In order to overcome the problem of positioning inaccuracy caused by nonlinear hysteresis of piezoelectric actuators, a hybrid model based on least-squares support vector machine and Bouc–Wen model is proposed to model the rate-dependent hysteresis of piezoelectric actuators. A rate-independent Bouc–Wen model and its parameters identification method is established as the basis of least-squares Bouc–Wen model. Least-squares support vector machine, which is optimized by particle swarm optimization, is introduced to improve the Bouc–Wen model into a rate-dependent model by adjusting parameters of Bouc–Wen dynamically. Experiment is carried out to validate both Bouc–Wen model and the proposed least-squares Bouc–Wen model. The results show that the proposed least-squares Bouc–Wen method is a valid and a more precise method compared to the rate-independent Bouc–Wen model.
XuWXWuYB. Piezoelectric actuator for machining on macro-to-micro cylindrical components by a precision rotary motion control. Mech Syst Signal Process2019; 114: 439–447.
2.
ChandrasekaranSBowenCRoscowJ, et al.Micro-scale to nano-scale generators for energy harvesting: self powered piezoelectric, triboelectric and hybrid devices. Phys Rep2019; 792: 1–33.
3.
LiuPBYanPÖzbayH. Design and trajectory tracking control of a piezoelectric nano-manipulator with actuator saturations. Mech Syst Signal Process2018; 111: 529–544.
4.
Xu DmLiuYXLiuJK, et al.Developments of a piezoelectric actuator with nano-positioning ability operated in bending modes. Ceram Int2017; 43: 21–26.
5.
GrybasIBubulisAJurenasV, et al.Investigation of a 1-DOF piezoelectric micro-positioning rotary stage. Precis Eng2019; 55: 361–375.
6.
WangCXXieXLChenYH, et al.Investigation on active vibration isolation of a Stewart platform with piezoelectric actuators. J Sound Vib2016; 383: 1–19.
7.
WangCXZhangXWLiuYL, et al.Stiffness variation method for milling chatter suppression via piezoelectric stack actuators. Int J Mach Tools Manuf2018; 124: 53–66.
8.
ZhaoXLXieHPanHP. Modeling rate-dependent hysteresis in piezoelectric actuators using T-S fuzzy system based on expanded input space method. Sens Actuat A2018; 283: 123–127.
9.
ZhangQDongYCPengY, et al.Asymmetric Bouc-Wen hysteresis modeling and inverse compensation for piezoelectric actuator via a genetic algorithm-based particle swarm optimization identification algorithm. J Intell Mater Syst Struct2019; 30: 1263–1275.
10.
EJQQianCZhuH, et al.Parameter-identification investigations on the hysteretic Preisach model improved by the fuzzy least square support vector machine based on adaptive variable chaos immune algorithm. J Low Freq Noise, Vib Active Control2017; 36: 227–242.
11.
NguyenPBChoiSBSongBK. A new approach to hysteresis modelling for a piezoelectric actuator using Preisach model and recursive method with an application to open-loop position tracking control. Sens Actuat A2018; 270: 136–152.
12.
LeeSHRoystonTJ. Modeling piezoceramic transducer hysteresis in the structural vibration control problem. J Acoust Soc Am2000; 108: 2843–2855.
13.
XuQSLiYM. Dahl model-based hysteresis compensation and precise positioning control of an XY parallel micromanipulator with piezoelectric actuation. J Dyn Syst Meas Control2010; 132: 1–12.
14.
WangGChenGQ. Identification of piezoelectric hysteresis by a novel Duhem model based neural network. Sens Actuat A2017; 264: 282–288.
15.
LinCJLinPT. Tracking control of a biaxial piezo-actuated positioning stage using generalized Duhem model. Comput Math Appl2012; 64: 766–787.
16.
StefanskiFMinorowiczBPerssonJ, et al.Non-linear control of a hydraulic piezo-valve using a generalized Prandtl-Ishlinskii hysteresis model. Mech Syst Signal Process2017; 82: 412–431.
17.
XieSLLiuHTMeiJP, et al.Modeling and compensation of asymmetric hysteresis for pneumatic artificial muscles with a modified generalized Prandtl-Ishlinskii model. Mechatronics2018; 52: 49–57.
18.
ParkJMoonW. Hysteresis compensation of piezoelectric actuators: the modified Rayleigh model. Ultrasonics2010; 50: 335–339.
19.
WangGChenGQBaiFZ. Modeling and identification of asymmetric Bouc-Wen hysteresis for piezoelectric actuator via a novel differential evolution algorithm. Sens Actuat A2015; 235: 105–118.
20.
ZhuWBianLXRuiXT. Online parameter identification of the asymmetrical Bouc–Wen model for piezoelectric actuators. Precis Eng2014; 38: 921–927.
21.
MaoXFWangYJLiuXD, et al.An adaptive weighted least square support vector regression for hysteresis in piezoelectric actuators. Sens Actuat A2017; 263: 423–429.
22.
MaYKZhangXNXuML, et al.Hybrid model based on Preisach and support vector machine for novel dual-stack piezoelectric actuator. Mech Syst Signal Process2013; 34: 156–172.
23.
XuQSWongPK. Hysteresis modeling and compensation of a piezostage using least squares support vector machines. Mechatronics2011; 21: 1239–1251.
24.
ZhangXLTanYHSuMY, et al.Neural networks based identification and compensation of rate-dependent hysteresis in piezoelectric actuators. Phys B: Condens Matter2010; 405: 2687–2693.
25.
LienJPYorkAFangTG, et al.Modeling piezoelectric actuators with hysteretic recurrent neural networks. Sens Actuat A2010; 163: 516–525.
26.
ZhaoXLHuiXPanHP. Modeling rate-dependent hysteresis in piezoelectric actuators using T-S fuzzy system based on expanded input space method. Sens Actuat A2018; 283: 123–127.
27.
JanaidehMRakotondrabeMAl-DarabsahI, et al.Internal model-based feedback control design for inversion-free feedforward rate-dependent hysteresis compensation of piezoelectric cantilever actuator. Control Eng Pract2018; 72: 29–41.
28.
AljanaidehOHabinezaDRakotondrabeM, et al.Experimental comparison of rate-dependent hysteresis models in characterizing and compensating hysteresis of piezoelectric tube actuators. Phys B: Condens Matter2016; 486: 64–68.
29.
ZhuWRuiXT. Hysteresis modeling and displacement control of piezoelectric actuators with the frequency-dependent behavior using a generalized Bouc-Wen model. Precis Eng2016; 43: 299–307.
30.
ZhuHTRuiXTYangFF, et al.An efficient parameters identification method of normalized Bouc-Wen model for MR damper. J Sound Vib2019; 448: 146–158.
31.
SolovyovASemenovMEMeleshenkoPA, et al.Bouc-Wen model of hysteretic damping. Procedia Eng2017; 201: 549–555.
32.
BartkowskiPZalewskiRChodkiewiczP. Parameter identification of Bouc-Wen model for vacuum packed particles based on genetic algorithm. Arch Civ Mech Eng2019; 19: 322–333.
33.
VapnikVN. The nature of statistical learning theory, New York: Springer, 1995.
34.
MaYKZhangXXuML, et al.Hybrid model based on Preisach and support vector machine for novel dual-stack piezoelectric actuator. Mech Syst Signal Process2013; 34: 156–172.
35.
García NietoPJGarcía-GonzaloEAlonso FernándezJR, et al.A hybrid PSO optimized SVM-based model for predicting a successful growth cycle of the Spirulina platensis from raceway experiments data. J Comput Appl Math2016; 291: 293–303.
36.
LiuWGuoGChenFJ, et al.Meteorological pattern analysis assisted daily PM2.5 grades prediction using SVM optimized by PSO algorithm. Atmos Pollut Res2019; 10: 1482–1491.
37.
ZhouTLuHLWangWW, et al.GA-SVM based feature selection and parameter optimization in hospitalization expense modeling. Appl Soft Comput2019; 75: 323–332.
38.
DingYMZhangWLYuL, et al.The accuracy and efficiency of GA and PSO optimization schemes on estimating reaction kinetic parameters of biomass pyrolysis. Energy2019; 176: 582–588.
39.
Bouc R. Forced vibration of mechanical systems with hysteresis. In: Proceedings of 4th conference on nonlinear oscillations, Prague, Czechoslovakia, 1967.
40.
WenYK. Method for random vibration of hysteretic systems. J Eng Mech Div1976; 102: 249–263.
