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An LMI-based robust controller design using global nonlinear sliding surfaces and application to chaotic systems

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Abstract

This paper addresses a novel global nonlinear sliding surface to achieve robustness and high performance for a class of uncertain nonlinear systems. Using the Lyapunov stability theorem, exponential stability analysis of the system states is proposed in the linear matrix inequality form. A new control law is designed to guarantee the elimination of the reaching phase and the existence of the sliding mode around the nonlinear surface right from the beginning. Two illustrative simulations are presented to demonstrate the robustness and effectiveness of the introduced design. It is worthwhile noticing that the proposed approach can be applied to a wide variety of uncertain nonlinear control problems.

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References

  1. Fei, J., Ding, H.: Adaptive sliding mode control of dynamic system using RBF neural network. Nonlinear Dyn. 70, 1563–1573 (2012)

    Article  MathSciNet  Google Scholar 

  2. Farivar, G., Asaei, B., Mehrnami, S.: An analytical solution for tracking photovoltaic module MPP. IEEE J. Photovolt. 3, 1053–1061 (2013)

    Article  Google Scholar 

  3. Mehrnami, S., Farhangi, S.: Innovative decision reference based algorithm for photovoltaic maximum power point tracking. J. Power Electron. 10, 528–537 (2010)

    Article  Google Scholar 

  4. Mehrnami, S., Mazumder, S.K.: Modulation scheme of the differential-mode Ćuk inverter for loss mitigation. In: Proceedings of the 2013 IEEE Energy Conversion Congress and Exposition, pp. 3419–3425. Denver, CO (2013)

  5. Mehrnami, S., Mazumder, S.K.: Discontinuous modulation scheme for a differential-mode Ćuk inverter. IEEE Trans. Power Electron. (2014). doi:10.1109/TPEL.2014.2314688

  6. Mehrnami, S., Mazumder, S.K.: Harmonic-compensation based control of a nonlinear differential-mode Ćuk inverter. In: Proceedings of the 2013 4th IEEE International Symposium on Power Electronics for Distributed Generation Systems, pp. 1–3. Rogers, AR (2013)

  7. Mobayen, S.: Design of LMI-based global sliding mode controller for uncertain nonlinear systems with application to Genesio’s chaotic system. Complex (2014). doi:10.1002/cplx.21545

  8. Mobayen, S.: Design of a robust tracker and disturbance attenuator for uncertain systems with time delays. Complex (2014). doi:10.1002/cplx.21569

  9. Mobayen, S.: Robust tracking controller for multivariable delayed systems with input saturation via composite nonlinear feedback. Nonlinear Dyn. 76, 827–838 (2014)

    Article  MathSciNet  Google Scholar 

  10. Mobayen, S., Majd, V.J., Sojoodi, M.: An LMI-based composite nonlinear feedback terminal sliding-mode controller design for disturbed MIMO systems. Math. Comput. Simul. 85, 1–10 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  11. Zhihong, M., Yu, X.H.: Terminal sliding mode control of MIMO linear systems. IEEE Trans. Circuits Syst. Fundam. Theory Appl. 44, 1065–1070 (1997)

    Article  MathSciNet  Google Scholar 

  12. Mobayen, S.: Finite-time robust-tracking and model-following controller for uncertain dynamical systems. J. Vib. Control (2014). doi:10.1177/1077546314538991

  13. Mobayen, S., Yazdanpanah, M.J., Majd, V.J.: A finite-time tracker for nonholonomic systems using recursive singularity-free FTSM. In: 2011 American Control Conference, pp. 1720–1725. San Francisco, CA (2011)

  14. Mobayen, S., Majd, V.J.: Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances. Nonlinear Dyn. 70, 171–180 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  15. Wang, H., Han, Z.Z., Xie, Q.Y., Zhang, W.: Finite-time chaos control via nonsingular terminal sliding mode control. Commun. Nonlinear Sci. Numer. Simulat. 14, 2728–2733 (2009)

  16. Gao, C., Liu, Z., Xu, R.: On exponential stabilization for a class of neutral-type systems with parameter uncertainties: an integral sliding mode approach. Appl. Math. Comput. 219, 11044–11055 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  17. Pisano, A., Usai, E.: Sliding mode control: a survey with application in math. Math. Comp. Simul. 81, 954–979 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  18. Aghababa, M.P., Akbari, M.E.: A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances. Appl. Math. Comput. 218, 5757–5768 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  19. Edward, C., Spurgeon, S.K.: Sliding Mode Control: Theory and Application. Taylor and Francis, London (1998)

    Google Scholar 

  20. Chang, J.L.: Dynamic output feedback integral sliding mode control design for uncertain systems. Int. J. Robust Nonlinear Control 22, 841–857 (2012)

    Article  MATH  Google Scholar 

  21. Ting, H.C., Chang, J.L., Chen, Y.P.: Output feedback integral sliding mode controller of time-delay systems with mismatch disturbances. Asian J. Control 14, 85–94 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  22. Mobayen, S.: Design of CNF-based nonlinear integral sliding surface for matched uncertain linear systems with multiple state-delays. Nonlinear Dyn. 77, 1047–1054 (2014)

    Article  MathSciNet  Google Scholar 

  23. Castanos, F., Fridman, L.: Analysis and design of integral sliding manifolds for systems with unmatched perturbations. IEEE Trans. Autom. Control 51, 853–858 (2006)

    Article  MathSciNet  Google Scholar 

  24. Mobayen, S.: Fast terminal sliding mode controller design for nonlinear second-order systems with time-varying uncertainties. Complex (2014). doi:10.1002/cplx.21600

  25. Tokat, S., Eksin, I., Guzelkaya, M.: Sliding mode control of high order systems using a constant nonlinear sliding surface on a transformed coordinate axis. J. Vib. Control 14, 909–927 (2008)

    Article  MathSciNet  Google Scholar 

  26. Yu, X., Zhihong, M.: On finite time mechanism: terminal sliding modes. In: 1996 IEEE International Workshop on Variable Structure Systems, pp. 164–167. Tokyo (1996)

  27. Bandyopadhyay, B., Fulwani, D.: A robust tracking controller for uncertain MIMO plant using nonlinear sliding surface. In: Proceedings of IEEE International Conference on Industrial Technology (ICIT 2009), pp. 1–6. Gippsland (2009)

  28. Bandyopadhyay, B., Fulwani, D.: High performance tracking controller for discrete plant using nonlinear sliding surface. IEEE Trans. Ind. Electron. 56, 3628–3637 (2009)

  29. Liu, L., Han, Z., Li, W.: Global sliding mode control and application in chaotic systems. Nonlinear Dyn. 56, 193–198 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  30. Scherer, C., Weiland, S.: Linear Matrix Inequalities in Control. Lecture Notes. Delft University, The Netherlands (2005)

    Google Scholar 

  31. Moulay, E., Peruquetti, W.: Finite time stability and stabilization of a class of continuous systems. J. Math. Anal. Appl. 323, 1430–1443 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  32. Lü, J.H., Chen, G.R., Cheng, D.Z., Celikovsky, S.: Bridge the gap between the Lorenz system and the Chen system. Int. J. Bifurcat. Chaos 12, 2917–26 (2002)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Electrical Engineering Department, University of Zanjan, P.O. Box 38791-45371, Zanjan, Iran

    Saleh Mobayen

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  1. Saleh Mobayen
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Correspondence to Saleh Mobayen.

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Mobayen, S. An LMI-based robust controller design using global nonlinear sliding surfaces and application to chaotic systems. Nonlinear Dyn 79, 1075–1084 (2015). https://doi.org/10.1007/s11071-014-1724-3

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  • DOI: https://doi.org/10.1007/s11071-014-1724-3

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