Output feedback control of multicellular converters

  • I. AmeurEmail author
  • N. Gazzam
  • M. Benmiloud
  • A. Benalia


This paper presents an output feedback control for the multicellular converter using hybrid systems theory. First, we study the observability of the continuous state of the converter under predetermined finite switching sequence. Using some dynamical properties of the converter, a time independent necessary and sufficient condition is given for the continuous state observability. This interesting condition allows the avoidance of the usual matrix exponential computations for the observability analysis and leads to major notes on the multicellular converter observability. Second, as an application of the above results, we consider the case of the 2-cell converter where we establish a new switching control scheme that guarantees the existence and the finite-time stability of a limit cycle. The corresponding repetitive switching sequence of the limit cycle is used to prove the continuous state observability. We next design a super twisting sliding mode observer that guarantees the finite continuous state convergence. Simulation results confirm the effectiveness and the robustness of the output control scheme under different perturbations: variations of the input voltage and load resistance.


Multicellular converter Observability analysis Switching control Limit cycle Super twisting observer Output feedback control 


  1. 1.
    Meynard TA, Foch H (1992) Multi-level conversion: high voltage choppers and voltage-source inverters. In: 23rd Annual IEEE power electronics specialists conference PESC’92 Record. pp. 397–403Google Scholar
  2. 2.
    Wilkinson RH, Meynard TA, du Toit Mouton H (2006) Natural balance of multicell converters: the general case. IEEE Trans Power Electron 21(6):1658–1666CrossRefGoogle Scholar
  3. 3.
    Benmiloud M, Benalia A, Defoort M, Djemai M (2016) On the limit cycle stabilization of a DC/DC three-cell converter. Control Eng Pract 49:29–41CrossRefGoogle Scholar
  4. 4.
    Benmiloud M, Benalia A (2016) Finite-time stabilization of the limit cycle of two-cell DC/DC converter: hybrid approach. Nonlinear Dyn 83:319–332MathSciNetCrossRefGoogle Scholar
  5. 5.
    Gateau, G (1997) Contribution la commande des convertisseurs statiques multicellulaires srie : commande non linaire et commande floue, PhD thesis, Institut National Polytechnique de ToulouseGoogle Scholar
  6. 6.
    Djemai M, Busawn K, Benmansour K, Marouf A (2011) High-order sliding mode control of a DC motor drive via a switched controlled multi-cellular converter. Int J Syst Sci 42(11):1869–1882. MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gazzam N, Benmiloud M, Benalia A (2015) Observability analysis of multicellular converters: hybrid approach. In: 2015 3rd international conference on control, engineering & information technology (CEIT). IEEEGoogle Scholar
  8. 8.
    Defoort M, Van Gorp J, Djemai M (2015) Multicellular converter: a benchmark for control and observation for hybrid dynamical systems. In: Djemai M, Defoort M (eds) Hybrid dynamical systems. Springer, Berlin, pp 293–313Google Scholar
  9. 9.
    Khelouat S, Laleg-Kirati TM, Benalia A, Djemai M, Boukhetala D (2013) On sliding mode observer for a hybrid three-cell converter. In: 2013 3rd international conference on systems and control, ICSC 2013, pp. 613–618Google Scholar
  10. 10.
    Goshen-Meskin D, Bar-Itzhack IY (1992) Observability analysis of piece-wise constant systems. I. Theory. IEEE Trans Aerosp Electron Syst 28(4):1056–1067CrossRefGoogle Scholar
  11. 11.
    Benmiloud M, Benalia A, Djemai M (2014) Hybrid sliding mode control for two cells converter. In: 2014 13th international workshop on variable structure systems (VSS). IEEE, pp. 1–6Google Scholar
  12. 12.
    Van Gorp J, Defoort M, Djemai M, Manamanni N (2012) Hybrid observer for the multicellular converter. In: IFAC proceedings volumes (IFAC-PapersOnline), pp. 259–264Google Scholar
  13. 13.
    Bejarano FJ, Ghanes M, Barbot J-P (2010) Observability and observer design for hybrid multicell choppers. Int J Control 83:617–632MathSciNetCrossRefGoogle Scholar
  14. 14.
    Liu J, Laghrouche S, Harmouche M, Wack M (2014) Adaptive-gain second-order sliding mode observer design for switching power converters. Control Eng Pract 30:124–131CrossRefGoogle Scholar
  15. 15.
    Ghanes M, Bejarano F, Barbot JP (2009) On sliding mode and adaptive observers design for multicell converter. In: 2009 American Control Conference. IEEE, pp. 2134–2139.Google Scholar
  16. 16.
    Hauroigné P, Riedinger P, Iung C (2012) Observer-based output-feedback of a multicellular converter: control Lyapunov function—Sliding mode approach. In: IEEE conference on decision and control (CDC), pp. 1727–1732Google Scholar
  17. 17.
    Defoort M, Djemai M, Floquet T, Perruquetti W (2010) On finite time observer design for multicellular converter. In: Proceedings 2010 11th International workshop on variable structure systems VSS, pp. 56–61Google Scholar
  18. 18.
    Kang W, Barbot JP (2007) Discussions on observability and invertibility. IFAC Proc 7:426–431CrossRefGoogle Scholar
  19. 19.
    Defoort M, Djemai M, Floquet T, Perruquetti W (2011) Robust finite time observer design for multicellular converters. Int J Syst Sci 42:1859–1868MathSciNetCrossRefGoogle Scholar
  20. 20.
    Benmansour K, De Leon J, Djemai M (2006) Adaptive observer for multi-cell chopper. In: Second international symposium communication control signal process. ISCCSP, pp. 1–4Google Scholar
  21. 21.
    Gazzam N, Benalia A (2016) Observability analysis and observer design of multicellular converters. In: 2016 8th international conference on modelling, identification and control, pp. 763–767Google Scholar
  22. 22.
    Gazzam N, Benalia A (2018) Voltage estimation of DC/DC converters. Electrotehnica Electronica Automatica 66(1):73–79Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.LACoSERE LaboratoryAmar Telidji UniversityLaghouatAlgeria
  2. 2.Department of EngineeringUniversity of CambridgeCambridgeUK

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