压电陶瓷执行器的动态模型辨识与控制  

Identification and control of dynamic modeling for piezoceramic actuator

作　　者：陈辉[1,2] 谭永红[3] 周杏鹏[1] 张亚红[4] 董瑞丽[3] 

机构地区：[1]东南大学自动化学院,江苏南京210096 [2]桂林电子科技大学电子工程与自动化学院,广西桂林541004 [3]上海师范大学信息与机电工程学院,上海200234 [4]桂林航天工业高等专科学校信息工程系,广西桂林541004

出　　处：《光学精密工程》2012年第1期88-95,共8页Optics and Precision Engineering

基　　金：国家自然科学基金资助项目(No.60971004);上海市科委重点基金资助项目;(No.09220503000;10JC1412200);上海市自然科学基金资助项目(No.09ZR1423400);上海市教育委员会科研创新基金资助项目(No.09ZZ141;11YZ92);上海师范大学重点学科基金资助项目(No.DZL811;DRL904)

摘　　要：为了提高精密定位系统中压电陶瓷的控制精度,研究了压电执行器的动态模型及逆模型。根据Weierstrass第一逼近定理,提出了以多项式函数逼近Duhem模型中的分段连续函数f(·)和g(·),并应用递推最小二乘算法辨识Du-hem模型的参数α及f(·)和g(·)的多项式系数,建立了压电陶瓷执行器的非线性参数化动态模型。利用辨识结果建立压电陶瓷执行器的动态逆模型,避免对压电陶瓷执行器进行复杂的模型求逆;介绍了通过逆补偿和PID复合控制对压电陶瓷系统进行的控制。实验结果表明:仅通过逆补偿,可在0～200μm使得控制绝对误差小于0.8μm;在前馈逆补偿和PID环控制下,绝对误差可小于40nm,结果验证了算法的有效性。该算法结构简单,适应性强,便于工程实现。The dynamic model and inverse model of a piezoceramic actuator were proposed to improve its control precision in a precision position system. According to the Weierstrass approximation theorem, the polynomials f（·） and g（·） in the Duhem function was developed, and the dynamic modeling of nonlinear parameters of the piezoceramic actuator was given by using recursive least squares to identify the model parameters and polynomial coefficients in the Duhem model. Then, an inverse dynamic modeling of the piezoceramic actuator was established based on identified results to simplify the unknown parameter computation process greatly. Finally, the dynamic inverse compensation was incorporated in a closed-loop PID controller to control the piezoceramic actuator. Experimental results indicate that the maximum absolute error with the inverse compensation is less than 0.8 μm and that with the inverse compensation and PID is less than 40 nm in an amplitude range of 200 μm. The experimental result shows that the proposed identification scheme has improved the nonlinear characteristic of the piezoceramic actuator effectively.

关 键 词：压电陶瓷执行器 Duhem模型 Weierstrass多项式逼近 递推最小二乘法 动态迟滞模型 动态逆迟滞模型 逆补偿 

分 类 号：TP273.1[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]