Hysteresis nonlinearity widely exists in the piezoelectric actuator (PEA), and the hysteresis nonlinearity has strong dynamic characteristics that lead to deterioration of tracking performance. To decrease the positioning error caused by hysteresis nonlinearity, a generalized Bouc-Wen (GBW) hysteresis model and its compensation method are proposed in this paper. First, based on the Bouc-Wen hysteresis model, two asymmetric terms and a second-order IIR filter are applied to describe the asymmetric hysteresis and high-frequency phase lag characteristics of PEA. Then, the model parameters with strong relevance to frequency variation are modified as frequency-dependent parameters. Meanwhile, based on the particle swarm optimization (PSO) algorithm, a novel parameter identification algorithm is designed for identifying the parameters of GBW hysteresis model. Then, an inverse feedforward controller is constructed based on the GBW hysteresis model, and a composite compensation control algorithm combining PID controller and repetitive controller is developed to reduce the unmodeled dynamics errors and unknown external disturbances. Finally, the comparison experiment results show that the accuracy and performance of the GBW model proposed in this paper are much better than the classical Bouc-Wen (CBW) model and the enhanced Bouc-Wen (EBW) model, and the developed compensation controller has excellent control performance and robustness.
ChenXLiW (2015) A monolithic self-sensing precision stage: Design, modeling, calibration, and hysteresis compensation. IEEE/ASME Transactions on Mechatronics20: 812–823.
2.
ChenXXuLZhangS, et al. (2022) Parameter identification of the Bouc-Wen model for the magnetorheological damper using fireworks algorithm. Journal of Mechanical Science and Technology36: 2213–2224.
3.
GanJZhangX (2018) An enhanced Bouc-Wen model for characterizing rate-dependent hysteresis of piezoelectric actuators. Review of Scientific Instruments89: 115002.
4.
GanJZhangX (2019a) A review of nonlinear hysteresis modeling and control of piezoelectric actuators. AIP Advances9: 040702.
5.
GanJZhangX (2019b) Nonlinear hysteresis modeling of piezoelectric actuators using a generalized Bouc–Wen model. Micromachines10: 183.
6.
GanJZhangXWuH (2016) Tracking control of piezoelectric actuators using a polynomial-based hysteresis model. AIP Advances6: 065204.
7.
GomisBOIkhouaneFCastell-VilanovaP, et al. (2007) Modeling a hysteretic piezoelectric actuator employing a modified Bouc-Wen model. In: 2007 European control conference (ECC), Kos, Greece, 2–5 July.
8.
HuangDMinDJianY, et al. (2019) Current-cycle iterative learning control for high-precision position tracking of piezoelectric actuator system via active disturbance rejection control for hysteresis compensation. IEEE Transactions on Industrial Electronics67: 8680–8690.
9.
IslamMNSeethalerRJ (2013) Sensorless position control for piezoelectric actuators using a hybrid position observer. IEEE/ASME Transactions on Mechatronics19(2): 667–675.
10.
JiHYangSWuZ, et al. (2005) Precision control of piezoelectric actuator using support vector regression nonlinear model and neural networks. In: International conference on machine learning & cybernetics, Guangzhou, China, 18–21 August.
11.
KwonOSeolDQiaoH, et al. (2020) Recent progress in the nanoscale evaluation of piezoelectric and ferroelectric properties via scanning probe microscopy. Advanced Science7: 1901391.
12.
LallartMLiKYangZC, et al. (2020) Simple and efficient inverse hysteretic model and associated experimental procedure for precise piezoelectric actuator control and positioning. Sensors and Actuators A: Physical301: 111674.
13.
LiCJichunXLizhongX, et al. (2018) Nonlinear dynamics of a piezoelectric precision drive system used for robot joint. International Journal of Applied Electromagnetics and Mechanics58: 57–77.
14.
LiWChenXLiZ (2013) Inverse compensation for hysteresis in piezoelectric actuator using an asymmetric rate-dependent model. Review of Scientific Instruments84: 073702.
15.
LinCChenP (2012) Hysteresis compensation and high-performance tracking control of piezoelectric actuators. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering226: 1050–1059.
16.
LingJFengZZhengD, et al. (2021) Robust adaptive motion tracking of piezoelectric actuated stages using online neural-network-based sliding mode control. Mechanical Systems and Signal Processing150: 107235.
17.
LiuYDuDQiN, et al. (2019) A distributed parameter Maxwell-slip model for the hysteresis in piezoelectric actuators. IEEE Transactions on Industrial Electronics66: 7150–7158.
18.
LuJXieWZhouH (2016) Combined fitness function based particle swarm optimization algorithm for system identification. Computers Industrial Engineering95: 122–134.
19.
PelliciariMBriseghellaBTondoloF, et al. (2020) A degrading Bouc–Wen model for the hysteresis of reinforced concrete structural elements. Structure and Infrastructure Engineering16: 917–930.
20.
RafałKMagdalenaR (2017) Modeling of mechanical behaviour of high-frequency piezoelectric actuators using Bouc-Wen model. Nephron Clinical Practice24: 413–424.
21.
RakotondrabeM (2011) Bouc–Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators. IEEE Transactions on Automation Science & Engineering8: 428–431.
22.
SabarianandDVKarthikeyanPMuthuramalingamT (2020) A review on control strategies for compensation of hysteresis and creep on piezoelectric actuators based micro systems. Mechanical Systems and Signal Processing140: 106634.
23.
SalahMSaleemA (2021) Hysteresis compensation-based robust output feedback control for long-stroke piezoelectric actuators at high frequency. Sensors and Actuators A: Physical319: 112542.
24.
ShaoMHuangJWeiS, et al. (2020) An improved PSO algorithm for parameter identification of Bouc-Wen model for piezoelectric actuator. In: 2020 39th Chinese control conference (CCC), Shenyang, China, 27–29 July.
25.
ShivashankarPGopalakrishnanS (2020) Review on the use of piezoelectric materials for active vibration, noise, and flow control. Smart Materials and Structures29: 053001.
26.
SibalijaTV (2019) Particle swarm optimisation in designing parameters of manufacturing processes: A review (2008–2018). Applied Soft Computing Journal84: 105743.
27.
SoflaMSSadighMJZareinejadM (2021) Design and dynamic modeling of a continuum and compliant manipulator with large workspace. Mechanism and Machine Theory164: 104413.
28.
SongJKiureghianAD (2006) Generalized Bouc–Wen model for highly asymmetric hysteresis. Journal of Engineering Mechanics132: 610–618.
29.
SuBLinYWangJ, et al. (2022) Sewage treatment system for improving energy efficiency based on particle swarm optimization algorithm. Energy Reports8: 8701–8708.
30.
TangHLiY (2015) Feedforward nonlinear PID control of a novel micromanipulator using Preisach hysteresis compensator. Robotics and Computer Integrated Manufacturing34: 124–132.
31.
WangGChenG (2017) Identification of piezoelectric hysteresis by a novel Duhem model based neural network. Sensors and Actuators A: Physical264: 282–288.
32.
WangGChenGBaiF (2015) High-speed and precision control of a piezoelectric positioner with hysteresis, resonance and disturbance compensation. Microsystem Technologies22: 1–11.
33.
WangWWangRChenZ, et al. (2020) A new hysteresis modeling and optimization for piezoelectric actuators based on asymmetric Prandtl-Ishlinskii model. Sensors and Actuators A: Physical316: 112431.
34.
WenYK (1976) Method for random vibration of hysteretic systems. Journal of the Engineering Mechanics Division102: 249–263.
35.
XuQ (2017) Continuous integral terminal third-order sliding mode motion control for piezoelectric nanopositioning system. IEEE/ASME Transactions on Mechatronics22: 1828–1838.
36.
YiSYangBMengG (2019) Microvibration isolation by adaptive feedforward control with asymmetric hysteresis compensation. Mechanical Systems and Signal Processing114: 644–657.
37.
YuSXieMWuH, et al. (2020) Composite proportional-integral sliding mode control with feedforward control for cell puncture mechanism with piezoelectric actuation. ISA Transactions124: 427–435.
38.
ZablotskayaTY (2020) Analyzing the classical and extended Bouc-Wen model parameters. In: 2020 2nd international conference on control systems, mathematical modeling, automation and energy efficiency (SUMMA), Lipetsk, Russia, 11–13 November.
39.
ZhangQDongYPengY, et al. (2019) Asymmetric Bouc–Wen hysteresis modeling and inverse compensation for piezoelectric actuator via a genetic algorithm–based particle swarm optimization identification algorithm. Journal of Intelligent Material Systems and Structures30: 1263–1275.
40.
ZhongJLiLNishidaR, et al. (2020) Design and evaluation of a PEA-driven fast steering mirror with a permanent magnet preload force mechanism. Precision Engineering62: 95–105.
41.
ZhongJNishidaRShinshiT (2022) Design and precision tracking control of a high-bandwidth fast steering mirror for laser beam machining. Precision Engineering73: 128–139.
42.
ZongXZhangNWangP (2013) Study on control strategy of nonlinear systems with hysteresis inverse model feed-forward compensation based on Preisach. Advanced Materials Research823: 261–264.
