基于Duhem前馈逆补偿的压电陶瓷迟滞非线性自适应滑模控制  

Piezoelectric Ceramic Hysteresis Nonlinear Adaptive Sliding Mode Control Based on Duhem Feedforward Inverse Compensation

作　　者：徐子睿 许素安 富雅琼 洪凯星 徐红伟 XU Zirui;XU Suan;FU Yaqiong;HONG Kaixing;XU Hongwei(College of Mechanical and Electrical Engineering,China Jiliang University,Hangzhou 310018,China)

机构地区：[1]中国计量大学机电工程学院

出　　处：《传感技术学报》2019年第8期1209-1214,共6页Chinese Journal of Sensors and Actuators

基　　金：国家重点研发计划课题项目(2017YFF0205501);国家自然科学基金项目(51105348)

摘　　要：针对压电陶瓷的动态迟滞非线性,研究了基于Duhem逆模型前馈补偿的滑模自适应控制策略。首先,利用多项式逼近Duhem模型中的未知分段函数f(.)和g(.),采用递推最小二乘法进行系统辨识,并求取逆模型,将其作为前馈控制器。考虑压电陶瓷迟滞非线性随输入信号频率变化,且难以完全抵消,模型参数存在不确定性等问题,设计一种自适应滑模控制律,利用Lyapunov稳定性定理及仿真实验证明了该控制律可以使系统全局渐进稳定。最后,进行了压电陶瓷迟滞补偿实验和位移跟踪实验。实验结果表明,前馈逆补偿控制下的压电陶瓷位移迟滞量减小了96.1%。与直接控制相比,前馈逆补偿控制下位移跟踪的最大绝对误差减小了27.0%,平均绝对值误差减小了17.9%,具有更好的跟踪精度和动态性能。Aiming at the dynamic hysteresis nonlinearity of piezoelectric ceramics,the sliding mode adaptive control strategy based on Duhem inverse model feedforward compensation is studied.Firstly,the unknown piecewise functions f(.)and g(.)in the Duhem model are approximated by polynomial.The recursive least squares method is used to identify the system,and the inverse model is obtained as the feedforward controller.Considering the hysteresis nonlinearity of piezoelectric ceramics with the change of input signal frequency,it is difficult to completely cancel out,and parameters of the model have uncertainties.An adaptive sliding mode control law is designed.The control law is proved by Lyapunov stability theorem and simulation experiments.It can make the system globally stable.Finally,piezoelectric ceramic hysteresis compensation experiment and displacement tracking experiment were carried out.The experimental results show that the displacement hysteresis of piezoelectric ceramics under the feedforward inverse compensation control is reduced by 96.1%.Compared with direct control,the maximum absolute error of displacement tracking under feedforward inverse compensation control is reduced by 27.0%,and the average absolute value error is reduced by 17.9%,which has better tracking accuracy and dynamic performance.

关 键 词：压电陶瓷 迟滞非线性 Duhem模型 递推最小二乘法 逆补偿 自适应滑模控制 

分 类 号：TP273.3[自动化与计算机技术—检测技术与自动化装置]