Modeling and sliding mode control based on inverse compensation of piezo-positioning system  

压电定位系统建模及滑模逆补偿控制

作　　者：LI Zhi-bin XIN Yuan-ze ZHANG Jian-qiang SUN Chong-shang 李智斌;辛源泽;张建强;孙崇尚(山东科技大学电气与自动化工程学院,山东青岛266590;南京大学高端控制与智能运维研发中心,江苏苏州215163)

机构地区：[1]College of Electrical Engineering and Automation,Shandong University of Science and Technology,Qingdao 266590,China [2]Center for Advanced Control and Smart Operations,Nanjing University,Suzhou 215163,China

出　　处：《中国光学(中英文)》2025年第1期170-185,共16页Chinese Optics

基　　金：国家自然科学基金(No.U23A20336,No.52227811,No.61933006);山东省自然科学基金(No.ZR2021QF117,No.ZR2021QF140)。

摘　　要：In order to enhance the control performance of piezo-positioning system,the influence of hysteresis characteristics and its compensation method are studied.Hammerstein model is used to represent the dynamic hysteresis nonlinear characteristics of piezo-positioning actuator.The static nonlinear part and dynamic linear part of the Hammerstein model are represented by models obtained through the Prandtl-Ishlinskii(PI)model and Hankel matrix system identification method,respectively.This model demonstrates good generalization capability for typical input frequencies below 200 Hz.A sliding mode inverse compensation tracking control strategy based on P-I inverse model and integral augmentation is proposed.Experimental results show that compared with PID inverse compensation control and sliding mode control without inverse compensation,the sliding mode inverse compensation control has a more ideal step response and no overshoot,moreover,the settling time is only 6.2 ms.In the frequency domain,the system closed-loop tracking bandwidth reaches 119.9 Hz,and the disturbance rejection bandwidth reaches 86.2 Hz.The proposed control strategy can effectively compensate the hysteresis nonlinearity,and improve the tracking accuracy and antidisturbance capability of piezo-positioning system.为了提高压电定位系统(Piezo-positioning system)的控制性能,对迟滞特性产生的影响及其补偿控制方法进行了研究。利用Hammerstein模型表征压电陶瓷定位器的动态迟滞非线性特性,分别以Prandtl-Ishlinskii(P-I)模型和Hankel矩阵系统辨识法求得的模型表示Hammerstein模型的静态非线性部分和动态线性部分。此模型对于200 Hz以内的典型输入频率具有较好的泛化能力。在此基础上,还提出了基于P-I逆模型与积分增广的滑模逆补偿跟踪控制策略。实验结果表明,相较于PID逆补偿控制和无逆补偿的滑模控制,滑模逆补偿控制具有更加理想的阶跃响应,无超调且调节时间仅为6.2 ms,在频域内系统闭环跟踪带宽达到119.9 Hz,且扰动抑制带宽达到86.2 Hz。所提控制策略实现了迟滞非线性的有效补偿,提高了压电定位系统的跟踪精度与抗扰性能。

关 键 词：piezo-positioning system hysteresis nonlinearity Hammerstein model Prandtl-Ishlinskii(P-I)model system identification sliding mode control 

分 类 号：O482.31[理学—固体物理]