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Control of mechanical systems with Stribeck friction and backlash. (English) Zbl 1155.93365

Summary: The control of mechanical systems in the presence of nonlinear friction and backlash is treated in a hybrid system approach. To deal with friction induced nonlinearities, the Stribeck friction model is linearized and the resulting model of the controlled plant is a hybrid system, the dynamics of which is given by linear models in the different partitions of the state space. During controller design it is assumed that the size of the backlash gap is unknown and the load side position and velocity cannot be measured. For motion control an LQ controller is applied. A condition is formulated for the control law parameters to guarantee the asymptotic stability of the control system. The LQ control algorithm is also extended for trajectory tracking tasks. Simulation results are presented to show the applicability of the theoretical results.

MSC:

93C10 Nonlinear systems in control theory
93B18 Linearizations
70Q05 Control of mechanical systems
93D20 Asymptotic stability in control theory
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[1] Armstrong-Hèlouvry, Brian, Stick slip and control in low-speed motion, IEEE Transactions on Automatic Control, 38, 10, 1483-1496 (1990)
[2] Carlos, Caundas de Wit; Ollson, H.; Åstrom, K. J.; Lischinsky, P., A new model for control of systems with friction, IEEE Transactions on Automatic Control, 40, 3, 419-425 (1995) · Zbl 0821.93007
[3] Swevers, Jan; Al-Bender, Farid; Ganseman, Chris G.; Prajogo, Tutuko, An integrated friction model structure with improved presliding behavior for accurate friction compensation, IEEE Transactions on Automatic Control, 45, 5, 675-685 (2000) · Zbl 0984.70008
[4] Lampaert, Vincent; Swevers, Jan; Al-Bender, Farid, Modification of the Leuven integrated friction model structure, IEEE Transactions on Automatic Control, 47, 4, 683-687 (2002) · Zbl 1364.93516
[5] Dupont, Pierre; Armstrong, Brian; Altpeter, Friedhelm, Single state elastoplastic friction models, IEEE Transactions on Automatic Control, 47, 5, 787-792 (2002) · Zbl 1364.74065
[6] Armstrong-Hèlouvry, Brian, Control of Machines with Friction (1991), Kluver Academic Press: Kluver Academic Press Boston · Zbl 0782.93003
[7] Hensen, H. A.; van de Molengraft, M. J.G.; Steinbuch, M., Friction induced hunting limit cycles: A comparison between the LuGre and switch friction model, Automatica, 39, 2131-2137 (2003) · Zbl 1254.74085
[8] Putra, D.; Nijmeijer, H.; van deWouw, N., Analysis of undercompensation and overcompensation of friction in 1DOF mechanical systems, Automatica, 43, 1387-1394 (2007) · Zbl 1130.74033
[9] Basilio Bona, Marina Indri, Friction compensation in robotics: An overview, in: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, Seville, Spain, 2005; Basilio Bona, Marina Indri, Friction compensation in robotics: An overview, in: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, Seville, Spain, 2005
[10] Garagic, Denis; Krishnaswamy, Srinivasah, Adaptive friction compensation for precision machine tool drive, Control Engineering Practice, 12, 1451-1464 (2004)
[11] Panteley, E.; Ortega, R.; Gafvert, M., An adaptive friction compensator for global tracking in a robotic manipulator, Systems and Control Letters, 33, 307-313 (1998) · Zbl 0902.93048
[12] Xie, Wen-Fang, Sliding-mode-observer-based adaptive control for servo actuator with friction, IEEE Transactions on Industrial Electronics, 54, 3, 1517-1528 (2007)
[13] Makkar, C.; Sawyer, W. G.; Hu, G.; Dixon, W. E., Lyapunov-based tracking control in the presence of uncertain nonlinear parameterizable friction, IEEE Transactions on Automatic Control, 52, 10, 1988-1994 (2007) · Zbl 1366.93443
[14] M. Feemster, P. Vedagrbha, D.M. Dawson, D. Haste, Adaptive control techniques for friction compensation, in: Proc. of the American Control Conference, Philadelphia, Pennsylvania,, 1998, pp. 1488-1492; M. Feemster, P. Vedagrbha, D.M. Dawson, D. Haste, Adaptive control techniques for friction compensation, in: Proc. of the American Control Conference, Philadelphia, Pennsylvania,, 1998, pp. 1488-1492
[15] Nordin, Mattias; Gutman, Per-Olof, Controlling mechanical systems with backlash—A survey, Automatica, 38, 1633-1649 (2002) · Zbl 1030.70013
[16] Barreiro, Antonio; Banos, Alfonso, Input-output stability of systems with backlash, Automatica, 42, 1017-1024 (2006) · Zbl 1135.93029
[17] S. Tarbouriech, C. Prieur, Stability analysis for sandwich systems with backlash: An LMI approach, in: Proc. of 5th IFAC Symposium on Robust Control Design, Toulouse, France, 2006; S. Tarbouriech, C. Prieur, Stability analysis for sandwich systems with backlash: An LMI approach, in: Proc. of 5th IFAC Symposium on Robust Control Design, Toulouse, France, 2006
[18] Tao, Gang; Kokotovic, Petar, Adaptive Control of Systems with Sensor and Actuator Nonlinearities (1996), John Wiley & Sons: John Wiley & Sons New York · Zbl 0953.93002
[19] Rostalski, Philipp; Besselmann, Thomas; Baric, Miroslav; van Belzen, Femke; Morari, Manfred, Hybrid approach to modeling, control and state estimation of mechanical systems with backlash, International Journal of Control, 80, 11, 1729-1740 (2007) · Zbl 1130.93357
[20] Lagerberg, Adam; Egardt, Bo, Backlash estimation with application to automotive powertrains, IEEE Transactions on Control Systems Technology, 15, 3, 483-493 (2007)
[21] Tao, Gang; Ma, Xiaoli; Ling, Yi, Optimal and nonlinear decoupling control of systems with sandwiched backlash, Automatica, 37, 165-176 (2001) · Zbl 0959.93500
[22] Nariman, Sepehri; Sassani, F.; Lawrence, P. D.; Ghasempoor, A., Simulation and experimental studies of gear backlash and stick-slip friction in hydraulic excavator swing motion, ASME Journal of Dynamic Systems, Measurements and Control, 118, 463-467 (1996) · Zbl 0875.73229
[23] Menon, K.; Krishnamurthy, K., Control of low velocity friction and gear backlash in a machine tool feed drive system, Mechatronics, 9, 33-52 (1999)
[24] Suraneni, S.; Kar, I. N.; Ramana Murthy, O. V.; Bhatt, R. K.P., Adaptive stick slip friction and backlash compensation using dynamic fuzzy logic system, Applied Soft Computing, 6, 26-37 (2005)
[25] Márton, Lőrinc; Lantos, Béla, Modeling, identification and compensation of stick-slip friction, IEEE Trans. on Industrial Electronics, 54, 1, 511-521 (2007)
[26] Márton, Lőrinc, On analysis of limit cycles in positioning systems near Striebeck velocities, Mechatronics, 48, 46-52 (2008)
[27] Octavian Beldiman, Linda Bushnell, Stability, linearization and control of switched systems, in: Proc. of the American Control Conference, San Diego, California, 1999, pp. 2950-2954; Octavian Beldiman, Linda Bushnell, Stability, linearization and control of switched systems, in: Proc. of the American Control Conference, San Diego, California, 1999, pp. 2950-2954
[28] Rantzer, Anders; Johansson, Mikael, Piecewise linear quadratic optimal control, IEEE Transactions on Automatic Control, 45, 4, 629-637 (2000) · Zbl 0969.49016
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