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State and Faults Estimation Based on Proportional Integral Sliding Mode Observer for Uncertain Takagi–Sugeno Fuzzy Systems and its Application to a Turbo-Reactor

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Abstract

This paper deals with the problem of state and faults estimation for nonlinear uncertain systems described by Takagi–Sugeno fuzzy structures (called also multiple models). In this work, actuator faults are considered as unknown inputs. The state and faults estimation is made using a structure of sliding mode observer where an integral term is added. This new structure of observer is called proportional integral sliding mode observer. The added integral term permits the unknown input estimation. For the sensor faults estimation, a mathematical transformation is used. The application of this mathematical transformation to the initial system output let to conceive an augmented system where the initial sensor fault appears as an unknown input. The observer convergence conditions are formulated in the form of Linear Matrix Inequalities allowing computing the observer gains. The proposed proportional integral sliding mode observer is applied to a numerical example showing the efficiency of the fault and the state estimation. In order to show the efficiency of the proposed method, it is applied to a turbo-reactor system.

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  • 23 March 2018

    In the original publication the affiliations are inconsistent. The correct affiliations are provided in this correction article.

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Authors and Affiliations

  1. LARATSI, ENIM, University of Sousse, Sousse, Tunisia

    Ilyes Elleuch

  2. LARA Automatic, ENIT, Sousse, Tunisia

    Atef Khedher

  3. LARATSI, ENIM, Sousse, Tunisia

    Kamel Ben Othman

Authors
  1. Ilyes Elleuch
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  2. Atef Khedher
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  3. Kamel Ben Othman
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Correspondence to Ilyes Elleuch.

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A correction to this article is available online at https://doi.org/10.1007/s40815-018-0480-9.

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Elleuch, I., Khedher, A. & Othman, K.B. State and Faults Estimation Based on Proportional Integral Sliding Mode Observer for Uncertain Takagi–Sugeno Fuzzy Systems and its Application to a Turbo-Reactor. Int. J. Fuzzy Syst. 19, 1768–1781 (2017). https://doi.org/10.1007/s40815-017-0365-3

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  • DOI: https://doi.org/10.1007/s40815-017-0365-3

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