Predictive Control with Dynamic Hysteresis ‎Reference ‎Trajectory: Application to a Structural Base-‎Isolation ‎Model

Document Type : Special Issue Paper

Authors

1 Departament of Mathematics, Universitat Politècnica de Catalunya-UPC, BarcelonaTech, Escola d’Enginyeria de Barcelona Est-EEBE, Spain

2 Departament of Mathematics, Universitat Politècnica de Catalunya-UPC, BarcelonaTech, Escola d’Enginyeria de Barcelona Est-‎EEBE, Spain

3 Departament of Mathematics, Universitat Politècnica de Catalunya-UPC, Escola Superior d'Enginyeries Industrial, Aeroespacial i ‎Audiovisual de Terrassa ESEIAAT‎, Spain

Abstract

Over the last decades, in the field of control engineering, Model Predictive Control (MPC) has been successfully ‎employed in many industrial processes. This due to, among other aspects, its capability to include constrains within ‎the design control formulation and also its ability to perform on-line optimization. For instance, in the civil ‎engineering field, different MPC approaches have been well developed to formulate active control algorithms able ‎to reduce civil structural responses to earthquakes. Thus, in this paper, a customized version of a conventional ‎Predictive Control (PC) strategy is proposed to mitigate the displacement on a base-isolated system with a ‎nonlinear hysteresis behavior, that is excited by a seismic event. The proposal consists of including a dynamic ‎hysteresis system into the control scheme to generate a reference trajectory that will softly drive the base-isolated ‎structure to a rest status. The proposed control scheme is evaluated through numerical experiments, and then its ‎performance is compared with respect to the conventional Predictive Control methodology. According to the ‎numerical experiments, the approach here presented results more efficient than the conventional method due to ‎the use of a suitable linear model of the structural system plus a new Driver Block with dynamic hysteresis within ‎the Predictive Control scheme‎.

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Main Subjects

[1] Sasa, R.V., Levine, W.S, Handbook of model predictive control, Springer, 2018. ‎
‎[2] Basil, K., Cannon, M., Model predictive control, Classical, Robust and Stochastic, Springer, 2016. ‎
‎[3] Sanchez, J.M., Rodellar, J., ADEX optimized adaptive controllers and systems, Springer, 2015. ‎
‎[4] Rebeck, M.J., Rawlings, J.B., Model predictive control with discrete actuators: Theory and application, Automatica, 78, 2017, 258-265. ‎
‎[5] Pannek, J., Grüne, L., Nonlinear Model Predictive Control, Springer, 2011. ‎
‎[6] Sanchez, J.M., Rodellar, J., Adaptive predictive control: from the concepts to plant optimization, Prentice Hall, 1996. ‎
‎[7] Wang, L., Model predictive control: design and implementation using Matlab, American control conference, 2009. ‎
‎[8] Mehndiratta, M., Kayacan, E., Patel, S., Kayacan, E., Chowdhary, G., Learning-based fast nonlinear model predictive control for custom-made 3D printed ground and aerial robots, in Handybook of Model Predictive Control, 2019, pp. 581-605.‎
‎[9] Ostafew, C.J., Schoellig, A.P., Barfoot, T.D., Learning‐based nonlinear model predictive control to improve vision‐based mobile robot path tracking, ‎Journal of Field Robotics, 33(1), 2016, 133-152. ‎
‎[10] Zhijun, L., Yuxia, Y., Fan, K., Wei, H., Chun-Yi, S., Robust vision-based tube model predictive control of multiple mobile robots for leader–follower ‎formation, IEEE Transactions on Industrial Electronics, 64(4), 2019, 3096-3106. ‎
‎[11] Goodwin, G.C., Medioli, A.M., Murray, K., Sykes, R., Stephen, C., Applications of MPC in the area of health care, in Handbook of Model Predictive ‎Control, Springer, 2019, pp. 529-550.‎
‎[12] Linkers, D.A., Mahfonf, M., Generalized predictive control in clinical anaesthesia, in Advances in Model-Based Predictive Control, Oxford University ‎Press, 1994. ‎
‎[13] Doyle III, Francis, J., Dassau, E., Gondhalekar, R.L., Daily periodic target-zone modulation in the model predictive control problem for artificial pancreas for type I diabetes applications, Patent 10, 507, 284, 17 Dec 2019.‎
‎[14] Goodwin, G.C., Seron, M.M., Feedback and feedforward control in the context of model predictive control with application to the management of ‎type 1 diabetes mellitus, Control Engineering Practice, 89, 2019, 228-237. ‎
‎[15] Filey, D.P., Jianbo, L., Davor, D.H., Autonomous vehicle operation based on interactive model predictive control, Patent 10, 239, 529, 26 Mar 2019.‎
‎[16] Xiaoqiang, S., Yingfeng, C., Shaohua, W., Xing, X., Long C., Optimal control of intelligent vehicle longitudinal dynamics via hybrid model predictive ‎control, Robotics and Autonomous Systems, 112, 2019, 190-200. ‎
‎[17] Vazquez, S., Rodriguez, J., Rivera, M., Franquelo, L.G., Norambuena, M., Model predictive control for power converters and drives: Advances and ‎trends, IEEE Transactions on Industrial Electronics, 64(2), 2016, 935-947. ‎
‎[18] Lashab, A., Sera, D., Guerrero, J.M., A dual-discrete model predictive control-based MPPT for PV systems, IEEE Transactions on Power Electronics, ‎‎34(10), 2019, 18795226. ‎
‎[19] Yinghao, S., Jiefeng, H., Zilin, L., Guerrero, J.M., A model predictive control for renewable energy based AC microgrids without any PID regulators, ‎IEEE Transactions on Power Electronics, 33(11), 2018 , 9122-9126. ‎
‎[20] Takács, G., Rohal-Ilkiv, B., Model Predictive Vibration Control, Springer, 2012. ‎
‎[21] Ponce de Leon, N.I., Acho, L., Rodellar, J., Adaptive predictive control of a base-isolated hysteretic system, 21 st International Conference on System ‎Theory, Control and Computing, Sinaia, 2017. ‎
‎[22] Lyan-Ywan, L., Ging-Long, L., Predictive control of smart isolation system for precision equipment subjected to near-fault earthquakes, ‎Engineering Structures, 30(11), 2008, 3045-3064. ‎
‎[23] Rodellar, J., Barbat, A. H., Predictive control of structure, Journal of Engineering Mechanics, 113(6), 1987, 797-812. ‎
‎[24] Rodellar, J., Chung L.L., Soong, T.T., Experimental digital control of structures, Journal of Engineering Mechanics, 115(6), 1989, 1245-1261. ‎
‎[25] Mousavi, S.M., Ellsworth, W.L., Zhu, W., Chuang, L.Y., Beroza, G.C., Earthquake transformer—an attentive deep-learning model for simultaneous ‎earthquake detection and phase picking, Nature, 11(1), 2020, 1-12. ‎
‎[26] Bedfrod, J.R., Moreno, M., Deng, Z., Oncken, O., Schurr, B., Jhon, T., Báez J.C., Bevis, M., Months-long thousand-kilometre-scale wobbling before ‎great subduction earthquakes, Nature, 580(7805), 2020, 628-635. ‎
‎[27] Ramallo, J.C., Johnson, E.A., Spencer, B.F., Smart base isolation systems, Journal of Engineering Mechanics, 128(10), 2002, 1088-1099. ‎
‎[28] Ikhouane, F., Rodellar, J., Systems with hysteresis: analysis, identification and control using the Bouc-Wen model, Wiley, 2007. ‎
‎[29] Shieh-Kung, H., Chin-Hsiung L., Combination of decentralized sliding mode control and online wavelet analysis for control of equipment with ‎isolation system, Structural Control and Health Monitoring, 26(5), 2019, 2339. ‎
‎[30] Pozo, F., Ikhouane, F., Pujol, G., Rodellar, J., Adaptive backstepping control of hysteretic base-isolated structures, Journal of Vibration and Control, 12(4), 2006, 373-394. ‎
‎[31] Ikhouane, F., Mañosa, V., Rodellar, J., Adaptive control of a hysteretic structural system, Automatica, 41(2), 2005, 225-231. ‎
‎[32] Bittanti, S., Laub, A.J., Willems, J.C., The Ricatti Equation, Springer-Verlag, 1991. ‎
‎[33] Folient, G.C., Hysteresis modeling of wood joints and structural systems, Journal of Structural Engineering, 121(6), 1995, 1013-1022. ‎
‎[34] Vidal, Y., Acho, L., Pozo, F., Robust fault detection in hystereticbase-isolation systems, Mechanical Systems and Signal Processing, 29, 2012, 447-456. ‎
‎[35] Tutivén, C., Vidal, Y., Acho, L., Rodellar, J., Hysteresis-based design of dynamic reference trajectories to avoid saturation in controlled wind ‎turbines, Asian Journal of Control, 19(2), 2017, 438-449. ‎
‎[36] Ponce de Leon, N.I., Acho, L., Rodellar, J., An on-line statistic algorithm to fault detection in controlled systems: a study case, in Intelligent systems, ‎International IEEE Conference, Madeira, 2018. ‎