Authors

Johan Koopman, Dimitri Jeltsema, Michel Verhaegen

Abstract

A port-Hamiltonian formulation of the LuGre friction model is presented that can be used as a building block in the physical modeling of systems with friction. Based on the dissipation structure matrix of this port-Hamiltonian LuGre model, an alternative proof can be given for the passivity conditions that are known in the literature. As a specific example, the interconnection of a mass with the port-Hamiltonian LuGre model is presented. It is shown that the lossless interconnection structure and dissipation structure of the port-Hamiltonian LuGre model are consistent with those of the interconnection. Additionally, to render the friction model continuously differentiable, a smooth re-parametrization of the friction curve is proposed that extends and simplifies the existing results.

Citation

  • Journal: 2008 47th IEEE Conference on Decision and Control
  • Year: 2008
  • Volume:
  • Issue:
  • Pages: 3181–3186
  • Publisher: IEEE
  • DOI: 10.1109/cdc.2008.4739351

BibTeX

@inproceedings{Koopman_2008,
  title={{Port-Hamiltonian formulation and analysis of the LuGre friction model}},
  DOI={10.1109/cdc.2008.4739351},
  booktitle={{2008 47th IEEE Conference on Decision and Control}},
  publisher={IEEE},
  author={Koopman, Johan and Jeltsema, Dimitri and Verhaegen, Michel},
  year={2008},
  pages={3181--3186}
}

Download the bib file

References

  • (0)
  • Willems, J. C. Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis vol. 45 321–351 (1972) – 10.1007/bf00276493
  • Swevers, J., Al-Bender, F., Ganseman, C. G. & Projogo, T. An integrated friction model structure with improved presliding behavior for accurate friction compensation. IEEE Transactions on Automatic Control vol. 45 675–686 (2000) – 10.1109/9.847103
  • van der schaft, L2-Gain and Passivity Techniques in Nonlinear Control (1999)
  • olsson, Control systems with friction (1996)
  • Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
  • Li Chun Bo & Pavelescu, D. The friction-speed relation and its influence on the critical velocity of stick-slip motion. Wear vol. 82 277–289 (1982) – 10.1016/0043-1648(82)90223-x
  • Barahanov, N. & Ortega, R. Necessary and sufficient conditions for passivity of the LuGre friction model. IEEE Transactions on Automatic Control vol. 45 830–832 (2000) – 10.1109/9.847131
  • Armstrong-Hélouvry, B., Dupont, P. & De Wit, C. C. A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica vol. 30 1083–1138 (1994) – 10.1016/0005-1098(94)90209-7
  • Makkar, C., Dixon, W. E., Sawyer, W. G. & Hu, G. A new continuously differentiable friction model for control systems design. Proceedings, 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics. doi:10.1109/aim.2005.1511048 – 10.1109/aim.2005.1511048
  • eberard, conservative systems with ports on contact manifolds. Proc of 16th IFAC World Congress (2005)
  • Deur, J., Asgari, J. & Hrovat, D. A 3D Brush-type Dynamic Tire Friction Model. Vehicle System Dynamics vol. 42 133–173 (2004) – 10.1080/00423110412331282887
  • Canudas-de-Wit, C., Tsiotras, P., Velenis, E., Basset, M. & Gissinger, G. Dynamic Friction Models for Road/Tire Longitudinal Interaction. Vehicle System Dynamics vol. 39 189–226 (2003) – 10.1076/vesd.39.3.189.14152
  • (0)
  • Jeltsema, D., Ortega, R. & M.A. Scherpen, J. An energy-balancing perspective of interconnection and damping assignment control of nonlinear systems. Automatica vol. 40 1643–1646 (2004) – 10.1016/j.automatica.2004.04.007
  • Hirschorn, R. M. & Miller, G. Control of nonlinear systems with friction. IEEE Transactions on Control Systems Technology vol. 7 588–595 (1999) – 10.1109/87.784422