Skip to main content
SpringerLink
Log in

Hysteresis modeling of magneto-rheological damper using self-tuning Lyapunov-based fuzzy approach

  • Published:
International Journal of Precision Engineering and Manufacturing Aims and scope Submit manuscript

Abstract

Magneto-rheological (MR) fluid damper is a semi-active control device that has recently received more attention because they offer the adaptability of active control devices without requiring the associated large power sources. But inherent nonlinear nature of the MR fluid damper is one of the challenging aspects for utilizing this device to achieve the high performance. So development of an accurate MR fluid damper model is necessary to take the advantages from its unique characteristics. The focus of this paper is to develop an alternative method for modeling a MR fluid damper by using a so-called self-tuning Lyapunov-based fuzzy model (STLFM). Here, the model is constructed in the form of a center average fuzzy interference system, of which the fuzzy rules are designed based on the Lyapunov stability condition. In addition, in order to optimize the STLFM, the back propagation learning rules are used to adjust the fuzzy weighting net. Firstly, experimental data of a damping system using this damper is used to optimize the model. Next, the optimized model is used to estimate online the damping performance in the real-time conditions. The modeling results prove convincingly that the developed model could represent satisfactorily the behavior of the MR fluid damper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

\(V(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x} )\) :

Lyapunov function candidate

f MR_est :

estimated damping force, N

f MR :

real damping force, N

in 1 :

damper supplied current, A

in 2 :

damper rod displacement, mm

in 3 :

damper velocity, cm/s

u LFI :

output of Lyapunov-based Fuzzy Inference

k GFI :

output of Gain Fuzzy Inference

E :

error function

N :

number of triangle membership functions

a j :

center of j th triangle of membership function

b j :

width of j th triangle of membership function

μ j (w q ):

height of the control GFI output

w j (w q ):

weight of the control GFI output

w k :

weight of LFI output

µ(w k ):

height of LFI output

μ ij (w k ):

consequent fuzzy output function

δ ij :

activating factor

η a , η a and η c :

learning rates

References

  1. Di Monaco, F., Ghandchi Tehrani, M., Elliott, S. J., Bonisoli, E., and Tornincasa, S., “Energy Harvesting using Semi-Active Control,” Journal of Sound and Vibration, Vol. 332, No. 23, pp. 6033–6043, 2013.

    Article  Google Scholar 

  2. Turnip, A., Park, S., and Hong, K. S., “Sensitivity Control of a MRDamper Semi-Active Suspension,” Int. J. Precis. Eng. Manuf., Vol. 11, No. 2, pp. 209–218, 2010.

    Article  Google Scholar 

  3. Lee, G. M., Ju, Y. H., and Park, M. S., “Development of a Low Frequency Shaker using MR Dampers,” Int. J. Precis. Eng. Manuf., Vol. 14, No. 9, pp. 1647–1650, 2013.

    Article  Google Scholar 

  4. Bitaraf, M. and Hurlebaus, S., “Semi-Active Adaptive Control of Seismically Excited 20-Story Nonlinear Building,” Engineering Structures, Vol. 56, No. pp. 2107–2118, 2013.

    Article  Google Scholar 

  5. Weber, F., “Semi-Active Vibration Absorber based on Real-Time Controlled MR Damper,” Mechanical Systems and Signal Processing, Vol. 46, No. 2, pp. 272–288, 2014.

    Article  Google Scholar 

  6. Lee, H. G., Sung, K. G., Choi, S. B., Park, M. K., and Park, M. K., “Performance Evaluation of a Quarter-Vehicle MR Suspension System with Different Tire Pressure,” Int. J. Precis. Eng. Manuf., Vol. 12, No. 2, pp. 203–210, 2011.

    Article  Google Scholar 

  7. Kim, H. J., “Passive and Semi-Active Shock Reduction for Prototype HSRMD Avoiding Human Damage,” Int. J. Precis. Eng. Manuf., Vol. 12, No. 2, pp. 219–225, 2011.

    Article  Google Scholar 

  8. Ahmed, G. M. S., Reddy, P. R., and Seetharamaiah, N., “Experimental Investigation of Magneto Rheological Damping Effect on Surface Roughness of Work Piece during End Milling Process,” Int. J. Precis. Eng. Manuf., Vol. 13, No. 6, pp. 835–844, 2012.

    Article  Google Scholar 

  9. Yi, K. and Song, B., “A New Adaptive Sky-Hook Control of Vehicle Semi-Active Suspensions,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 213, No. 3, pp. 293–303, 1999.

    Google Scholar 

  10. Mizuno, T., Kobori, T., Hirai, J. I., Matsunaga, Y., and Niwa, N., “Development of Adjustable Hydraulic Dampers for Seismic Response Control of Large Structure,” Proc. of ASME PVP Conference, pp. 163–170, 1992.

    Google Scholar 

  11. Kwok, N. M., Ha, Q. P., Nguyen, T. H., Li, J., and Samali, B., “A Novel Hysteretic Model for Magnetorheological Fluid Dampers and Parameter Identification using Particle Swarm Optimization,” Sensors and Actuators A: Physical, Vol. 132, No. 2, pp. 441–451, 2006.

    Article  Google Scholar 

  12. Choi, S. B., Lee, S. K., and Park, Y. P., “A Hysteresis Model for the Field-Dependent Damping Force of a Magnetorheological Damper,” Journal of Sound and Vibration, Vol. 245, No. 2, pp. 375–383, 2001.

    Article  Google Scholar 

  13. Vadtala, I. H., Soni, D. P., and Panchal, D. G., “Semi-Active Control of a Benchmark Building using Neuro-Inverse Dynamics of MR Damper,” Procedia Engineering, Vol. 51, pp. 45–54, 2013.

    Article  Google Scholar 

  14. Wang, D. H. and Liao, W. H., “Modeling and Control of Magnetorheological Fluid Dampers using Neural Networks,” Smart Materials and Structures, Vol. 14, No. 1, pp. 111, 2005.

    Article  Google Scholar 

  15. Stanway, R., Sproston, J., and Stevens, N., “Non-Linear Modelling of an Electro-Rheological Vibration Damper,” Journal of Electrostatics, Vol. 20, No. 2, pp. 167–184, 1987.

    Article  Google Scholar 

  16. Dominguez, A., Sedaghati, R., and Stiharu, I., “Modelling the Hysteresis Phenomenon of Magnetorheological Dampers,” Smart Materials and Structures, Vol. 13, No. 6, pp. 1351, 2004.

    Article  Google Scholar 

  17. Bouc, R., “Forced Vibration of Mechanical Systems with Hysteresis,” Proc. of the 4th Conference on Non-Linear Oscillation, p. 315, 1967.

    Google Scholar 

  18. Wen, Y. K., “Method for Random Vibration of Hysteretic Systems,” Journal of the Engineering Mechanics Division, Vol. 102, No. 2, pp. 249–263, 1976.

    Google Scholar 

  19. Kwok, N. M., Ha, Q. P., Nguyen, M. T., Li, J., and Samali, B., “Bouc-Wen Model Parameter Identification for a MR Fluid Damper using Computationally Efficient GA,” ISA transactions, Vol. 46, No. 2, pp. 167–179, 2007.

    Article  Google Scholar 

  20. Çemeci, S. and Engin, T., “Modeling and Testing of a Field- Controllable Magnetorheological Fluid Damper,” International Journal of Mechanical Sciences, Vol. 52, No. 8, pp. 1036–1046, 2010.

    Article  Google Scholar 

  21. Peng, G. R., Li, W. H., Du, H., Deng, H. X., and Alici, G., “Modelling and Identifying the Parameters of a Magneto-Rheological Damper with a Force-Lag Phenomenon,” Applied Mathematical Modelling, Vol. 38, No. 15–16, pp. 3763–3773, 2014.

    Article  Google Scholar 

  22. Spencer, B. F., Dyke, S. J., Sain, M. K., and Carlson, J. D., “Phenomenological Model of a Magneto-Rheological Damper,” Journal of Engineering Mechanics, Vol. 123, No. 3, pp. 230–238, 1996.

    Google Scholar 

  23. Chang, C. C. and Roschke, P., “Neural Network Modeling of a Magnetorheological Damper,” Journal of Intelligent Material Systems and Structures, Vol. 9, No. 9, pp. 755–764, 1998.

    Article  Google Scholar 

  24. Schurter, K. C. and Roschke, P. N., “Fuzzy Modeling of a Magnetorheological Damper using Anfis,” Prof. of the 9th IEEE International Conference on Fuzzy Systems, Vol. 1, pp. 122–127, 2000.

    Google Scholar 

  25. Wang, D. H. and Liao, W. H., “Neural Network Modeling and Controllers for Magnetorheological Fluid Dampers,” Proc. of the 10th IEEE International Conference on Fuzzy Systems, Vol. 3, pp. 1323–1326, 2001.

    Google Scholar 

  26. Margaliot, M. and Langholz, G., “Fuzzy Lyapunov-based Approach to the Design of Fuzzy Controllers,” Fuzzy Sets and Systems, Vol. 106, No. 1, pp. 49–59, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  27. Roy, A. and Sharma, K. D., “Gravitational Search Algorithm and Lyapunov Theory based Stable Adaptive Fuzzy Logic Controller,” Procedia Technology, Vol. 10, pp. 581–586, 2013.

    Article  Google Scholar 

  28. Margaliot, M. and Langholz, G., “Design and Analysis of Fuzzy Schedulers using Fuzzy Lyapunov Synthesis,” Engineering Applications of Artificial Intelligence, Vol. 14, No. 2, pp. 183–188, 2001.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Mechanical Engineering, University of Ulsan, Daehakro 93, Namgu, Ulsan, South Korea, 680-749

    Dao Thanh Liem

  2. School of Mechanical Engineering, University of Ulsan, Daehakro 93, Namgu, Ulsan, South Korea, 680-749

    Dinh Quang Truong & Kyoung Kwan Ahn

Authors
  1. Dao Thanh Liem
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dinh Quang Truong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kyoung Kwan Ahn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kyoung Kwan Ahn.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liem, D.T., Truong, D.Q. & Ahn, K.K. Hysteresis modeling of magneto-rheological damper using self-tuning Lyapunov-based fuzzy approach. Int. J. Precis. Eng. Manuf. 16, 31–41 (2015). https://doi.org/10.1007/s12541-015-0004-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12541-015-0004-6

Keywords

Search

Navigation