Abstract
A non-smooth neural network is proposed for modeling of hysteresis with non-smooth characteristic and multi-valued mapping. In the proposed non-smooth neural network, the non-smooth neurons with multi-valued mapping are constructed for depicting the non-smoothness and multi-valued mapping of hysteresis inherent in piezo-actuators. For parameter estimation, the training algorithm based on non-smooth iterative technique is proposed. In this case, the parameters of the non-smooth neurons can be determined automatically based on the optimization of the cost function. Finally, the experimental results are illustrated to demonstrate the modeling performance of the proposed modeling method.
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References
Hu, H: Compensation of hysteresis in Piezoceramic actuators and control of nanopositioning system. Ph.D. thesis of University of Toronto, Canada (2003)
Ge, P., Jouaneh, M.: Modeling hysteresis in piezoceramic actuators. Precis. Eng. 17, 211–221 (1995)
Mayergoyz, I.D.: Dynamic Preisach models of hysteresis. IEEE Trans. Magn. 24(6), 2925–2927 (1988)
Su, C., Wang, Q., Chen, X., Rakheja, S.: Adaptive variable structure control of a class of nonlinear systems with unknown Prandtl-Ishlinskii hysteresis. IEEE Trans. Autom. Control 50(12), 2069–2074 (2005)
Kugi, A., Thull, D., Kuhnen, K.: An infinite-dimensional control concept for piezoelectric structures with complex hysteresis. Struct. Control Health Monit. 13, 1099–1119 (2006)
Selmic, R., Lewis, F.L.: Neural net backlash compensation with Hebbian tuning using dynamic inversion. Automatica 37, 1269–1277 (2001)
Dong, R., Tan, Y., Chen, H., Xie, Y.: A neural networks based model for rate-dependent hysteresis for piezoceramic actuators. Sens. Actuators A: Phys. 143(2), 370–376 (2008)
Zhang, X., Tan, Y.: A hybrid model for rate-dependent hysteresis in piezoelectric actuators. Sens. Actuators A: Phys. 157(1), 54–60 (2010)
Clarke, F.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)
Xie, Y., Tan, Y., Dong, R.: Nonlinear modeling and decoupling control of XY micropositioning stages with piezoelectric actuators. IEEE/ASME Trans. Mechatron. 18(3), 821–832 (2013)
Liu, W., Cheng, L., Hou, Z., Yu, J., Tan, M.: An inversion-free predictive controller for piezoelectric actuators based on a dynamic linearized neural network model. IEEE/ASME Trans. Mechatron. 21(1), 214–226 (2016)
Dang, X., Tan, Y.: RBF neural networks hysteresis modelling for piezoceramic actuator using hybrid model. Mech. Syst. Sig. Process. 21(1), 430–440 (2007)
Saghafifar, M., Kundu, A., Nafalski, A.: Dynamic magnetic hysteresis modelling using Elman recurrent neural network. Int. J. Appl. Electromagnet. Mech. 13(1–4), 209–214 (2002)
Acknowledgments
The work presented in this paper has been funded by the National Science Foundation of China under Grants 61671303 and 61571302.
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Tan, Y., Dong, R. (2018). Modeling Hysteresis Using Non-smooth Neural Networks. In: Huang, T., Lv, J., Sun, C., Tuzikov, A. (eds) Advances in Neural Networks – ISNN 2018. ISNN 2018. Lecture Notes in Computer Science(), vol 10878. Springer, Cham. https://doi.org/10.1007/978-3-319-92537-0_15
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DOI: https://doi.org/10.1007/978-3-319-92537-0_15
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