压电驱动器的非对称迟滞模型  

A Model for Asymmetric Hysteresis of Piezoelectric Actuators

作　　者：裘进浩[1] 陈海荣[1] 陈远晟[1] 杜建周[1] 

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,南京210016

出　　处：《纳米技术与精密工程》2012年第3期189-197,共9页Nanotechnology and Precision Engineering

基　　金：国家自然科学基金资助项目(90923029);长江学者和创新团队发展计划资助项目(IRT0968);江苏省自然科学基金资助项目(BK2009020);江苏高校优势学科建设工程资助项目;江苏省普通高校研究生科研创新计划资助项目(CXZZ11-194);南京航空航天大学博士学位论文创新与创优基金资助项目(BCXJ11-02);南京航空航天大学基本科研业务费专项科研项目(NJ2010010;NZ2010001)

摘　　要：为了补偿压电驱动器的非对称迟滞,提出了改进型Maxwell迟滞模型.Goldfarb提出的经典Maxwell迟滞模型由多个基础单元并联叠加而成,其基础单元为单个弹簧-物块单元,迟滞特性为平行四边形,故只能描述对称迟滞.为了能描述压电驱动器非对称迟滞,提出了基础单元迟滞特性为梯形的模型.为了简化算法程序,将梯形单元优化为两个三角形单元组合而成.为了验证该模型,以压电工作台为实验对象,运用该迟滞模型的逆模型进行迟滞补偿控制.单独的迟滞逆模型前馈开环控制实验结果表明,位移跟踪相对误差从7.37%降到了1.56%,输入输出基本呈线性关系.逆模型结合PID复合反馈闭环控制实验结果表明,位移跟踪相对误差进一步降低到0.53%,输入输出呈很好的线性关系.这表明本文所建立的迟滞模型能很好地描述压电驱动器非对称迟滞特性.To compensate for the asymmetric hysteresis of piezoelectric actuators,a modified Maxwell model was proposed.The classic Maxwell model developed by Goldfarb is a linear superstition of many single elasto-silde elements,which inherits the symmetry property of the element.To describe the asymmetric hysteresis of piezoelectric actuators,a new model with modified element was proposed for hysteresis modeling.The loop formed by a single elasto-silde element is symmetric,but the modified element shows an asymmetry loop like trapezoid.Two triangle operators which are equal to one modified element were designed for program optimization.To validate the proposed model,a series of experiments were performed on a piezoelectric stage.A feedforward controller based on the new model was designed to compensate for the hysteresis of the stage,and a feedback controller was designed to reduce the tracking error.The results show that the maximum of relative tracking error was 0.53% with feedforward and feedback control,but it was 1.56% with feedforward control and 7.37% without control.It indicates that the proposed model can accurately describe the asymmetric hysteresis of piezoelectric actuators,and that the relationship between input and output is linearized by the inverse model.

关 键 词：压电驱动器 Maxwell模型 迟滞补偿 PID 位移跟踪 

分 类 号：TN384[电子电信—物理电子学] TP273[自动化与计算机技术—检测技术与自动化装置]