**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31529

##### Advances on LuGre Friction Model

**Authors:**
Mohammad Fuad Mohammad Naser,
Faycal Ikhouane

**Abstract:**

LuGre friction model is an ordinary differential equation that is widely used in describing the friction phenomenon for mechanical systems. The importance of this model comes from the fact that it captures most of the friction behavior that has been observed including hysteresis. In this paper, we study some aspects related to the hysteresis behavior induced by the LuGre friction model.

**Keywords:**
Hysteresis,
LuGre model,
operator,
(strong) consistency.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1088126

**References:**

[1] R. A. Adams and J. J. F. Fournier, Sobolev Spaces, Elsevier, 2003.

[2] F. Al-Bender, V. Lampaert, and J. Swevers, “Modeling of dry sliding friction dynamics: From heuristic models to physically motivated models and back”, Chaos, vol. 14, no. 2, pp. 446-445, 2004.

[3] K. J. Astrom and C. Canudas-de-Wit, “Revisiting the LuGre friction model”, IEEE Control Syst. Mag, vol. 28, no. 6, pp. 101-114, 2008.

[4] N. Barahanov and R. Ortega, “Necessary and sufficient conditions for passivity of the LuGre friction model”, IEEE Trans. Autom. Control, vol. 45, no. 4, pp 830–832 , 2000.

[5] C. Canudas de Wit, H. Olsson, K. Astrom and P. Lischinsky, “A new model for control of systems with friction”, IEEE Trans. Autom. Control, vol. 40, no. 3, pp. 419-425, 1995.

[6] C.C. De Wit, H. Olsson, K. J. Astrom, P. Lischinsky, “Dynamic friction models and control design”, American Control Conference, pp. 1920-1926, 1993.

[7] P.R. Dahl, “A solid friction model”, The Aerospace Corporation El Segundo, TOR-0158 (3107-18), California, 1968.

[8] P. Dahl, “Solid friction damping of mechanical vibrations”, AIAA J., vol. 14, no. 2, pp. 1675-1682, 1976.

[9] J.H. Dieterich, “Time-dependent friction in rocks”, J. Geophysical Res., vol. 77, pp. 3690-3697, 1972.

[10] A. F. Filippov, Differential Equations with Discontinuous Right-Hand Sides, Kluwer, 1988.

[11] L. Freidovich, A. Robertsson, A. Shiriaev and R. Johansson, “LuGremodel- based friction compensation”, IEEE Trans. Control Syst. Technol., vol. 18, no. 1, pp. 194-200, 2010.

[12] F. Ikhouane, “Characterization of hysteresis processes”, Math. Control Signals Systems, DOI 0.1007/s00498-012-0099-6.

[13] H. K. Khalil, Nonlinear Systems, 3rd ed., Prentice Hall, Upper Saddle River, New Jersey, 2002, ISBN 0130673897.

[14] K.-Y. Lian, C.-Y. Hung, C.-S. Chiu, and P. Liu, “Induction motor control with friction compensation: an approach of virtual-desired-variable synthesis”, IEEE J. Emerg. Sel. Topics Power Electron., vol. 20, no. 5, pp. 1066-1074, 2005.

[15] H. Logemann, E.P. Ryan, and I. Shvartsman I, “A class of differentialdelay systems with hysteresis: Asymptotic behaviour of solutions”, Nonlinear Anal., vol. 69, pp. 363-391, 2008.

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

[17] M. Marques, Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction, Cambridge, MA: Birkhaser, 1993.

[18] J. Oh, and D.S. Bernstein, “Semilinear Duhem model for rateindependent and rate-dependent hysteresis”, IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 631-645, 2005.

[19] A. K. Padthe, B. Drincic, J. Oh, D. D. Rizos, S. D. Fassois, and D. S. Berstein, “Duhem modeling of friction-induced hysteresis”, IEEE Control Syst. Mag., vol. 28, no. 5, pp. 90-107, 2008.

[20] E. Rabinowicz. “Friction and Wear of Materials”, New York: Wiley, 1995.

[21] D. Rizos and S. Fassois, “Friction identification based upon the LuGre and Maxwell slip models”, IEEE Trans. Control Syst. Technol., vol. 17, no. 1, pp. 153-160, 2009.

[22] D. D. Rizos and S. Fassois, “Presliding friction identification based upon the Maxwell slip model structure”, Chaos, vol. 14, no. 2, pp. 431-445, 2004.

[23] W. Rudin, Real and Complex Analysis, McGraw-Hill, 3rd ed., 1986.

[24] P. P. San, B. Ren, S. S. Ge, T. H. Lee, J.-K. Liu, “Adaptive neural network control of hard disk drives with hysteresis friction nonlinearity”, IEEE Trans. Control Syst. Technol., vol. 19, no. 2, pp. 351-358, 2011.

[25] F. A. Shirazi, J. Mohammadpour, K.M. Grigoriadis, G. Song, “Identification and control of an MR damper with stiction effect and its application in structural vibration mitigation”, IEEE Trans. Control Syst. Technol., vol. 20, no. 5, pp. 1285-1301, 2012.

[26] J. Swevers, F. Al-Bender, C.G. Ganseman, T. Projogo, “An integrated friction model structure with improved presliding behavior for accurate friction compensation”, IEEE Trans. Autom. Control, vol. 45, no. 4, pp. 675-686, 2000.

[27] Y. Tan, J. Chang, H. Tan, “Adaptive backstepping control and friction compensation for AC servo with inertia and load uncertainties”, IEEE Trans. Ind. Electron., vol. 50, no. 5, pp. 944-952, 2003.

[28] D. E. Varberg, “On absolutely continuous functions”, The American Mathematical Monthly, vol. 72, no. 8, pp. 831–841, 1965.

[29] I. Virgala1, P. Frankovsky’, M. Kenderova, “Friction effect analysis of a DC motor”, American Journal of Mechanical Engineering, DOI: 10.12691/ajme-1-1-1.

[30] A. Visintin, Differential Models of Hysteresis, Springer-Verlag, Berlin, Heidelberg, 1994.

[31] X. D. Wu, S. G. Zuo, L. Lei, X. W. Yang and Y. Li, “Parameter identification for a LuGre model based on steady-state tire conditions”, Int J Automot Techn, vol. 12, no. 5, pp. 671–677, 2011.