Abstract
Voice coil motor (VCM) has obvious rate-dependent hysteresis characteristics, which means that when the frequency of the input signal changes, the travel distance and the shape of the hysteresis loop will change significantly. Based on the Nonlinear Auto-Regressive with Exogenous Inputs (NARX) neural network model, a rate-dependent hysteresis model consisting of a transfer function sub-model of the VCM and a NARX neural network sub-model is proposed for VCM in this paper. Different from the commonly used rate-dependent operator model, the proposed model has a relatively simple mathematic format. By introducing the transfer function of VCM, the initial prediction of the amplitude and phase shift is realized dynamically, which ensures the nonlinear fitting effect of the NARX neural network. Comparisons of the model responses with the measured data under different frequencies of input current signals indicate that the proposed model can dynamically describe the nonlinear rate-dependent hysteresis of VCM with very high accuracy. On this basis, the inverse model is designed by adopting the method of direct inverse, and the effectiveness of the inverse model in trajectory tracking is preliminarily verified by simulation.
Similar content being viewed by others
Data availability
The data that support the findings of this study are available from the corresponding author, upon reasonable request.
References
Ahmad I, Abdurraqeeb AM (2017) Tracking control of a piezoelectric actuator with hysteresis compensation using RST digital controller. Microsyst Technol-Micro-Nanosyst-Inf Storage Process Syst 23:2307–2317. https://doi.org/10.1007/s00542-016-3213-8
Aljanaideh O, Al-Tahat MD, Al M, Janaideh, (2016) Rate-bias-dependent hysteresis modeling of a magnetostrictive transducer. Microsyst Technol-Micro Nonosyst-Inf Storage Process Syst. https://doi.org/10.1007/s00542-015-2566-8
Amirkhani S, Tootchi A, Chaibakhsh A (2021) Fault detection and isolation of gas turbine using series-parallel NARX model. ISA Trans. https://doi.org/10.1016/j.isatra.2021.03.019
Ang WT, Khosla PK, Riviere CN (2007) Feedforward controller with inverse rate-dependent model for piezoelectric actuators in trajectory-tracking applications. IEEE/ASME Trans Mechatron 12:134–142. https://doi.org/10.1109/TMECH.2006.892824
Atsumi T, Yabui S (2020) Quadruple-stage actuator system for magnetic-head positioning system in hard disk drives. IEEE Trans Indust Electron 67(11):9184–9194. https://doi.org/10.1109/tie.2019.2955432
Azizi A (2017) Introducing a novel hybrid artificial intelligence algorithm to optimize network of industrial applications in modern manufacturing. Complexity. https://doi.org/10.1155/2017/8728209
Azizi A (2019) Hybrid artificial intelligence optimization technique. In: Azizi A (ed) Applications of artificial intelligence techniques in industry 40. Springer, Singapore, pp 27–47. https://doi.org/10.1007/978-981-13-2640-0_4
Azizi A (2020) A case study on computer-based analysis of the stochastic stability of mechanical structures driven by white and colored noise: utilizing artificial intelligence techniques to design an effective active suspension system. Complexity. https://doi.org/10.1155/2020/7179801
Azizi A (2020) Applications of artificial intelligence techniques to enhance sustainability of industry 4.0: design of an artificial neural network model as dynamic behavior optimizer of robotic arms. Complexity. https://doi.org/10.1155/2020/8564140
Azizi A, Entesari F, Osgouie KG, Cheragh M (2013) Intelligent mobile robot navigation in an uncertain dynamic environment. Appl Mech Mater 367:388–392
Chang Y-H, Hao G, Liu C-S (2021) Design and characterisation of a compact 4-degree-of-freedom fast steering mirror system based on double Porro prisms for laser beam stabilization. Sens Actuators A: Phys. https://doi.org/10.1016/j.sna.2021.112639
Changshi L (2015) Comprehension of the ferromagnetic hysteresis via an explicit function. Comput Mater Sci 110:295–301. https://doi.org/10.1016/j.commatsci.2015.08.019
Chen Y, Sun N, Liang D, Qin Y, Fang Y (2021) A neuroadaptive control method for pneumatic artificial muscle systems with hardware experiments. Mech Syst Signal Process. https://doi.org/10.1016/j.ymssp.2020.106976
Chen YY, Huang MH, Tsai YL (2021) Nonlinear control design of piezoelectric actuators with micro positioning capability, microsystem technologies-micro-and nanosystems-information. Storage Process Syst 27:1589–1599. https://doi.org/10.1007/s00542-019-04437-9
Cheng L, Liu W, Hou Z-G, Yu J, Tan M (2015) Neural-network-based nonlinear model predictive control for piezoelectric actuators. IEEE Trans Industr Electron 62:7717–7727. https://doi.org/10.1109/tie.2015.2455026
Davino D, Natale C, Pirozzi S, Visone C (2005) A fast compensation algorithm for real-time control of magnetostrictive actuators. J Magn Magn Mater. https://doi.org/10.1016/j.jmmm.2004.11.435
Dong R, Tan Y, Xie Y (2016) Identification of micropositioning stage with piezoelectric actuators. Mech Syst Signal Process 75:618–30. https://doi.org/10.1016/j.ymssp.2015.12.032
Du C, Xie L, Zhang J (2010) Compensation of VCM actuator pivot friction based on an operator modeling method. IEEE Trans Control Syst Technol 18:918–926. https://doi.org/10.1109/tcst.2009.2027430
Du Z, Zhou C, Cao Z, Wang S, Cheng L, Tan M (2021) A neural network-based model predictive controller for displacement tracking of piezoelectric actuator with feedback delays. Int J Adv Rob Syst 18(6):172988142110576
Ito S, Unger S, Schitter G (2017) Vibration isolator carrying atomic force microscope’s head. Mechatronics 44:32–41. https://doi.org/10.1016/j.mechatronics.2017.04.008
Li Z, Shan J, Gabbert U (2018) Inverse compensation of Hysteresis using Krasnoselskii-Pokrovskii Model. IEEE-ASME Trans Mechatron 23:966–971. https://doi.org/10.1109/tmech.2018.2805761
Li W, Nie L, Liu Y, Zhou M (2020) Rate dependent krasnoselskii-pokrovskii modeling and inverse compensation control of piezoceramic actuated stages. Sens (Basel). https://doi.org/10.3390/s20185062
Lin R, Li Y, Zhang Y, Wang T, Wang Z, Song Z et al (2019) Design of a flexure-based mixed-kinematic XY high-precision positioning platform with large range. Mech Mach Theory. https://doi.org/10.1016/j.mechmachtheory.2019.103609
Ma Y, Liu H, Zhu Y, Wang F, Luo Z (2017) Model-based system identification on nonlinear. Rotor-Bear Syst Appl Sci. https://doi.org/10.3390/app7090911
Pan J, Or SW, Zou Y, Cheung NC (2015) Sliding-mode position control of medium‐stroke voice coil motor based on system identification observer. IET Electr Power Appl 9:620–627. https://doi.org/10.1049/iet-epa.2014.0486
Pop NC, Caltun OF (2011) Jiles-Atherton magnetic hysteresis parameters identification. Acta Phys Pol A 120:491–496
Pujol J (2007) The solution of nonlinear inverse problems and the Levenberg-Marquardt method. Geophysics 72:W1–W16. https://doi.org/10.1190/1.2732552
Sanchez-Duran JA, Oballe-Peinado O, Castellanos-Ramos J, Vidal-Verdu F (2012) Hysteresis correction of tactile sensor response with a generalized Prandtl-Ishlinskii model. Microsyst Technol-Micro-Nanosyst-Inf Storage Process Syst 18:1127–1138. https://doi.org/10.1007/s00542-012-1455-7
Shan G, Li Y, Zhang Y, Wang Z, Qian J (2016) Experimental characterization, modeling and compensation of rate-independent hysteresis of voice coil motors. Sens Actuators A-Phys 251:10–9. https://doi.org/10.1016/j.sna.2016.09.030
Tao Y-D, Li H-X, Zhu L-M (2019) Rate-dependent hysteresis modeling and compensation of piezoelectric actuators using gaussian process. Sens Actuators A: Phys 295:357–365. https://doi.org/10.1016/j.sna.2019.05.046
Visone C (2008) Hysteresis Modelling and Compensation for Smart Sensors and Actuators. Int Workshop Multi-Rate Process Hysteresis. https://doi.org/10.1088/1742-6596/138/1/012028
Wang R, Yin X, Wang Q, Jiang L (2020) Direct amplitude control for voice coil motor on high frequency reciprocating rig. IEEE/ASME Trans Mechatron 25:1299–1309. https://doi.org/10.1109/tmech.2020.2973938
Wang T, Li Y, Zhang Y, Lin R, Dou Z (2021) Design of a flexure-based parallel XY micropositioning stage with millimeter workspace and high bandwidth. Sens Actuators Phys 331:112899. https://doi.org/10.1016/j.sna.2021.112899
Xie S, Ren J (2019) High-speed AFM imaging via iterative learning-based model predictive control. Mechatronics 57:86–94. https://doi.org/10.1016/j.mechatronics.2018.11.008
Xu Q, Wong P-K (2011) Hysteresis modeling and compensation of a piezostage using least squares support vector machines. Mechatronics 21:1239–1251. https://doi.org/10.1016/j.mechatronics.2011.08.006
Yang M-J, Gu G-Y, Zhu L-M (2013) Parameter identification of the generalized prandtl–ishlinskii model for piezoelectric actuators using modified particle swarm optimization. Sens Actuators A: Phys 189:254–265. https://doi.org/10.1016/j.sna.2012.10.029
Yang M-J, Li C-X, Gu G-Y, Zhu L-M (2015) Modeling and compensating the dynamic hysteresis of piezoelectric actuators via a modified rate-dependent Prandtl-Ishlinskii model. Smart Mater Struct. https://doi.org/10.1088/0964-1726/24/12/125006
Zhang YX, Li YZ, Shan GQ, Chen YF, Wang ZY, Qian JQ (2018) Real-time scan speed control of the atomic force microscopy for reducing imaging time based on sample topography. Micron 106:1–6. https://doi.org/10.1016/j.micron.2017.12.004
Zhang H, Wu Z, Xu Q (2020) Design of a new XY flexure micropositioning stage with a large hollow platform. Actuators. https://doi.org/10.3390/act9030065
Zhang Y, Liu H, Ma T, Hao L, Li Z (2021) A comprehensive dynamic model for pneumatic artificial muscles considering different input frequencies and mechanical loads. Mech Syst Signal Process. https://doi.org/10.1016/j.ymssp.2020.107133
Acknowledgements
The authors wish to thank the National Natural Science Foundation of China (No. 62271032, 62171012 and 61771033).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Lin, R., Li, Y., Xu, Z. et al. Dynamic rate-dependent hysteresis modeling and trajectory prediction of voice coil motors based on TF-NARX neural network. Microsyst Technol 29, 1319–1331 (2023). https://doi.org/10.1007/s00542-023-05504-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00542-023-05504-y