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Rejection of nonharmonic disturbances for a class of uncertain nonlinear systems with nonlinear exosystems

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Abstract

This paper proposes an asymptotic rejection algorithm for rejecting exotic disturbances in nonlinear systems. Disturbances produced by nonlinear exosystems are nonharmonic and periodic. A new internal model is proposed to deal with these disturbances. Furthermore, an adaptive output feedback controller is designed to ensure that the system’s state variables asymptotically converge to zero, and disturbances can be completely rejected. The proposed algorithm has various applications, such as active vibration control. The proposed algorithm is demonstrated to completely reject the nonharmonic periodic disturbances produced by a van der Pol oscillator.

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References

  1. Hu T, Teel A R. Characterization of forced vibration for difference inclusions: A Lyapunov approach. IEEE Trans Circ Syst I: Reg Paper, 2007, 54: 1367–1379

    Article  MathSciNet  Google Scholar 

  2. Chen C, Ding Z, Lennox B. Rejection of nonharmonic disturbances in nonlinear systems with semi-global stability. IEEE Trans Circ Syst II: Expr Briefs, 2008, 55: 1289–1293

    Article  Google Scholar 

  3. Feng G, Palaniswami M. Unified treatment of internal model principle based adaptive control algorithms. Int J Control, 1991, 54: 883–901

    Article  MATH  Google Scholar 

  4. Bodson M, Sacks A, Khosla P. Harmonic generation in adaptive feedforward cancellation schemes. IEEE Trans Automat Control, 1994, 39: 1939–1944

    Article  MathSciNet  MATH  Google Scholar 

  5. Huang J. Nonlinear Output Regulation: Theroy and Application. Philadelphia, PA: SIAM, 2004

    Book  Google Scholar 

  6. Huang J, Rugh W J. On a nonlinear multivariable servomechanism problem. Automatica, 1990, 26: 963–972

    Article  MathSciNet  MATH  Google Scholar 

  7. Bodson M, Douglas S C. Adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequencies. Automatica, 1997, 33: 2213–2221

    Article  MathSciNet  MATH  Google Scholar 

  8. Marino R, Santosuosso G L, Tomei P. Robust adaptive compensation of biased sinusoidal disturbances with unknown frequencies. Automatica, 2003, 39: 1755–1761

    Article  MathSciNet  MATH  Google Scholar 

  9. Nikiforov V O. Adaptive non-linear tracking with complete compensation of unknown disturbances. Eur J Control, 1998, 4: 132–139

    Article  MATH  Google Scholar 

  10. Ding Z. Asymptotic rejection of unknown sinusoidal disturbances in nonlinear systems. Automatica, 2007, 43: 174–177

    Article  Google Scholar 

  11. Isidori A, Byrnes C I. Output regulation of nonlinear systems. IEEE Trans Automat Control, 1990, 35: 131–140

    Article  MathSciNet  MATH  Google Scholar 

  12. Byrnes C I, Priscoli F D, Isidori A, et al. Structurally stable output regulation of nonlinear systems. Automatica, 1997, 33: 369–385

    Article  MATH  Google Scholar 

  13. Huang J. Remarks on the robust output regulation problem for nonlinear systems. IEEE Trans Automat Control, 2001, 46: 2028–2031

    Article  MathSciNet  MATH  Google Scholar 

  14. Ye X, Huang J. Decentralized adaptive output regulation for large-scale nonlinear systems. IEEE Trans Automat Control, 2003, 48: 276–281

    Article  MathSciNet  Google Scholar 

  15. Feng G, Zhang T. Output regulation of discrete-time piecewise-liner systems with application to controlling chaos. IEEE Trans Circ Syst II: Expr Briefs, 2006, 53: 249–253

    Article  Google Scholar 

  16. Ding Z. Decentralized output regulation of large scale nonlinear systems with delay. Kybernetika, 2009, 45: 33–48

    MathSciNet  MATH  Google Scholar 

  17. Liu L, Chen Z, Huang J. Parameter convergence and minimal internal model with an adaptive output regulation problem. Automatica, 2009, 45: 1206–1311

    Google Scholar 

  18. Byrnes C I, Isidori A. Nonlinear internal model for output regulation. IEEE Trans Automat Control, 2004, 49: 2244–2247

    Article  MathSciNet  Google Scholar 

  19. Chen Z, Huang J. Robust output regulation with nonlinear exosystems. Automatica, 2005, 41: 1447–1454

    Article  MATH  Google Scholar 

  20. Ding Z. Output regulation of uncertain nonlinear systems with nonlinear exosystems. IEEE Trans Automat Control, 2006, 51: 498–503

    Article  MathSciNet  Google Scholar 

  21. Xi Z, Ding Z. Global adaptive output regulation of a class of nonlinear systems with nonlinear exosystems. Automatica, 2007, 43: 143–149

    Article  MathSciNet  MATH  Google Scholar 

  22. Xi Z, Ding Z. Adaptive rejection of nonlinear disturbances in extended nonlinear output feedback systems. Int J Control, 2008, 81: 1417–1423

    Article  MathSciNet  MATH  Google Scholar 

  23. Sun W, Huang J. Output regulation for a class of uncertain nonlinear systems with nonlinear exosystems and its application. Sci China Ser F-Inf Sci, 2009, 52: 2172–2179

    Article  MathSciNet  MATH  Google Scholar 

  24. Sun W, Huang J, Sun Z. Global robust stabilization for a class of time-varying output feedback systems. Int J Robot Autom, 2011, 26: 93–99

    MathSciNet  Google Scholar 

  25. Krstic M, Kanellakopoulos I, Kokotovic P. Nonlinear and Adaptive Control Design. New York: John Wiley and Sons, 1995

    Google Scholar 

  26. Ding Z. Adaptive stabilization of a class of nonlinear systems with unstable internal dynamics. IEEE Trans Automat Control, 2003, 48: 1788–1792

    Article  MathSciNet  Google Scholar 

  27. Ding Z. Adaptive disturbance rejection of nonlinear systems in an extended output feedback form. IET Control Theory A, 2007, 1: 298–303

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Information Engineering, Nanchang Hangkong University, Nanchang, 330063, China

    Yuan Jiang

  2. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    ShuTang Liu

  3. School of Computer and Information Engineering, Guangxi Teachers Education University, Nanning, 530001, China

    RuLiang Wang

Authors
  1. Yuan Jiang
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  2. ShuTang Liu
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  3. RuLiang Wang
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Correspondence to Yuan Jiang.

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Jiang, Y., Liu, S. & Wang, R. Rejection of nonharmonic disturbances for a class of uncertain nonlinear systems with nonlinear exosystems. Sci. China Inf. Sci. 56, 1–12 (2013). https://doi.org/10.1007/s11432-011-4481-7

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  • DOI: https://doi.org/10.1007/s11432-011-4481-7

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