ONLINE INVERSION OF A NONLINEAR OPERATOR MODEL USING SLOPE-INTERCEPT METHOD
Keywords:
Nonlinear operators, Piezo-electrical, Prandtl-Ishilinskii Online InverseAbstract
Systems include nonlinear behaviours always require careful control to treat them. We usually try to eliminate them by cancelling or dominating the nonlinearity. One common method is to find an inversion and cascade it to the nonlinearity. This requires modelling it first. Hysteresis nonlinearity can be found in many applications such as nano-positioning, where smart materials are used. Researchers found several methods to model it physically or mathematically. As the behaviour of hysteresis is complicated, most of models use mathematical operators to characterize the hysteresis behaviour. Yet, most of these operators are modelled and run off-line. On the contrary, in this work, we model the hysteresis on line and invert it immediately. This method is important particularly, when the hysteresis changes with time and requires remodelling. Simulations are run and compared with other methods such the very famous one uses the Prandtl-Ishilinskii (PI) operator and present good results
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R. Smith, Smart Material Systems: Model Developments. Society of Industrial and Applied Mathematics, 2005. DOI: https://doi.org/10.1137/1.9780898717471
M. Armin, P. N. Roy, and S. K. Das, “A survey on modelling and compensation for hysteresis in high speed nanopositioning of afms: Observation and future recommendation,” International Journal of Automation and Computing, 2020. DOI: https://doi.org/10.1007/s11633-020-1225-4
K. Kuhnen and Janocha, “Adaptive inverse control of piezoelectric actuators with hysteresis operator,” in Proceedings of the European Control Conference, Karsruhe, Germany, 1999. DOI: https://doi.org/10.23919/ECC.1999.7099402
M. Janaideh, M. Rakotondrabe, I. Al-Darabsah, and O. Aljanaideh, “Internal model-based feedback control design for inversion-free feedforward rate-dependent hysteresis compensation of piezoelectric cantilever actuator,” Control Engineering Practice, vol. 72, pp. 29–41, 2018. DOI: https://doi.org/10.1016/j.conengprac.2017.11.001
S.-H. Liu, T.-S. Huang, and J.-Y. Yen, “Tracking control of shape- memory-alloy actuators based on self-sensing feedback and inverse hysteresis compensation,” Sensors, no. 10, pp. 112 –127, 2010. DOI: https://doi.org/10.3390/s100100112
M. Edardar and A. Abougarair, “Tracking control with hysteresis compensation using neural networks,” in Proceedings of IEEE 1st International Maghreb Meeting of the Conference on Sciences and Techniques of Automatic Control and Computer Engineering, 2021. DOI: https://doi.org/10.1109/MI-STA52233.2021.9464365
G. Tao and P. Kokotovic, “Adaptive control of plants with unknown hystereses,” IEEE Transactions on Automatic Control, vol. 40, no. 2, pp. 200–212, 1995. DOI: https://doi.org/10.1109/9.341778
R. Iyer and X. Tan, “Control of hysteretic systems through inverse compensation: Inversion algorithms, adaptation, and embedded imple- mentation,” IEEE Control Systems Magazine, vol. 29, no. 1, pp. 83–99, 2009. DOI: https://doi.org/10.1109/MCS.2008.930924
K. Kuhnen, “Modeling, identification and compensation of complex hysteretic nonlinearities - a modified Prandtl-Ishlinskii approach,” European Journal of Control, vol. 9, no. 4, pp. 407–418, 2003. DOI: https://doi.org/10.3166/ejc.9.407-418
Y. Feng, Y.-M. Hu, C. A. Rabbath, and C.-Y. Su, “Robust adaptive control for a class of perturbed strictfeedback non-linear systems with unknown prandtl-ishlinskii hysteresis,” International Journal of Control, vol. 81, no. 11, pp. 1699–1708, 2014. DOI: https://doi.org/10.1080/00207170701813851
Y. Liu1, J. Shan, and U. Gabbert, “Feedback/feedforward control of hysteresis compensated piezoelectric actuators for high-speed scanning applications,” Smart Materials and Structures, vol. 24, 2015. DOI: https://doi.org/10.1088/0964-1726/24/1/015012
S. Valadkhan, K. Morris, and A. Khajepour, “Robust PI control of hysteretic systems,” in Proceedings of the 47th IEEE Conference on Decision and Control, pp. 3787–3792, 2008. DOI: https://doi.org/10.1109/CDC.2008.4739041
M. Edardar, X. Tan, and H. K. Khalil, “Sliding-mode tracking control of piezo-actuated nanopositioner,” in Proceedings of the 2012 Ameri- can Control Conference, pp. 3825–3830, 2012. DOI: https://doi.org/10.1109/ACC.2012.6315559
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