压电陶瓷驱动器迟滞建模方法研究
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摘要
压电陶瓷驱动器是原子力显微镜(AFM)的关键组件。AFM在生物、材料及半导体等领域应用广泛,而利用AFM获得高精确的测试结果依然面临诸多挑战。其中,压电陶瓷驱动器具有迟滞、非线性等特点,在大范围高频工作状态下,对定位精度的影响更显著,这严重限制了AFM的进一步应用。本文围绕大范围压电陶瓷驱动器的迟滞性展开研究,设计一种基于改进型多项式拟合算法的迟滞建模方法,使得拟合模型可随输入信号频率的变化而变化,充分提高压电陶瓷迟滞模型的准确性。实验表明,该方法可为压电陶瓷驱动器建立准确的迟滞模型,建模过程简单,通过设计基于该迟滞逆模型的前馈控制算法,可使驱动范围在100μm的压电陶瓷驱动器的线性度提高至1.5%。
Piezoelectric driver is an important part of Atomic force microscopy( AFM). AFM is widely used in fields of biology,chemistry,materials and semiconductor. However,many challenges still exist in the application of AFM to achieve highly accurate measurement results. Due to the hysteresis and nonlinearity of PZT,its positioning accuracy is low at high frequency or large range,limiting the further application of AFM. The paper proposed an improved polynomial fitting method to improve the accuracy of the hysteresis model. The model could change its parameters as the signal frequency changes. Experiments prove that the method could build accurate model to describe the hysteresis of PZT with large range. The modeling process is easy. The nonlinearity of PZT( driving range 100 μm) could be improved to 1.5% by designing a feedforward controller based on the inverse model.
Piezoelectric driver is an important part of Atomic force microscopy( AFM). AFM is widely used in fields of biology,chemistry,materials and semiconductor. However,many challenges still exist in the application of AFM to achieve highly accurate measurement results. Due to the hysteresis and nonlinearity of PZT,its positioning accuracy is low at high frequency or large range,limiting the further application of AFM. The paper proposed an improved polynomial fitting method to improve the accuracy of the hysteresis model. The model could change its parameters as the signal frequency changes. Experiments prove that the method could build accurate model to describe the hysteresis of PZT with large range. The modeling process is easy. The nonlinearity of PZT( driving range 100 μm) could be improved to 1.5% by designing a feedforward controller based on the inverse model.
引文
[1] 范伟,林瑜阳,李钟慎.压电陶瓷驱动器的迟滞特性[J].光学精密工程,2016,24(5):1112-1117.
[2] Liu Che,Guo Yanling.Modeling and Positioning of a PZT Precision Drive System[J].Sensors(Basel,Switzerland),2017,17(11):2577.
[3] Wang Y,Wan J,Hu X,et al.A Rate Adaptive Control Method for Improving the Imaging Speed of Atomic Force Microscopy[J].Ultramicroscopy,2015,155:49-54.
[4] Ando T,Uchihashi T,Kodera N.High-Speed AFM and Applications to Biomolecular Systems[J].Annual Review of Biophysics,2013,42(42):393-414.
[5] 王硕.压电陶瓷微位移器驱动电源设计及研究[D].合肥:合肥工业大学,2014.
[6] Tan Xiaobo,Baras John S,Adaptive Identification and Control of Hysteresis in Smart Materials[J].IEEE Transactions on Automatic Control,2005,50(6):827-839.
[7] Wang Y,Hu X,Xu L,et al.Improving the Scanning Speed of Atomic Force Microscopy at the Scanning Range of Several Tens of Micrometers[J].Ultramicroscopy,2013,124:102-107.
[8] 节德刚,孙立宁,曲东升,等.压电陶瓷微位移系统的模糊PID 控制方法[J].哈尔滨工业大学学报,2005,37(2):145-147.
[9] Wei Tech Ang,Pradeep K Khosla,Cameron N Riviere.Feedforward Controller ith Inverse Rate-Dependent Model for Piezoelectric Actuators in Trajectory Tracking Applications[J].IEEE Transactions on Mechatronics,2007,12(2):134-142.
[10] 朱斌,朱玉川,李宇阳.压电叠堆执行器迟滞建模与前馈补偿研究[J].压电与声光,2018,40(1):38-46.
[11] 曲东升,孙立宁,高有将.压电陶瓷致动器自适应逆控制方法的研究[J].压电与声光,2002,24(5):354-357.
[12] 方楚,郭劲,徐新行等.压电陶瓷迟滞非线性前馈补偿器[J].光学精密工程,2016,24(9):2217-2223.
[13] 于志亮,刘杨,王岩,等.基于改进PI模型的压电陶瓷迟滞特性补偿控制[J].仪器仪表学报,2017,38(1):129-135.
[14] 李黎,刘向东,侯朝桢.Preisach逆模型补偿的压电陶瓷执行器自适应滑模控制[J].北京理工大学学报,2008,28(3):237-240.
[15] 徐运扬,徐康康,沈平.AFM压电陶瓷驱动器类Hammerstein建模与参数辨识[J].传感技术学报,2015,28(1):23-27.
[16] 杨晓京,彭芸浩,李尧.基于Bouc-Wen类迟滞模型的压电微动台建模[J].传感器与微系统,2017,36(6):26-31.
[17] 王栋,于鹏,周磊,等.基于梯形算子的AFM驱动器非对称迟滞性校正[J].仪器仪表学报,2015,36(1):32-39.
[18] 许素安,金玮,梁宇恩,等.压电陶瓷迟滞神经网络建模与线性补偿控制[J].传感技术学报,2017,30(12):1884-1889.
[19] 钱飞,许素安,刘亚睿,等.基于多项式拟合的压电陶瓷迟滞神经网络建模[J].计算机仿真,2015,32(1):361-366.
[20] 王建红,林健,张建华,等.压电致动器迟滞特性的多项式拟合建模[J].机床与液压,2015,43(19):71-74.
[21] Wang Yanyan,Wu Sen,Xu Linyan.A New Precise Positioning Method for Piezoelectric Scanner of AFM[J].Ultramicroscopy,2019,196:67-73.
[22] 荣伟彬,曲东升,孙立宁,等.压电陶瓷微位移器件迟滞模型的研究[J].压电与声光,2003,25(1):22-25.
[23] 司守奎,孙兆亮.数学建模算法与应用[M].第2版.北京:国防工业出版社,2015:92-94.
[2] Liu Che,Guo Yanling.Modeling and Positioning of a PZT Precision Drive System[J].Sensors(Basel,Switzerland),2017,17(11):2577.
[3] Wang Y,Wan J,Hu X,et al.A Rate Adaptive Control Method for Improving the Imaging Speed of Atomic Force Microscopy[J].Ultramicroscopy,2015,155:49-54.
[4] Ando T,Uchihashi T,Kodera N.High-Speed AFM and Applications to Biomolecular Systems[J].Annual Review of Biophysics,2013,42(42):393-414.
[5] 王硕.压电陶瓷微位移器驱动电源设计及研究[D].合肥:合肥工业大学,2014.
[6] Tan Xiaobo,Baras John S,Adaptive Identification and Control of Hysteresis in Smart Materials[J].IEEE Transactions on Automatic Control,2005,50(6):827-839.
[7] Wang Y,Hu X,Xu L,et al.Improving the Scanning Speed of Atomic Force Microscopy at the Scanning Range of Several Tens of Micrometers[J].Ultramicroscopy,2013,124:102-107.
[8] 节德刚,孙立宁,曲东升,等.压电陶瓷微位移系统的模糊PID 控制方法[J].哈尔滨工业大学学报,2005,37(2):145-147.
[9] Wei Tech Ang,Pradeep K Khosla,Cameron N Riviere.Feedforward Controller ith Inverse Rate-Dependent Model for Piezoelectric Actuators in Trajectory Tracking Applications[J].IEEE Transactions on Mechatronics,2007,12(2):134-142.
[10] 朱斌,朱玉川,李宇阳.压电叠堆执行器迟滞建模与前馈补偿研究[J].压电与声光,2018,40(1):38-46.
[11] 曲东升,孙立宁,高有将.压电陶瓷致动器自适应逆控制方法的研究[J].压电与声光,2002,24(5):354-357.
[12] 方楚,郭劲,徐新行等.压电陶瓷迟滞非线性前馈补偿器[J].光学精密工程,2016,24(9):2217-2223.
[13] 于志亮,刘杨,王岩,等.基于改进PI模型的压电陶瓷迟滞特性补偿控制[J].仪器仪表学报,2017,38(1):129-135.
[14] 李黎,刘向东,侯朝桢.Preisach逆模型补偿的压电陶瓷执行器自适应滑模控制[J].北京理工大学学报,2008,28(3):237-240.
[15] 徐运扬,徐康康,沈平.AFM压电陶瓷驱动器类Hammerstein建模与参数辨识[J].传感技术学报,2015,28(1):23-27.
[16] 杨晓京,彭芸浩,李尧.基于Bouc-Wen类迟滞模型的压电微动台建模[J].传感器与微系统,2017,36(6):26-31.
[17] 王栋,于鹏,周磊,等.基于梯形算子的AFM驱动器非对称迟滞性校正[J].仪器仪表学报,2015,36(1):32-39.
[18] 许素安,金玮,梁宇恩,等.压电陶瓷迟滞神经网络建模与线性补偿控制[J].传感技术学报,2017,30(12):1884-1889.
[19] 钱飞,许素安,刘亚睿,等.基于多项式拟合的压电陶瓷迟滞神经网络建模[J].计算机仿真,2015,32(1):361-366.
[20] 王建红,林健,张建华,等.压电致动器迟滞特性的多项式拟合建模[J].机床与液压,2015,43(19):71-74.
[21] Wang Yanyan,Wu Sen,Xu Linyan.A New Precise Positioning Method for Piezoelectric Scanner of AFM[J].Ultramicroscopy,2019,196:67-73.
[22] 荣伟彬,曲东升,孙立宁,等.压电陶瓷微位移器件迟滞模型的研究[J].压电与声光,2003,25(1):22-25.
[23] 司守奎,孙兆亮.数学建模算法与应用[M].第2版.北京:国防工业出版社,2015:92-94.