Nonlinear Dynamics

, Volume 96, Issue 4, pp 2613–2626 | Cite as

Identification of fractional Hammerstein system with application to a heating process

  • Karima HammarEmail author
  • Tounsia Djamah
  • Maamar Bettayeb
Original Paper


In this paper, fractional Hammerstein system identification is considered, where the linear block is of fractional order. The original discrete Hammerstein system is first converted to a fractional polynomial nonlinear state-space model (PNLSS), which allows a better parameterization of the model. An output-error identification approach is developed based on the robust Levenberg–Marquardt algorithm, whose nevralgic point is the calculation of parametric sensitivity functions. These last are developed as a multivariable fractional PNLSS model which effectively reduces the computational effort. Various simulations are used to test the method’s efficiency and its statistical performance is analyzed using Monte Carlo simulation. Finally, the method is evaluated through a heating experimental benchmark. The obtained results show good agreement with the real system outputs.


Nonlinear system Fractional order system Hammerstein model Polynomial nonlinear state-space model Output-error method 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Karima Hammar
    • 1
    Email author
  • Tounsia Djamah
    • 1
  • Maamar Bettayeb
    • 2
  1. 1.Laboratoire de Conception et Conduite des Systèemes de Production (L2CSP)UMMTOTizi-OuzouAlgeria
  2. 2.Department of Electrical and Computer Engineering, University of Sharjah UAE and (CEIES)King Abdulaziz UniversityJeddahSaudi Arabia

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