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Observer design for a nonlinear diffusion system based on the Kirchhoff transformation

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Abstract

This paper deals with the state estimation for a nonlinear diffusion system. An observer that reconstructs the whole state, from the available measurements, is proposed based on an equivalent linear diffusion model obtained using the Kirchhoff tangent transformation. This bijective mapping allows to apply the available and powerful state estimation theory of linear distributed parameter systems and simplifies the observer design. Hence, an observer can be designed for the obtained equivalent linear diffusion system and by using the Kirchhoff transformation, the whole state of the original nonlinear diffusion system is recovered. The observability analysis of the nonlinear diffusion system and the convergence of the proposed observer are also investigated based on the equivalent linear diffusion system. The effectiveness of the proposed observer is shown, through numerical simulation runs, in the case of a heated steel rod by considering both an uniformly distributed and a punctual boundary sensing.

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Authors and Affiliations

  1. Laboratoire de Conception et Conduite des Systèmes de Production, Université Mouloud MAMMERI, 15 000, Tizi-Ouzou, Algeria

    Dyhia Benameur, Ahmed Maidi & Saïd Djennoune

  2. Laboratoire Réactions et Génie des Procédés, UMR 7274-CNRS, Lorraine Université, ENSIC, 1, rue Grandville, BP 20451, 54001, Nancy Cedex, France

    Jean-Pierre Corriou

Authors
  1. Dyhia Benameur
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  2. Ahmed Maidi
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  3. Saïd Djennoune
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  4. Jean-Pierre Corriou
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Correspondence to Ahmed Maidi.

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Benameur, D., Maidi, A., Djennoune, S. et al. Observer design for a nonlinear diffusion system based on the Kirchhoff transformation. Int. J. Dynam. Control 6, 154–166 (2018). https://doi.org/10.1007/s40435-017-0313-y

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  • DOI: https://doi.org/10.1007/s40435-017-0313-y

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