基于双曲函数的Preisach类迟滞非线性建模与逆控制  

Modeling and inverse control of Preisach type hysteresis nonlinearity using hyperbola functions

作　　者：陈远晟[1] 裘进浩[1] 季宏丽[1] RonanLe Breton 

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室,江苏南京210016 [2]萨瓦大学材料与机电系统实验室

出　　处：《光学精密工程》2013年第5期1205-1212,共8页Optics and Precision Engineering

基　　金：国家自然科学基金重大研究计划培育项目(No.90923029);长江学者和创新团队发展计划资助项目(No.IRT0968);国家自然科学基金中美合作与交流项目(No.51161120326);江苏省自然科学基金创新学者攀登项目(No.BK2009020);江苏省普通高校研究生科研创新计划资助项目(No.CXZZ11_0194);江苏高校优势学科建设工程资助项目;国家留学基金管理委员会公派留学基金资助项目

摘　　要：为了补偿压电双晶片驱动器的迟滞非线性,提出了基于双曲函数的Preisach类迟滞非线性建模方法,并用该模型设计了压电双晶片驱动器的逆控制器。首先,用两个双曲函数分别拟合迟滞主环的上升段与下降段,利用坐标变换描述依附于主环的一阶曲线;然后,根据Preisach模型理论的记忆擦除性与次环一致性,基于一阶上升与下降曲线分别描述了次环的上升段与下降段。由于这种建模方法所需的参数远小于Preisach等经典迟滞模型,非常适用于压电驱动器等智能材料系统。实验结果显示,基于这种迟滞非线性模型设计的逆控制器,控制后的最大误差比控制前减小了44.26%,有效地提高了压电双晶片驱动器的定位控制精度。To compensate the hysteresis nonlinearity of a piezoelectric biomorph actuator,a new model with hyperbola functions was proposed to describe the Preisach type hysteresis nonlinearity,and an inverse controller was designed with the proposed model.Two hyperbola functions were used to fit the curves of hysteresis major loop and then the first-order ascending and descending branches were described by the coordinate conversion.Based on the wiping-out and congruency property of Preisach model,the minor loops were modeled by the corresponding first-order curves.As the parameters of the proposed model are much less than those of classic hysteresis models,such as Preisach model,the proposed model is suitable for the smart material systems including piezoelectric actuators.Experimental results show that the inverse controller designed with the proposed model can compensate the hysteresis of piezoelectric biomorph actuator,and the maximum control error with inverse controller has reduced by 44.26%.

关 键 词：PREISACH模型 压电驱动器 迟滞非线性 精密定位 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置] TN384[自动化与计算机技术—控制科学与工程]