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Discontinuous H control of underactuated mechanical systems with friction and backlash

  • Raúl Rascón
  • Joaquin Alvarez
  • Luis T. Aguilar
Regular Papers Control Theory and Applications

Abstract

Nonlinear H -control is extended to discontinuous mechanical systems with degree of underactuation one, where nonlinear phenomena such as Coulomb friction and backlash are considered. The problem in question is to design a feedback controller via output measurements so as to obtain the closed-loop system in which all trajectories are locally ultimate bounded, and the underactuated link is regulated to a desired position while also attenuating the influence of external perturbations and nonlinear phenomena. It is considered that positions are the only measurements available for feedback in the system. Performance issues of the discontinuous H -regulation controller are illustrated in an experimental study made for a rectilinear plant with friction modified to have a gap in the point of contact between bodies.

Keywords

Backlash discontinuous H control friction mechanical systems 

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References

  1. [1]
    A. Isidori, “A tool for semiglobal stabilization of uncertain non minimum-phase nonlinear systems via output feedback,” IEEE Transactions on Automatic Control, vol. 48, no. 10, pp. 1817–1827, 2000. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    M. Nordin and P.-O. Gutman, “Controlling mechanical systems with backlash-a survey,” Automatica, vol. 38, no. 10, pp. 1633–1649, 2002.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    V. Bagad, Mechatronics, Technical Publications, 2009.Google Scholar
  4. [4]
    M. Nordin, P. Bodin, and P.-O. Gutman, New models and identification methods for backlash and gear play, G. Tao, F. Lewis (Eds.), Adaptive Control of Nonsmooth Dynamic Systems, Springer London, pp. 1–30, 2001.CrossRefGoogle Scholar
  5. [5]
    Y. Orlov, L. Aguilar and J. C. Cadiou, “Switched chattering control vs. backlash/friction phenomena in electrical servomotors,” International Journal of Control, vol. 76, no. 9-10, pp. 959–967, 2003. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    H. Zabiri and Y. Samyudia, “A hybrid formulation and design of model predictive control for systems under actuator saturation and backlash,” Journal of Process Control, vol. 16, no. 7, pp. 693–709, 2006. [click]CrossRefGoogle Scholar
  7. [7]
    Y. Li, S. Tong, and T. Li, “Adaptive fuzzy output feedback control of uncertain nonlinear systems with unknown backlash-like hysteresis,” Information Sciences, vol. 198, pp. 130–146, 2012. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    G. Tao, X. Ma, and Y. Ling, “Optimal and nonlinear decoupling control of systems with sandwiched backlash,” Automatica, vol. 37, no. 2, pp. 165–176, 2001. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    L. Aguilar, Y. Orlov, and L. Acho, “Nonlinear H control of nonsmooth time varying systems with application to friction mechanical manipulators,” Automatica, vol. 39, no. 9, pp. 1531–1542, 2003. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    L. Aguilar, Y. Orlov, and L. Acho, “Nonlinear H tracking control of friction mechanical manipulator,” Proc. American Control Conference, pp. 268–272, 2002.Google Scholar
  11. [11]
    O. Montano and Y. Orlov, “Discontinuous H -control of mechanical manipulators with frictional joints,” 9th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), pp. 1–6, 2012. [click]Google Scholar
  12. [12]
    H. Hao, J. Bin, and Y. Hao, “Robust H reliable control for uncertain switched systems with circular disk pole constraints,” Journal of the Franklin Institute, vol. 350, no. 4, pp. 802–817, 2013. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    H. Li, X. Jing, and H. R. Karimi, “Output-feedback-based H control for vehicle suspension systems with control delay,” IEEE Transactions on Industrial Electronics, vol. 61, no. 1, pp. 436–446, 2014. [click]CrossRefGoogle Scholar
  14. [14]
    C. Lauwerys, J. Swevers, and P. Sas, “Robust linear control of an active suspension on a quarter car test-rig,” Control Engineering Practice, vol. 13, no. 5, pp. 577–586, 2005. [click]CrossRefGoogle Scholar
  15. [15]
    R. Rascón, J. Álvarez, and L. T. Aguilar, “Control robusto de posición para un sistema mecánico subactuado con fricción y holgura elástica,” Revista Iberoamericana de Automática e Informática Industrial RIAI, vol. 11, no. 3, pp. 275–284, 2014. [click]CrossRefGoogle Scholar
  16. [16]
    R. Rascón, J. Alvarez, and L. Aguilar, “Sliding mode control with H attenuator for unmatched disturbances in a mechanical system with friction and a force constraint,” 12th InternationalWorkshop on Variable Structure Systems (VSS), pp. 434–439, 2012. [click]Google Scholar
  17. [17]
    R. Rascón, J. Alvarez, and L. Aguilar, “Regulation and force control using sliding modes to reduce rebounds in a mechanical system subject to a unilateral constraint,” Control Theory & Applications, IET, vol. 6, no. 18, pp. 2785–2792, 2012. [click]MathSciNetCrossRefGoogle Scholar
  18. [18]
    P. R. Dahl, “Solid friction damping of mechanical vibrations,” AIAA Journal, vol. 14, no. 12, pp. 1675–1682, 1976. [click]CrossRefGoogle Scholar
  19. [19]
    C. Canudas de Wit, H. Olsson, K. Astrom, and P. Lischinsky, “A new model for control of systems with friction,” IEEE Transactions on Automatic Control, vol. 40, no. 3, pp. 419–425, 1995. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    S. Aouaouda, M. Chadli, P. Shi, and H. Karimi, “Discretetime H_=H sensor fault detection observer design for nonlinear systems with parameter uncertainty,” International Journal of Robust and Nonlinear Control, vol. 25, no. 3, pp. 339–361, 2015. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    C. Qin, H. Zhang, and Y. Luo, “Model-free H control design for unknown continuous-time linear system using adaptive dynamic programming,” Asian Journal of Control, vol. 18, no. 2, pp. 609–618, 2016. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    B. Luo, H.-N. Wu, and T. Huang, “Off-policy reinforcement learning for H control design,” IEEE Transactions on Cybernetics, vol. 45, no. 1, pp. 65–76, 2015. [click]CrossRefGoogle Scholar
  23. [23]
    R. Merzouki and N. M’Sirdi, “Compensation of friction and backlash effects in an electrical actuator,” J. Systems and Control Engineering, vol. 218, no. 2, pp. 75–84, 2004. [click]Google Scholar
  24. [24]
    A. F. Filippov, Differential Equations with Discontinuous Right-Handsides, Kluwer, Dordercht, Netherland, 1988.CrossRefGoogle Scholar
  25. [25]
    M. G. Safonov, D. J. N. Limebeer, and R. Y. Chiang, “Simplifying the H theory via loop-shifting, matrix-pencil and descriptor concepts,” International Journal of Control, vol. 50, no. 6, pp. 2467–2488, 1989. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “state-space solutions to standard H2 and H control problems,” IEEE Transactions on Automatic Control, vol. 34, no. 8, pp. 831–847, 1989. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    L. N. Virgin, Introduction to Experimental Nonlinear Dynamics: A Case Study in Mechanical Vibration, Cambridge University Press, 2000.zbMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Raúl Rascón
    • 1
  • Joaquin Alvarez
    • 2
  • Luis T. Aguilar
    • 3
  1. 1.UABC, Universidad Autónoma de Baja California, Facultad de IngenieríaBlvd. Benito Juárez y Calle de la Normal S/NBaja CaliforniaMéxico
  2. 2.CICESECentro de Investigación Científica y de Educación Superior de EnsenadaSan DiegoUSA
  3. 3.IPN, Instituto Politécnico NacionalTijuanaMéxico

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