SciELO - Scientific Electronic Library Online

vol.16 issue1EditorialA Reorder Buffer Design for High Performance Processors author indexsubject indexsearch form
Home Pagealphabetic serial listing  

Services on Demand




Related links

  • Have no similar articlesSimilars in SciELO


Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.16 n.1 México Jan./Mar. 2012




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:

2 Departamento de Electrónica y Telecomunicaciones, División de Física Aplicada, CICESE, Ensenada, B. C., Mexico. Correo:


Article received on 15/01/2010.
Accepted on 17/02/2011.



A technique to design a dynamic continuous controller to regulate a class of full–actuated mechanical systems with dry friction is proposed. It is shown that the control eliminates the steady–state 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 2–DOF underactuated mechanical system with dry friction in the non–actuated joint is described. Here, the control objective is to regulate the non–actuated 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.



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.





1. Almutairi, N.B. & Zribi, M. (2009). Sliding Mode Control of a Three–dimensional Overhead Crane. Journal of vibration and control, 15(11), 1679–1730.         [ 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), 679–692.         [ 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),679–686.         [ 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, 2192–2197.         [ Links ]

5. Boiko, I., Fridman, L., & Castellanos, M.I. (2004). Analysis of Second–Order Sliding–Mode Algorithms in the Frequency Domain. IEEE Transactions on Automatic Control, 49(6), 946–950.         [ Links ]

6. Chaoui, H., Sicard, P. & Gueaieb, W. (2009). ANN–Based Adaptive Control of Robotic Manipulators With Friction and Joint Elasticity. IEEE Transactions on Industrial Electronics, 56(8), 3174–3187.         [ 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), 629–701.         [ Links ]

8. Filippov, A.F. (1988). Differential Equations with Discontinuous Right–Hand Side. Dordrecht, The Netherlands: Kluwer Academic Publishers.         [ Links ]

9. Gomez–Estern, F. & van der Schaft, A.J. (2004). Physical damping in IDA–PBC controlled underactuated mechanical systems. European Journal of Control, 10(5), 451–468.         [ Links ]

10. Leine, R.I. (2000). Bifurcations in discontinuous mechanical systems of Filippov–type. 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), 257–264.         [ Links ]

12. Luo, A.C.J. & Rapp, B.M. (2009). Flow switchability and periodic motions in a periodically forced, discontinuous dynamical system. Nonlinear Analysis–Real World Applications, 10(5),3028–3044.         [ Links ]

13. Martinez, R. & Alvarez, J. (2008). A controller for 2–DOF underactuated mechanical systems with discontinuous friction. Nonlinear Dynamics, 53(3), 191–200.         [ Links ]

14. Martinez, R., Alvarez, J., & Orlov, Y. (2008). Hybrid Sliding–Mode–Based Control of Underactuated Systems with Dry Friction. IEEE Transactions on Industrial Electronics, 55(11), 3998–4003.         [ 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), 3724–3730.         [ Links ]

16. Navarro–López, E.M. & Cortés, D. (2007). Avoiding harmful oscillations in a drillstring through dynamical analysis. Journal of Sound and Vibration, 307(1–2), 152–171.         [ Links ]

17. Navarro–López, E.M. & Licéaga–Castro, E. (2009). Non desired transitions and sliding–mode control of a multi–DOF mechanical system with stick–slip oscillations. Chaos, Solitons & Fractals, 41(4), 2035–2044.         [ Links ]

18. Navarro–López, E. M. (2009). An alternative characterization of bit–sticking phenomena in a multi–degree–of–freedom controlled drillstring. Nonlinear Analysis: Real World Applications, 10(5), 3162–3174.         [ 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), 176–195.         [ Links ]

20. Orlov, Y.V. (2009). Discontinuous Systems. London: Springer.         [ Links ]

21. Orowska–Kowalska, T., Kaminski, M., & Szabat, K. (2010). Implementation of a Sliding–Mode Controller with an Integral Function and Fuzzy Gain Value for the Electrical Drive with an Elastic Joint. IEEE Transactions on Industrial Electronics, 57(4), 1309–1317.         [ Links ]

22. Park, M.S. & Chwa, D. (2009). Orbital Stabilization of Inverted–Pendulum Systems via Coupled Sliding–Mode Control. IEEE Transactions on Industrial Electronics, 56(9), 3556–3570.         [ Links ]

23. Riachy, S., Floquet, T., Orlov, Y., & Richard, J.P. (2006). Stabilization of the cart–pendulum system via quasi–homogeneous switched control. International Workshop on Variable Structure Systems VSS'06, Alghero, Italy, 139–142.         [ Links ]

24. Stewart, D.E. & Anitescu, M. (2010). Optimal control of systems with discontinuous differential equations. Numerische Mathematik, 14(4), 653–695.         [ 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, 2570–2575.         [ 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), 478–496.         [ Links ]

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License