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Computación y Sistemas
versión On-line ISSN 2007-9737versión impresa ISSN 1405-5546
Comp. y Sist. vol.16 no.1 Ciudad de México ene./mar. 2012
Artículos
Control of Mechanical Systems with Dry Friction
Control de sistemas mecánicos con fricción seca
Roque Martínez1 and Joaquín Álvarez2
1 Programa de Ingeniería Mecánica, Unidad Académica de Ingeniería, Universidad Autónoma de Zacatecas, Zacatecas, Zac., Mexico. Correo: rmartinez@uaz.edu.mx.
2 Departamento de Electrónica y Telecomunicaciones, División de Física Aplicada, CICESE, Ensenada, B. C., Mexico. Correo: jqalvar@cicese.mx.
Article received on 15/01/2010.
Accepted on 17/02/2011.
Abstract
A technique to design a dynamic continuous controller to regulate a class of fullactuated mechanical systems with dry friction is proposed. It is shown that the control eliminates the steadystate error and is robust with respect to parameter uncertainties. A simple method to find the parameters of the controller is also proposed. Moreover, an application of this result to control a 2DOF underactuated mechanical system with dry friction in the nonactuated joint is described. Here, the control objective is to regulate the nonactuated variable while the position and speed of the actuated joint remain bounded. Performance issues of the developed synthesis are illustrated with numerical and experimental results.
Keywords: Stability, friction, mechanical systems, underactuated systems.
Resumen
Se propone una estrategia de diseño de un controlador dinámico continuo para regular una clase de sistemas mecánicos totalmente actuados con fricción seca. Se demuestra que el control elimina el error en estado estacionario y que es robusto frente a cierto tipo de incertidumbres en los parámetros del sistema. Se propone también un método sencillo para calcular los parámetros del controlador. Además, se describe la aplicación de este resultado al control de sistemas subactuados de 2 grados de libertad, con fricción seca en la articulación no actuada. En este caso, el objetivo de control es regular la variable no actuada, manteniendo limitadas las amplitudes de la posición y de la velocidad de la articulación actuada. El desempeño del controlador propuesto se ilustra con resultados numéricos y experimentales.
Palabras clave: Estabilidad, fricción, sistemas mecánicos, sistemas subactuados.
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References
1. Almutairi, N.B. & Zribi, M. (2009). Sliding Mode Control of a Threedimensional Overhead Crane. Journal of vibration and control, 15(11), 16791730. [ Links ]
2. Armstrong, B. & Amin, B. (1996). PID Control in the Presence of Static Friction: A Comparison of Algebraic and Describing Function Analysis. Automatica, 32(5), 679692. [ Links ]
3. Bartolini, G. & Punta, E. (2000). Chattering elimination with second order sliding modes robust to Coulomb friction. ASME Journal of Dynamic Systems, Measurement and Control, 122(4),679686. [ Links ]
4. Bartolini, G. & Punta, E. (2000). Second order sliding mode control of systems with nonlinear friction. 39th IEEE Conference on Decision and Control, Sydney, Australia, 3, 21922197. [ Links ]
5. Boiko, I., Fridman, L., & Castellanos, M.I. (2004). Analysis of SecondOrder SlidingMode Algorithms in the Frequency Domain. IEEE Transactions on Automatic Control, 49(6), 946950. [ Links ]
6. Chaoui, H., Sicard, P. & Gueaieb, W. (2009). ANNBased Adaptive Control of Robotic Manipulators With Friction and Joint Elasticity. IEEE Transactions on Industrial Electronics, 56(8), 31743187. [ Links ]
7. di Bernardo, M., Budd, C.J., Champneys, A.R., Kowalczy, K.P., Nordmark, A.B., Tost, G.O. & Piiroinen, P.T. (2008). Bifurcations in Nonsmooth Dynamical Systems. Siam Review, 50(4), 629701. [ Links ]
8. Filippov, A.F. (1988). Differential Equations with Discontinuous RightHand Side. Dordrecht, The Netherlands: Kluwer Academic Publishers. [ Links ]
9. GomezEstern, F. & van der Schaft, A.J. (2004). Physical damping in IDAPBC controlled underactuated mechanical systems. European Journal of Control, 10(5), 451468. [ Links ]
10. Leine, R.I. (2000). Bifurcations in discontinuous mechanical systems of Filippovtype. Ph. D. Thesis, Technische Universiteit Eindhoven, Eindhoven, The Netherlands. [ Links ]
11. Li, Z., Wang, Q., & Gao, H. (2009). Control of friction oscillator by Lyapunov redesign based on delayed state feedback. Acta Mechanica Sinica, 25(2), 257264. [ Links ]
12. Luo, A.C.J. & Rapp, B.M. (2009). Flow switchability and periodic motions in a periodically forced, discontinuous dynamical system. Nonlinear AnalysisReal World Applications, 10(5),30283044. [ Links ]
13. Martinez, R. & Alvarez, J. (2008). A controller for 2DOF underactuated mechanical systems with discontinuous friction. Nonlinear Dynamics, 53(3), 191200. [ Links ]
14. Martinez, R., Alvarez, J., & Orlov, Y. (2008). Hybrid SlidingModeBased Control of Underactuated Systems with Dry Friction. IEEE Transactions on Industrial Electronics, 55(11), 39984003. [ Links ]
15. Marton, L., Hodel, A.S., Lantos, B., & Hung, J.Y. (2008). Underactuated Robot Control: Comparing LQR, Subspace Stabilization, and Combined Error Metric Approaches. IEEE Transactions on Industrial Electronics, 55(10), 37243730. [ Links ]
16. NavarroLópez, E.M. & Cortés, D. (2007). Avoiding harmful oscillations in a drillstring through dynamical analysis. Journal of Sound and Vibration, 307(12), 152171. [ Links ]
17. NavarroLópez, E.M. & LicéagaCastro, E. (2009). Non desired transitions and slidingmode control of a multiDOF mechanical system with stickslip oscillations. Chaos, Solitons & Fractals, 41(4), 20352044. [ Links ]
18. NavarroLópez, E. M. (2009). An alternative characterization of bitsticking phenomena in a multidegreeoffreedom controlled drillstring. Nonlinear Analysis: Real World Applications, 10(5), 31623174. [ Links ]
19. Olsson, H., Astrom, K., de Wit, C.C., Gafvert, M., & Lischinsky, P. (1998). Friction models and friction compensation. European Journal of Control, 4(3), 176195. [ Links ]
20. Orlov, Y.V. (2009). Discontinuous Systems. London: Springer. [ Links ]
21. OrowskaKowalska, T., Kaminski, M., & Szabat, K. (2010). Implementation of a SlidingMode Controller with an Integral Function and Fuzzy Gain Value for the Electrical Drive with an Elastic Joint. IEEE Transactions on Industrial Electronics, 57(4), 13091317. [ Links ]
22. Park, M.S. & Chwa, D. (2009). Orbital Stabilization of InvertedPendulum Systems via Coupled SlidingMode Control. IEEE Transactions on Industrial Electronics, 56(9), 35563570. [ Links ]
23. Riachy, S., Floquet, T., Orlov, Y., & Richard, J.P. (2006). Stabilization of the cartpendulum system via quasihomogeneous switched control. International Workshop on Variable Structure Systems VSS'06, Alghero, Italy, 139142. [ Links ]
24. Stewart, D.E. & Anitescu, M. (2010). Optimal control of systems with discontinuous differential equations. Numerische Mathematik, 14(4), 653695. [ Links ]
25. Utkin, V.I. (1992). Sliding modes in control and optimization. Berlin: Springer Verlag. [ Links ]
26. Woolsey, C.A., Bloch, A.M., Leonard, N.E., & Marsden, J.E. (2001). Physical dissipation and the method of controlled Lagrangians. The European Control Conference, Porto, Portugal, 25702575. [ Links ]
27. Woolsey, C., Bloch, A.M., Leonard, N.E., Reddy, C.K., Chang, D.E., & Marsden, J.E. (2004). Controlled Lagrangian systems with gyroscopic forcing and dissipation. European Journal of Control, 10(5), 478496. [ Links ]