应用于纳米定位应用中。然而,诸如滞后等非线性的存在会极大地降低操纵精度,甚至导致整个系统的不稳定。在本文中,我们基于微极化理论解释了滞后的原因,并提出了一种压电陶瓷变形速度定律。为此,我们基于畴壁理论分析了压电陶瓷致动器的变形速度定律。基于此分析,设计并实现了一种三阶段的普朗特-伊斯林斯基(PI)模型(以下简称三方PI模型)。根据压电陶瓷变形速度定律,该模型在压电陶瓷滞后曲线的不同部分制作单独的局部PI模型。三方PI模型的加权值和阈值通过二次规划优化算法获得。与经典PI模型相比,三方PI模型能够更准确地描述滞后曲线的不对称性。在实验中使用了三方PI逆控制器、PI逆控制器和Preisach逆控制器来补偿压电陶瓷致动器。实验结果表明,加入PI逆控制器和Preisach逆控制器使三方PI逆模型的跟踪性能提高了80%以上。