\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Approximate tracking of periodic references in a class of bilinear systems via stable inversion

Abstract Related Papers Cited by
  • This article deals with the tracking control of periodic references in single-input single-output bilinear systems using a stable inversion-based approach. Assuming solvability of the exact tracking problem and asymptotic stability of the nominal error system, the study focuses on the output behavior when the control scheme uses a periodic approximation of the nominal feedforward input signal $u_d$. The investigation shows that this results in a periodic, asymptotically stable output; moreover, a sequence of periodic control inputs $u_n$ uniformly convergent to $u_d$ produce a sequence of output responses that, in turn, converge uniformly to the output reference. It is also shown that, for a special class of bilinear systems, the internal dynamics equation can be approximately solved by an iterative procedure that provides of closed-form analytic expressions uniformly convergent to its exact solution. Then, robustness in the face of bounded parametric disturbances/uncertainties is achievable through dynamic compensation. The theoretical analysis is applied to nonminimum phase switched power converters.
    Mathematics Subject Classification: Primary: 93C10, 93C15; Secondary: 34H05.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    F. Amato, C. Cosentino, A. S. Fiorillo and A. Merola, Stabilization of bilinear systems via linear state-feedback control, IEEE Trans. Circ. Syst.-II, 56 (2009), 76-80.

    [2]

    R. O. Cáceres and I. Barbi, A boost DC-AC converter: Analysis, design and experimentation, IEEE Trans. Power Electronics, 14 (1999), 134-141.doi: doi:10.1109/63.737601.

    [3]

    M. Carpita and M. Marchesoni, Experimental study of a power conditioning system using sliding mode control, IEEE Trans. Power Electronics, 11 (1996), 731-742.doi: doi:10.1109/63.535405.

    [4]

    D. Cortés, Jq. Álvarez, J. Álvarez and A. Fradkov, Tracking control of the boost converter, IEEE Proceedings Control Theory Applications, 151 (2004), 218-224.doi: doi:10.1049/ip-cta:20040203.

    [5]

    S. Devasia, D. Chen and B. Paden, Nonlinear inversion-based output tracking, IEEE Trans. Automatic Control, 41 (1996), 930-942.doi: doi:10.1109/9.508898.

    [6]

    D. L. Elliott, "Bilinear Control Systems. Matrices in Action," Springer, 2009.

    [7]

    M. Farkas, "Periodic Motions," Springer-Verlag, 1994.

    [8]

    E. Fossas and J. M. Olm, Asymptotic tracking in DC-to-DC nonlinear power converters, Discrete Continuous Dynam. Systems - B, 2 (2002), 295-307.

    [9]

    E. Fossas and J. M. Olm, Galerkin method and approximate tracking in a nonminimum phase bilinear system, Discrete Continuous Dynam. Systems - B, 7 (2007), 53-76.

    [10]

    E. Fossas and J. M. Olm, A functional iterative approach to the tracking control of nonminimum phase switched power converters, Math. Control Signals Syst., 21 (2009), 203-227.doi: doi:10.1007/s00498-009-0044-5.

    [11]

    E. Fossas, J. M. Olm, A. Zinober and Y. Shtessel, Galerkin-based sliding mode tracking control of nonminimum phase DC-to-DC power converters, Internat. J. Robust Nonlinear Control, 17 (2007), 587-604.doi: doi:10.1002/rnc.1136.

    [12]

    H. K. Khalil, "Nonlinear Systems," 3rd edition, Prentice Hall, 2002.

    [13]

    R. R. Mohler, "Nonlinear Systems, vol. 2: Applications to Bilinear Control," Prentice Hall, 1991.

    [14]

    J. M. Olm, "Asymptotic Tracking with DC-to-DC Bilinear Power Converters," Ph. D thesis, Universitat Politècnica de Catalunya, 2004.

    [15]

    J. M. Olm, X. Ros-Oton and Y. B. Shtessel, Stable inversion of Abel equations: application to tracking control in DC-DC nonminimum phase boost converters, Automatica, (2010), in press.doi: doi:10.1109/CDC.2007.4434276.

    [16]

    A. Pavlov and K. Y. Pettersen, Stable inversion of non-minimum phase nonlinear systems: A convergent systems approach, in "Proceedings of the 46th IEEE Conference on Decision and Control," (2007), 3995-4000.

    [17]

    A. D. Polyanin, "Handbook of Exact Solutions for Ordinary Differential Equations," 2nd edition, Chapman & Hall/CRC, Boca Raton, 2003.

    [18]

    S. Sastry, "Nonlinear Systems. Analysis, Stability and Control," Springer-Verlag, 1999.

    [19]

    Y. Shtessel, A. Zinober and I. Shkolnikov, Sliding mode control of boost and buck-boost power converters control using method of stable system centre, Automatica, 39 (2003), 1061-1067.doi: doi:10.1016/S0005-1098(03)00068-2.

    [20]

    H. Sira-Ramírez, Sliding motions in bilinear switched networks, IEEE Trans. Circ. Syst., 34 (1987), 1359-1390.

    [21]

    H. Sira-Ramírez, DC-to-AC power conversion on a 'boost' converter, Internat. J. Robust Nonlinear Control, 11 (2001), 589-600.doi: doi:10.1002/rnc.575.

    [22]

    H. Sira-Ramírez, M. Spinetti-Rivera and E. Fossas, An algebraic parameter estimation approach to the adaptive observer-controller based regulation of the boost converter, in "Proceedings of the IEEE Int. Symp. Industrial Electronics," (2007), 3367-3372.

    [23]

    E. D. Sontag, Input to state stability: Basic concepts and results, in "Nonlinear and Optimal Control Theory" (eds. P. Nistri and G. Stefani), Springer-Verlag, (2007), 163-220.

    [24]

    E. D. Sontag and Y. Wang, New characterizations of input-to-state stability, IEEE Trans. Automatic Control, 41 (1996), 1283-1294.doi: doi:10.1109/9.536498.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(100) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return