压电陶瓷作动器的率相关迟滞建模与内模控制
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摘要
针对压电陶瓷作动器的率相关迟滞特性,建立了基于广义Bouc-Wen模型的Hammerstein率相关迟滞非线性模型,分别以广义Bouc-Wen模型和自回归历遍模型来代表Hammerstein模型中的静态非线性部分和线性动态部分,并辨识模型参数。在此基础上,得到Hammerstein模型的逆模型,通过构造其正、逆模型设计了内模控制方案,最后在试验平台上对控制方案进行了验证。实验结果表明,对100Hz以内期望信号的跟踪控制相对误差均小于9%,证明了所提出的模型和内模控制策略的有效性。
Aiming at the rate-dependent hysteresis characteristics of piezoelectric ceramic actuators,a Hammerstein rate-dependent hysteresis nonlinear model based on the generalized Bouc-Wen model is established.The generalized Bouc-Wen model and the autoregressive exogenous model are used to represent the static nonlinear part and the linear dynamic part in the Hammerstein model respectively,and the model parameters are identified.On this basis,the inverse model of Hammerstein model is obtained,and the internal model control scheme is designed by constructing its forward and inverse models.Finally,the control scheme is verified on the experimental platform.The experimental results show that the relative error of tracking control for the desired signal in the range of 100 Hz is less than 9%,which proves the effectiveness of the proposed model and internal model control strategy.
Aiming at the rate-dependent hysteresis characteristics of piezoelectric ceramic actuators,a Hammerstein rate-dependent hysteresis nonlinear model based on the generalized Bouc-Wen model is established.The generalized Bouc-Wen model and the autoregressive exogenous model are used to represent the static nonlinear part and the linear dynamic part in the Hammerstein model respectively,and the model parameters are identified.On this basis,the inverse model of Hammerstein model is obtained,and the internal model control scheme is designed by constructing its forward and inverse models.Finally,the control scheme is verified on the experimental platform.The experimental results show that the relative error of tracking control for the desired signal in the range of 100 Hz is less than 9%,which proves the effectiveness of the proposed model and internal model control strategy.
引文
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[11]刘长利,胡守柱,郭海林,等.叠堆式压电陶瓷驱动器的复合控制[J].光学精密工程,2016,24(9):2248-2254.LIU Changli,HU SHouzhu,GUO Hailin,et al.Feedforward control of stack piezoelectric actuator[J].Opt Precision Eng,2016,24(9):2248-2254.
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[13]郭咏新,张臻,毛剑琴,等.超磁致伸缩作动器的率相关Hammerstein模型与H∞鲁棒跟踪控制[J].自动化学报,2014,40(2):197-207.GUO Y X,ZHANG Z,MAO J Q,et al.Rate-dependent Hammerstein model and H∞robust tracking control of giant magnetostrictive actuators[J].Acta Automatica Sinica,2014,40(2):197-207.
[14]孟爱华,刘成龙,陈文艺,等.超磁致伸缩致动器的小脑神经网络前馈逆补偿-模糊PID控制[J].光学精密工程,2015,23(3):753-759.MENG Aihua,LIU Chenglong,CHEN Wenyi,et al.CMAC feedforward inverse compensation-fuzzy PIDcontrol for giant magnetostrictive actuator[J].Opt Precision Eng,2015,23(3):753-759.
[15]朱豫才.过程控制的多变量系统辨识[M].长沙:国防科技大学出版社,2005.
[16]赵志诚,文新宇.内模控制及其应用[M].北京:电子工业出版社,2012.
[2]LI Zhi,ZHANG Xiuyu,SU Chunyi,et al.Nonlinear control of systems preceded by Preisach hysteresis description:aprescribed adaptive control approach[J].IEEE Transactions on Control Systems Technology,2016,24(2):451-460.
[3]翟鹏,肖博涵,贺凯,等.超磁致伸缩致动器的复合反馈控制及其在变椭圆销孔精密加工中的应用[J].光学精密工程,2016,24(6):1389-1398.ZHAI Peng,XIAO Bohan,HE Kai,et al.Composite backward control for GMA and its application in high precision machining of variable ellipse pinhole[J].Opt Precision Eng,2016,24(6):1389-1398.
[4]RONG Ce,HE Zhongbo,LI Dongwei,et al.Online parameter identification of giant magnetostrictive actuator based on dynamic Jiles-Atherton model[J].Rsc Advances,2016,6:113-115.
[5]LIN C,LIN P.Tracking control of a biaxial pieo-actuated positioning stageusing generalized Duhem model[J].Computers&Mathematics with Applications,2012,64(5):766-787.
[6]FENG Ying,KUMKONGKAEW W,DU Juan,et al.Hysteresis modeling for IPMC actuators with rate-dependent Preisach model[C]//S.l.:Intelligent Control and Automation.IEEE,2015:1549-1554.
[7]LIU Zichao,PAN Wei,LU Changhou.A new rate-dependent Prandtl-Ishlinskii model for piezoelectric actuators[J].Applied Mechanics&Materials,2014,651/653:598-602.
[8]LI Wei,CHEN Xuedong,LI Zilong.Inverse compensation for hysteresis in piezoelectric actuator using an asymmetric rate-dependent model[J].Review of Scientific Instruments,2013,84(11):115003.
[9]范家华,马磊,周攀,等.基于径向基神经网络的压电作动器建模与控[J].控制理论与应用,2016,33(7):856-862.FAN Jiahua,MA Lei,ZHOU Pan,et al.Modeling and control of piezoelectric actuator based on radial basis function neural network[J].Control Theory&Applications,2016,33(7):856-862.
[10]谢扬球,谭永红.压电陶瓷执行器的非光滑三明治模型辨识与内模控制[J].控制理论与应用,2013,30(5):567-576.XIE Yangqiu,TAN Yonghong.Identification and control piezoceramic actuator using nonsmooth sandwich model[J].Control Theory&Applications,2013,30(5):567-576.
[11]刘长利,胡守柱,郭海林,等.叠堆式压电陶瓷驱动器的复合控制[J].光学精密工程,2016,24(9):2248-2254.LIU Changli,HU SHouzhu,GUO Hailin,et al.Feedforward control of stack piezoelectric actuator[J].Opt Precision Eng,2016,24(9):2248-2254.
[12]GAN M,ZHI Q,LI Yanlong.Sliding mode control with perturbation estimation and hysteresis compensator based on Bouc-Wen model in tackling fast-varying sinusoidal position control of a piezoelectric actuator[J].Journal of Systems Science and Complexity,2016,29(2):367-381.
[13]郭咏新,张臻,毛剑琴,等.超磁致伸缩作动器的率相关Hammerstein模型与H∞鲁棒跟踪控制[J].自动化学报,2014,40(2):197-207.GUO Y X,ZHANG Z,MAO J Q,et al.Rate-dependent Hammerstein model and H∞robust tracking control of giant magnetostrictive actuators[J].Acta Automatica Sinica,2014,40(2):197-207.
[14]孟爱华,刘成龙,陈文艺,等.超磁致伸缩致动器的小脑神经网络前馈逆补偿-模糊PID控制[J].光学精密工程,2015,23(3):753-759.MENG Aihua,LIU Chenglong,CHEN Wenyi,et al.CMAC feedforward inverse compensation-fuzzy PIDcontrol for giant magnetostrictive actuator[J].Opt Precision Eng,2015,23(3):753-759.
[15]朱豫才.过程控制的多变量系统辨识[M].长沙:国防科技大学出版社,2005.
[16]赵志诚,文新宇.内模控制及其应用[M].北京:电子工业出版社,2012.