压电微定位台的率相关动态迟滞建模及参数辨识
|
摘要
针对压电微定位台固有的率相关迟滞非线性严重限制其微定位精度的问题,研究了基于Backlash-Like的Hammerstein率相关迟滞非线性模型及其建模方法。以改进的Backlash-Like分段辨识模型描述压电微定位台的静态非线性特性,结合ARX(Auto Regressive eXogenous)模型,建立描述压电微定位台的率相关动态迟滞模型。同时,针对传统的粒子群算法(Particle Swarm Optimization,PSO)进行模型参数辨识时易陷入局部最优的问题,提出一种具有交叉变异策略的改进型粒子群算法进行模型的参数辨识。实验结果表明:与传统的Backlash-Like模型相比,改进的Backlash-Like分段辨识模型在输入电压为60V,频率为2Hz的信号时,模型辨识的最大误差由0.68μm下降到了0.104μm,最大相对误差由2.69%下降为0.35%。当压电微定位台输入电压为60V,频率分别为30Hz,60Hz和90Hz的单频信号时,Hammerstein率相关迟滞模型较Backlash-Like分段辨识模型,均方根误差由0.393 1～0.700 6μm下降至0.054 1～0.190 4μm,相对误差由1.721%～3.087%下降至0.236%～0.831%。验证了基于改进Backlash-Like的Hammerstein率相关迟滞模型较传统的Backlash-Like静态迟滞模型能精确地描述压电微定位台的率相关动态迟滞特性,具有较好的频率泛化能力,提高了压电微定位平台的定位精度。
The inherent rate-dependent hysteresis non-linearity of a piezoelectric micro-positioning station seriously limits its micro-positioning accuracy.To solve this problem,the Hammerstein rate-dependent hysteresis nonlinear model based on Backlash-Like hysteresis and its modeling method were investigated in this study.An improved Backlash-Like piece-wise identification model was first utilized to describe the static nonlinear characteristics of the piezoelectric micro-positioning station.Combined with the Auto Regressive eXogenous(ARX)model,a rate-dependent dynamic hysteresis model was then established to describe the piezoelectric micro-positioning station.In addition,to solve the problem in which the traditional Particle Swarm Optimization(PSO)method easily falls into a local optimum,an improved PSO method using a cross-mutation strategy was proposed to identify the parameters of the model.The experimental results show that,compared to the traditional Backlash-Like model,the maximum error of model identification is reduced from 0.68μm to 0.104μm and the maximum relative error is reduced from 2.69%to 0.35% when the input voltage is 60 Vand the voltage frequency is a single-frequency signal of 2 Hz.In addition,when the input voltage of the piezoelectric micro-positioning station is 60 Vand the voltage frequency is a single-frequency signal of 30,60,and90 Hz,as compared with the Backlash-Like piece-wise identification model,the root mean square error of the Hammerstein rate-dependent hysteresis model decrease from 0.338 7-0.700 6 to 0.035 1-0.190 4,and the relative error decrease from 1.478%-3.087% to 0.153%-0.831%.It was verified that the rate-dependent hysteresis model based on the improved Backlash-Like model could more accurately describe the rate-dependent dynamic hysteresis characteristics of a piezoelectric micro-positioning station as compared with the traditional Backlash-Like static hysteresis model.In addition,the model showed better frequency generalization,and the positioning accuracy of the piezoelectric micropositioning platform was improved.
The inherent rate-dependent hysteresis non-linearity of a piezoelectric micro-positioning station seriously limits its micro-positioning accuracy.To solve this problem,the Hammerstein rate-dependent hysteresis nonlinear model based on Backlash-Like hysteresis and its modeling method were investigated in this study.An improved Backlash-Like piece-wise identification model was first utilized to describe the static nonlinear characteristics of the piezoelectric micro-positioning station.Combined with the Auto Regressive eXogenous(ARX)model,a rate-dependent dynamic hysteresis model was then established to describe the piezoelectric micro-positioning station.In addition,to solve the problem in which the traditional Particle Swarm Optimization(PSO)method easily falls into a local optimum,an improved PSO method using a cross-mutation strategy was proposed to identify the parameters of the model.The experimental results show that,compared to the traditional Backlash-Like model,the maximum error of model identification is reduced from 0.68μm to 0.104μm and the maximum relative error is reduced from 2.69%to 0.35% when the input voltage is 60 Vand the voltage frequency is a single-frequency signal of 2 Hz.In addition,when the input voltage of the piezoelectric micro-positioning station is 60 Vand the voltage frequency is a single-frequency signal of 30,60,and90 Hz,as compared with the Backlash-Like piece-wise identification model,the root mean square error of the Hammerstein rate-dependent hysteresis model decrease from 0.338 7-0.700 6 to 0.035 1-0.190 4,and the relative error decrease from 1.478%-3.087% to 0.153%-0.831%.It was verified that the rate-dependent hysteresis model based on the improved Backlash-Like model could more accurately describe the rate-dependent dynamic hysteresis characteristics of a piezoelectric micro-positioning station as compared with the traditional Backlash-Like static hysteresis model.In addition,the model showed better frequency generalization,and the positioning accuracy of the piezoelectric micropositioning platform was improved.
引文
[1]XU Q S,LI Y M.Analytical modeling,optimization and testing of a compound bridge-type compliant displacement amplifier[J].Mechanism and Machine Theory,2011,46(2):183-200.
[2]LIU Y,LI J,HU X,et al..Modeling and control of piezoelectric inertia-friction actuators:review and future research directions[J].Mechanical Science,2015,6(2):95-104.
[3]CHEN L S,YEN J Y,CHEN J,et al..Precision tracking of a piezo-driven stage by charge feedback control[J].Precision Engineering,2013,37(4):793-804.
[4]李黎,刘向东,王伟,等.压电陶瓷执行器迟滞特性的广义非线性Preisach模型及其数值实现[J].光学精密工程,2017,15(5):706-712.LI L,LIU X D,WANG W,et al..Generalized nonlinear Preisach model for hysteresis nonlinearity of piezoceramic actuator and its numerical implementation[J].Opt.Precision Eng.,2017,15(5):706-712.(in Chinese)
[5]田雷,陈俊杰,崔玉国,等.基于PI迟滞模型的单压电变形镜开环控制[J].仪器仪表学报,2017,38(1),136-142.TIAN L,CHEN J J,CUI Y G.Open-loop control of unimorph piezoelectric deformable mirror based on PIhysteresis model[J].Chinese Journal of Scientific Instrument,2017,38(1),136-142.(in Chinese)
[6]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):129-136.YU ZH L,LIU Y,WANG Y,et al..Hysteresis compensa-tion and control of piezoelectric actuator based on an improved PI model[J].Chinese Journal of scientific Instrument,2017,38(1):129-136.(in Chinese)
[7]陈辉,谭永红,周杏鹏,等.压电陶瓷执行器的动态模型辨识与控制[J].光学精密工程,2012,20(1):88-95.CHEN H,TAN Y H,ZHOU X P,et al..Identification and control of dynamic modeling for piezoelectric actuator[J].Opt.Precision Eng.,2012,20(1):88-95.(in Chinese)
[8]LIN C J,LIN P T.Tracking control of a biaxial piezo-actuated positioning stage using generalized Dehum model[J].Computers and Mathematics with Applications,2012,64:766-787.
[9]朱炜,芮筱亭.压电执行器的Bouc-Wen模型在线参数辨识[J].光学精密工程,2015,23(1):1110-1116.ZHU W,RUI X T.Online parameter identification of Bouc-Wen model for piezoelectric actuators[J].Opt.Precision Eng.,2015,23(1):1110-1116.(in Chinese)
[10]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 CH L,HU SH ZH,GUO H L,et al..Feedforward control of stack piezoelectric actuator[J].Opt.Precision Eng.,2016,24(9):2255-2261.(in Chinese)
[11]SU C Y,STEPANENKO Y,SVOBODA J,et al..Robust adaptive control of a class of nonlinear systems with unknown Backlash-Like Hysteresis[J].IEEE Transac-tions on Automatic Control,2000,45(12):2427-2432.
[12]LAI G,ZHI L,YUN Z,et al..Adaptive fuzzy tracking control of nonlinear systems with asymmetric actuator Backlash based on a new smooth inverse[J].IEEE Transactions on Cybernetics,2016,46(6):1250-1262.
[13]杨晓京,李庭树,刘浩.压电超精密定位台的动态迟滞建模研究[J].仪器仪表学报,2017,38(10):2492-2499.YANG X J,LI T SH,LIU H.Dynamic hysteresis modeling of piezoelectric ultra precision positioning stage[J].Chinese Journal of scientific Instrument,2017,38(10):2492-2499.(in Chinese)
[14]赖志林,刘向东,耿洁.压电陶瓷执行器的类Hammerstein模型及其参数辨识[J].光学精密工程,2012,20(9):2087-2094.LAI ZH L,LIU X D,GENG J.Hammersteinbased model of piezoceramic actuator and its identification[J].Opt.Precision Eng.,2012,20(9):2087-2094.(in Chinese)
[15]王贞艳,张臻,周克敏,等.压电作动器的动态迟滞建模与H"鲁棒控制[J].控制理论与应用,2014,31(1):35-41.WANG ZH Y,ZHANG ZH,ZHOU K M,et al..Dynamic hysteresis modeling and H-infinity robust control of piezoelectric actuators[J].Control Theory&Applic-ations,2014,31(1):35-41.(in Chinese)
[16]胡凯明,文立华.PBP驱动器率相关迟滞特性研究及其线性化控制[J].机械工程学报,2016,52(12):205-212.HU K M,WEN L H.Research on rate-dependent hysteresis characteristics of PBP actuators and its linearization control[J].Journal of mechanical enginee-ring,2016,52(12):205-212.(in Chinese)
[2]LIU Y,LI J,HU X,et al..Modeling and control of piezoelectric inertia-friction actuators:review and future research directions[J].Mechanical Science,2015,6(2):95-104.
[3]CHEN L S,YEN J Y,CHEN J,et al..Precision tracking of a piezo-driven stage by charge feedback control[J].Precision Engineering,2013,37(4):793-804.
[4]李黎,刘向东,王伟,等.压电陶瓷执行器迟滞特性的广义非线性Preisach模型及其数值实现[J].光学精密工程,2017,15(5):706-712.LI L,LIU X D,WANG W,et al..Generalized nonlinear Preisach model for hysteresis nonlinearity of piezoceramic actuator and its numerical implementation[J].Opt.Precision Eng.,2017,15(5):706-712.(in Chinese)
[5]田雷,陈俊杰,崔玉国,等.基于PI迟滞模型的单压电变形镜开环控制[J].仪器仪表学报,2017,38(1),136-142.TIAN L,CHEN J J,CUI Y G.Open-loop control of unimorph piezoelectric deformable mirror based on PIhysteresis model[J].Chinese Journal of Scientific Instrument,2017,38(1),136-142.(in Chinese)
[6]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):129-136.YU ZH L,LIU Y,WANG Y,et al..Hysteresis compensa-tion and control of piezoelectric actuator based on an improved PI model[J].Chinese Journal of scientific Instrument,2017,38(1):129-136.(in Chinese)
[7]陈辉,谭永红,周杏鹏,等.压电陶瓷执行器的动态模型辨识与控制[J].光学精密工程,2012,20(1):88-95.CHEN H,TAN Y H,ZHOU X P,et al..Identification and control of dynamic modeling for piezoelectric actuator[J].Opt.Precision Eng.,2012,20(1):88-95.(in Chinese)
[8]LIN C J,LIN P T.Tracking control of a biaxial piezo-actuated positioning stage using generalized Dehum model[J].Computers and Mathematics with Applications,2012,64:766-787.
[9]朱炜,芮筱亭.压电执行器的Bouc-Wen模型在线参数辨识[J].光学精密工程,2015,23(1):1110-1116.ZHU W,RUI X T.Online parameter identification of Bouc-Wen model for piezoelectric actuators[J].Opt.Precision Eng.,2015,23(1):1110-1116.(in Chinese)
[10]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 CH L,HU SH ZH,GUO H L,et al..Feedforward control of stack piezoelectric actuator[J].Opt.Precision Eng.,2016,24(9):2255-2261.(in Chinese)
[11]SU C Y,STEPANENKO Y,SVOBODA J,et al..Robust adaptive control of a class of nonlinear systems with unknown Backlash-Like Hysteresis[J].IEEE Transac-tions on Automatic Control,2000,45(12):2427-2432.
[12]LAI G,ZHI L,YUN Z,et al..Adaptive fuzzy tracking control of nonlinear systems with asymmetric actuator Backlash based on a new smooth inverse[J].IEEE Transactions on Cybernetics,2016,46(6):1250-1262.
[13]杨晓京,李庭树,刘浩.压电超精密定位台的动态迟滞建模研究[J].仪器仪表学报,2017,38(10):2492-2499.YANG X J,LI T SH,LIU H.Dynamic hysteresis modeling of piezoelectric ultra precision positioning stage[J].Chinese Journal of scientific Instrument,2017,38(10):2492-2499.(in Chinese)
[14]赖志林,刘向东,耿洁.压电陶瓷执行器的类Hammerstein模型及其参数辨识[J].光学精密工程,2012,20(9):2087-2094.LAI ZH L,LIU X D,GENG J.Hammersteinbased model of piezoceramic actuator and its identification[J].Opt.Precision Eng.,2012,20(9):2087-2094.(in Chinese)
[15]王贞艳,张臻,周克敏,等.压电作动器的动态迟滞建模与H"鲁棒控制[J].控制理论与应用,2014,31(1):35-41.WANG ZH Y,ZHANG ZH,ZHOU K M,et al..Dynamic hysteresis modeling and H-infinity robust control of piezoelectric actuators[J].Control Theory&Applic-ations,2014,31(1):35-41.(in Chinese)
[16]胡凯明,文立华.PBP驱动器率相关迟滞特性研究及其线性化控制[J].机械工程学报,2016,52(12):205-212.HU K M,WEN L H.Research on rate-dependent hysteresis characteristics of PBP actuators and its linearization control[J].Journal of mechanical enginee-ring,2016,52(12):205-212.(in Chinese)