- Volume 30 Issue 2
Modeling nonlinear friction effects is a challenging problem. In this paper, a tracking controller is proposed for a system with uncertain nonlinear friction dynamics. Instead of using a specific friction model, we assume that the friction dynamics are represented by a function, which is unknown except its being continuously differentiable and Lipschitz continuous with known Lipschitz constants. It is shown that the scheme results in friction identification and trajectory position and velocity tracking. The analysis is done using Lyapunov-based stability method.
Adaptive control;Lyapunov method;Friction identification scheme
- P. A. Bliman, Mathematical study of the Dahl's friction model, European Journal of Mechanics 11 (1992), 835-848.
- P. A. Bliman and M. Sorine, Friction modelling by hysteresis operators, application to Dahl, stricktion, and Stribeck effects, Proceedings of Conference on Models and Hysteresis, Ternto, Italy (1991).
- S. I. Cho and I. J. Ha, A learning approach to tracking in mechanical systems with friction, IEEE Trans. Automat. Control 45 (2002), 111-116. https://doi.org/10.1109/9.827365
- P. Dahl, A solid friction model, Aerospace Corp. El Segundo CA, Tech. Report TOR-0158(3107-18)-1 (1968).
- D. A. Haessin Jr., and B. Friedland, On the modeling and simulation of friction, ASME Journal of Dynamic Systems, Measurements and Control 113 (1991), 354-362. https://doi.org/10.1115/1.2896418
- H. Khalil, Nonlinear Systems, Macmillan Co, 1992.
- C. Makkar, Nonlinear modeling, identification, and compensation for frictional disturbances (2006), Master thesis, University of Florida.
- C. Makkar, G. Hu, W. G. Sawyer, and W. E. Dixon, Lyapunov-based tracking control in the presence of uncertain nonlinear parameterizable friction, IEEE Trans. Automat. Control 52 (2007), 1988-1994. https://doi.org/10.1109/TAC.2007.904254
- P. Vedagarbha, D. M. Dawson, and M. Feemster, Tracking control of mechanical systems in the presence of nonlinear dynamic friction effects, IEEE Transactions on Control Systems Technology 7 (1997), 446-456. https://doi.org/10.1109/87.772160
- H. S. Yang, M. Berg, and B. I. Hong, Tracking control of mechanical systems with partially known friction model, Trans. on Control, Automation, and Systems Engr. 4 (2002), 311-318.