Reconstructing Magnetic Hysteresis Behavior with Flux Model and Identifying Parameters for Dual-Coil MR Actuator

Lei Tang; Wojciech Bankosz; Janusz Goldasz

doi:10.15282/ijame.21.3.2024.14.0897

Authors

Lei Tang Faculty of Electrical and Computer Engineering, Cracow University of Technology, Warszawska 24, 31-155 Krakow, Poland
Wojciech Bankosz Faculty of Electrical and Computer Engineering, Cracow University of Technology, Warszawska 24, 31-155 Krakow, Poland
Janusz Goldasz Faculty of Electrical and Computer Engineering, Cracow University of Technology, Warszawska 24, 31-155 Krakow, Poland

DOI:

https://doi.org/10.15282/ijame.21.3.2024.14.0897

Keywords:

MR actuator, Magnetic hysteresis, Flux hysteresis, Bouc-Wen model, Parameter identification, Hysteresis

Abstract

Magnetorheological (MR) actuators represent an important class of semi-active devices that have received extensive investigation and deployment in the field of vibration reduction systems. Their notable features include a significant reduction in energy consumption, along with an impressive tunable range of continuously controllable damping forces. The force output of these devices is a complex function that involves two hysteretic mechanisms: magnetic and mechanical (i.e. hydraulic). While the total hysteresis mechanism of these devices has been the subject of considerable study, comparatively little attention has been paid to their magnetic hysteretic behavior. In this study, the authors examine the behavior of the dual coil MR actuator’s control circuit and attempt to extract the magnetic flux information from the laboratory measurements of electrical signals applied to it. The study is further enhanced by the incorporation of the Bouc-Wen (B-W) hysteretic unit, which serves to replicate the flux-current (or magnetic) hysteretic relationship. The B-W model's parameters are identified through the use of a hybrid algorithm, namely the particle swarm optimization and fmincon hybrid optimizing strategy. It incorporates the advantages of both algorithms, resulting in an average improvement of 0.38% in standard deviation compared to fmincon, across 1A to 5A, when comparing the experimental and simulation data. This strategy is employed to fit the model predictions to the flux data, derived from the reconstructed flux and current in time histories. The findings of the study demonstrate that the B-W model is an effective tool for predicting the variation in magnetic flux in response to an exciting current. The results can be implemented for prototyping or validating a model-based controller for MR actuator systems.

References

I. Bahiuddin, N.A.A. Wahab, M..I Shapiai, S.A. Mazlan, N. Mohamad, F. Imaduddin et al., “Prediction of field-dependent rheological properties of magnetorheological grease using extreme learning machine method,” Journal of Intelligent Material Systems and Structures, vol. 30, no. 11, pp. 1727-1742, 2019.

J.D Dent, T.E. Lang, “A biviscous modified Bingham model of snow avalanche motion,” Annals of Glaciology, vol. 4, pp. 42-46, 1983.

S.J. Dyke, B.F. Spencer Jr, M.K. Sain and J.D. Carlson. “Modeling and control of magnetorheological dampers for seismic response reduction,” Smart Materials and Structures, vol. 5, no. 5, p. 565, 1996.

B.F. Spencer Jr, S.J. Dyke, M.K. Sain and J.D. Carlson, “Phenomenological model for magnetorheological dampers,” Journal of Engineering Mechanics, vol. 123, no. 3, pp. 230-238, 1997.

G. Yang, B.F. Spencer Jr, H.J. Jung and J.D. Carlson, “Dynamic modeling of large-scale magnetorheological damper systems for civil engineering applications,” Journal of Engineering Mechanics, vol. 130, no. 9, pp. 107-114, 2004.

S.B. Choi, S.K. Lee and Y.P. Park, “A hysteresis model for the field-dependent damping force of a magnetorheological damper,” Journal of Sound and Vibration, vol. 2, no. 245, pp. 375-383, 2001.

V. Warke, S.. Kumar, A Bongale, P. Kamat, K. Kotecha, G. Selvachandran et al., “Improving the useful life of tools using active vibration control through data-driven approaches: A systematic literature review,” Engineering Applications of Artificial Intelligence, vol. 128, p. 107367, 2024.

E.R. Wang, X.Q. Ma, S. Rakheja and C.Y. Su, “Modeling asymmetric hysteretic properties of an mr fluids damper,” In 2004 43rd IEEE Conference on Decision and Control (CDC)(IEEE Cat. No. 04CH37601), vol. 5, pp. 4643-4648, 2004.

D.M.D. da Silva, S.M. Avila, M.V.G. de Morais and A.A. Cavallini Jr, “Comparing optimization algorithms for parameter identification of sigmoid model for MR damper,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 46, no. 3, p. 134, 2024.

I.D. Mayergoyz, G. Friedman and C. Salling “Comparison of the classical and generalized Preisach hysteresis models with experiments,” IEEE Transactions on Magnetics, vol. 25, no. 5, pp. 3925-3927, 1989.

M.S. Seong, S.B. Choi and Y.M. Han, “Damping force control of a vehicle MR damper using a Preisach hysteretic compensator,” Smart Materials and Structures, vol. 18, no. 7, p. 074008, 2009.

D.C. Jiles and D.L. Atherton, “Theory of ferromagnetic hysteresis,” Journal of Magnetism and Magnetic Materials, vol. 61, no. 1-2, pp. 48-60, 1986.

L. Chua and K. Stromsmoe, “Lumped-circuit models for nonlinear inductors exhibiting hysteresis loops,” IEEE Transactions on Circuit Theory, vol. 17, no. 4, pp. 564-574, 1970.

J.W. Macki, P. Nistri and P. Zecca, “Mathematical models for hysteresis,” SIAM Review, vol. 35, no. 1, pp. 94-123, 1993.

J. Gołdasz, B. Sapiński, Ł. Jastrzębski and M. Kubik, “Dual hysteresis model of MR dampers,” Frontiers in Materials, vol. 7, p. 236, 2020.

J. Gołdasz and M. Kubik, “Hysteresis modeling in MR dampers,” In 2021 22nd International Carpathian Control Conference (ICCC), pp. 1-6, 2021.

X.X. Bai, F.L. Cai and P. Chen, “Resistor-capacitor (RC) operator-based hysteresis model for magnetorheological (MR) dampers,” Mechanical Systems and Signal Processing, vol. 117, pp. 157-169, 2019.

C.X. Li, “Precise real-time hysteretic force tracking of magnetorheological damper,” Smart Materials and Structures, vol. 29, no. 10, p. 104002, 2020.

Q.D. Bui, Q.H. Nguyen, X.X.F. Bai and D.D. Mai “A new hysteresis model for magneto–rheological dampers based on Magic Formula,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 235, no. 13, pp. 2437-2451, 2021.

Q.D. Bui, X.X. Bai and Q.H. Nguyen, “Dynamic modeling of MR dampers based on quasi–static model and Magic Formula hysteresis multiplier,” Engineering Structures, vol. 245, p. 112855, 2021.

A. Kumar, D.K. Gupta, S.R. Ghatak and S.R. Prusty, “A comparison of PSO, GA and FA-based PID controller for load frequency control of two-area hybrid power system,” In Smart Technologies for Power and Green Energy: Proceedings of STPGE 2022, Singapore: Springer Nature Singapore, pp. 281-292, 2022.

F. Marini and B. Walczak, “Particle swarm optimization (PSO): A tutorial,” Chemometrics and Intelligent Laboratory Systems, vol. 149, pp. 153-65, 2015.

L. Tang, N.L. Ren and S. Funkhouser, “Semi-active suspension control with PSO tuned LQR controller based on MR damper,” International Journal of Automotive and Mechanical Engineering, vol. 20, no. 2, pp. 10512-10522, 2023.

M.A. Razman, G. Priyandoko and A.R. Yusoff, “Bouc-Wen model parameter identification for a MR fluid damper using particle swarm optimization,” In Advanced Materials Research, vol. 903, pp. 279-284, 2014.

Y.Q. Guo, M. Li, Y. Yang, Z.D. Xu and W.H. Xie, “A particle-swarm-optimization-algorithm-improved Jiles–Atherton model for magnetorheological dampers considering magnetic hysteresis characteristics,” Information, vol. 15, no. 2, p. 101, 2024.

M. Jain, V. Saihjpal, N. Singh and S.B. Singh, “An overview of variants and advancements of PSO algorithm,” Applied Sciences, vol. 12, no. 17, p. 8392, 2022.

J. Gołdasz, B. Sapiński, J. Gołdasz and B. Sapiński, “Configurations of MR dampers,” Insight into magnetorheological shock absorbers, pp. 25-49, 2015.

J. Goldasz, B. Sapinski and L. Jastrzebski, “On the application of Bouc-Wen hysteresis approach for modeling of MR actuators,” In ACTUATOR 2018; 16th International Conference on New Actuators, pp. 1-5, 2018.

M. Kubík and J. Goldasz, “Multiphysics model of an MR damper including magnetic hysteresis,” Shock and Vibration, vol. 2019, no. 1, p. 3246915, 2019.