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Higher Order Sliding Mode Based Accurate Tracking of Unmatched Perturbed Outputs

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Advances in Sliding Mode Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 440))

Abstract

Three approaches for higher-order sliding-mode based unmatched uncertainty compensation are summarized. Firstly, an algorithm is proposed based on the block control and quasi-continuous higher order sliding modes techniques. This method provides for the finite-time exact tracking of a smooth desired signal in spite of unmatched perturbations and allows the reduction of the controller gains in the case of partial knowledge of the system model. Thereafter, the combination of integral high-order sliding modes with the hierarchical quasi-continuous controller is proposed allowing finite-time convergence theoretically. Finally, high-order sliding mode observers are employed for exact state and uncertainties/perturbations reconstruction. A sliding mode control design is proposed which ensures theoretically exact compensation of the uncertainties/perturbations for the corresponding unmatched states based on the identified perturbation values. An inverted pendulum simulation example is considered for illustrating the feasibility of the proposed approach.

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References

  1. Adhami-Mirhosseini, A., Yazdanpanah, M.J.: Robust Tracking of perturbed systems by nested sliding mode control. In: Proc. of the International conference on Control and Automation, Budapest, Hungary, pp. 44–48 (2005)

    Google Scholar 

  2. Angulo, M., Fridman, L., Levant, A.: Exact Finite-Time Output Based Control using High-Order Sliding Modes. International Journal of Systems Science 42(11), 1847–1857 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bartolini, G., Ferrara, A., Giacomini, L., Usai, E.: A combined backstepping/second order sliding mode approach to control a class of non-linear systems. In: Proceedings of the IEEE International Workshop on Variable Structure Systems, Tokyo, Japan, pp. 205–210 (1996)

    Google Scholar 

  4. Bejarano, F.J., Fridman, L.: High order sliding mode observer for linear systems with unbounded unknown inputs. International Journal of Control 83(9), 1920–1929 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cao, W., Xu, J.: Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems. IEEE Trans. Automat. Contr. 49, 1355–1360 (2004)

    Article  MathSciNet  Google Scholar 

  6. Castaños, F., Fridman, L.: Analysis and Design of Integral Sliding manifolds for Systems With Unmatched Perturbations. IEEE Trans. Automat. Contr. 51(5), 853–858 (2006)

    Article  Google Scholar 

  7. Choi, H.H.: An LMI-based switching surface design method for a class of mismatched uncertain systems. IEEE Trans. Automat. Contr. 48, 1634–1638 (2003)

    Article  Google Scholar 

  8. Choi, H.H.: Output feedback variable structure control design with an H 2 performance bound constraint. Automatica 48(9), 2403–2408 (2008)

    Article  Google Scholar 

  9. Davis, R., Spurgeon, S.K.: A nonlinear control strategy for robust sliding mode performance in the presence of unmatched uncertainty. International Journal of Control 57, 1107–1123 (1993)

    Article  MathSciNet  Google Scholar 

  10. Davis, R., Spurgeon, S.K.: Robust implementation of sliding mode control schemes. International Journal of System Science 24, 733–743 (1993)

    Article  Google Scholar 

  11. Drazenovic, B.: The Invariance Conditions in Variable Structure Systems. Automatica 5(3), 287–295

    Google Scholar 

  12. Edwards, C., Spurgeon, S.K.: Sliding Mode Control. Taylor and Francis, London (1998)

    Google Scholar 

  13. Yan, X.G., Spurgeon, S.K., Edwards, C.: Dynamic sliding mode control for a class of systems with mismatched uncertainty. European Journal of Control 11(1), 1–10 (2005)

    Article  MathSciNet  Google Scholar 

  14. Estrada, A., Fridman, L.: Integral HOSM Semiglobal Controller for Finite-Time Exact Compensation of Unmatched Perturbations. IEEE Trans. Automat. Contr. 55(11), 2644–2649 (2010)

    Article  MathSciNet  Google Scholar 

  15. Estrada, A., Fridman, L.: Quasi-continuous HOSM control for systems with unmatched perturbations. Automatica 46(11), 1916–1919 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ferrara, A., Giacomini, L.: On multi-input backstepping design with second order sliding modes for a class of uncertain nonlinear systems. International Journal of Control 71(5), 767–788 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  17. Ferreira de Loza, A., Bejarano, F.J., Fridman, L.: Unmatched uncertainties compensation based on high-order sliding mode observation. International Journal on Robust and Nonlinear Control (2012), doi:10.1002/rnc.2795

    Google Scholar 

  18. Filippov, A.F.: Differential Equations with Discontinuous Right-Hand Side. Kluwer, Dordrecht (1988)

    Google Scholar 

  19. Fridman, L.: Singularly perturbed analysis of chattering in relay control systems. IEEE Transactions on Automatic Control 47(12), 2079–2084 (2079)

    Article  MathSciNet  Google Scholar 

  20. Huerta-Avila, H., Loukianov, A.G., Cañedo, J.M.: Nested Integral Sliding Modes of Large Sacale Power Systems. In: Proc. of the 46th IEEE Conference on Decision and Control, New Orleans, LA, USA, pp. 1993–1998 (December 2007)

    Google Scholar 

  21. Freeman, R.A., Kokotovic, P.V.: Robust Nonlinear Control Design. Birkhauser, Boston (1996)

    Book  MATH  Google Scholar 

  22. Isidori, A.: Nonlinear Control Systems, 2nd edn. Springer, New York (1989)

    MATH  Google Scholar 

  23. Kanellakopoulos, I., Kokotović, P.V., Morse, A.S.: Systematic design of adaptive controllers for feedback linearizable system. IEEE Trans. on Automatic Control 36(11), 1241–1253 (1991)

    Article  MATH  Google Scholar 

  24. Krstic, M., Kanellakopoulous, I., Kokotovic, P.: Nonlinear and Adaptive Control Design. Wiley Interscience, NY (1995)

    Google Scholar 

  25. Levant, A., Alelishvili, L.: Integral High-Order Sliding Modes. IEEE Trans. Automat. Contr. 52(7), 1278–1282 (2007)

    Article  MathSciNet  Google Scholar 

  26. Levant, A.: Quasi-Continuous High-Order Sliding-Mode Controllers. IEEE Trans. Automat. Contr. 50(11), 1812–18162 (2005)

    Article  MathSciNet  Google Scholar 

  27. Levant, A.: High-order sliding modes: differentiation and output-feedback control. International Journal of Control 76, 924–941 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  28. Levant, A., Michael, A.: Adjustment of high-order sliding-mode controllers. International Journal of Robust and Nonlinear Control 19(15), 1657–1672 (2009)

    Article  MathSciNet  Google Scholar 

  29. Loukyanov, A., Utkin, V.: Methods of reducing equations for dynamic systems to a regular form. Automatic and Remote Control 42(4), 413–420 (1993)

    Google Scholar 

  30. Loukianov, A.G.: Nonlinear Block Control with Sliding Mode. Automation and Remote Control 59(7), 916–933 (1998)

    MathSciNet  Google Scholar 

  31. Loukianov, A.G.: Robust Block Decomposition Sliding Mode Control Design. Mathematical Problems in Engineering 8(4-5), 349–365 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  32. Loukianov, A., Caedo, J., Fridman, L., Soto Cota, A.: High order block sliding mode controller for a synchronous generator with an exciter system. IEEE Transactions on Industrial Electronics 58(1), 337–347 (2011)

    Article  Google Scholar 

  33. Molinari, B.P.: A strong controllability and observability in linear multivariable control. IEEE Transactions on Automatic Control 21(5), 761–764 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  34. Scarratt, J.C., Zinober, A.S.I., Mills, R.E., Rios-Bolivar, M., Ferrara, A., Giacomini, L.: Dynamical adaptive first and second-order sliding backstepping control of nonlinear nontriangular uncertain systems. ASME Journal of Dynamic Systems, Measurement and Control 122(4), 746–752 (2000)

    Article  Google Scholar 

  35. Shtessel, Y.B., Buffington, J., Banda, S.: Multiple Time Scale Flight Control Using Re-configurable Sliding Modes. In: Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, Florida, USA, pp. 4196–4201 (December 1998)

    Google Scholar 

  36. Won, M.C., Hedrick, J.K.: Multiple surface sliding control of a class of uncertain nonlinear systems. International Journal of Control 64(4), 693–706 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  37. Utkin, V.I.: Sliding modes in control and optimization. Springer, Berlin (1992)

    Book  MATH  Google Scholar 

  38. Utkin, V.I., Guldner, J., Shi, J.: Sliding Mode Control in Electromechanical Systems. Taylor & Francis, London (1999)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Control, Division of Electrical Engineering, Engineering Faculty, National Autonomous University of Mexico, UNAM, Ciudad Universitaria, 04510, Mexico, D.F.

    Leonid Fridman

  2. Ecole Centrale de Nantes, LUNAM Université, IRCCyN UMR CNRS 6597, Nantes, France

    Antonio Estrada

  3. IMS-Lab, Automatic Control Group, University of Bordeaux, 351 Cours de la Libération, 33405, Talence, France

    Alejandra Ferreira de Loza

Authors
  1. Leonid Fridman
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  2. Antonio Estrada
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  3. Alejandra Ferreira de Loza
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Corresponding author

Correspondence to Leonid Fridman .

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Editors and Affiliations

  1. , Interdisciplinary Programme in Systems, Indian Institute of Technology Bombay, ACRE Building 114 B, Mumbai, 400 076, Maharashtra, India

    B Bandyopadhyay

  2. , Dept. of Electrical Engineering, Indian Institute of Technology Delhi, Room No : II/335, New Delhi, 110 016, India

    S Janardhanan

  3. , Department of Electronics, University of Kent, Jennison Building - Room 1.54, Kent, CT2 7NT, United Kingdom

    Sarah K. Spurgeon

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Fridman, L., Estrada, A., de Loza, A.F. (2013). Higher Order Sliding Mode Based Accurate Tracking of Unmatched Perturbed Outputs. In: Bandyopadhyay, B., Janardhanan, S., Spurgeon, S. (eds) Advances in Sliding Mode Control. Lecture Notes in Control and Information Sciences, vol 440. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36986-5_6

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  • DOI: https://doi.org/10.1007/978-3-642-36986-5_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36985-8

  • Online ISBN: 978-3-642-36986-5

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