Identification Methods for Fractional Order Nonlinear Models

  • Walid Allafi

    Student thesis: Doctoral ThesisDoctor of Philosophy


    This thesis considers the development of novel parameter estimation and system identification methods for fractional-order continuous-time nonlinear systems from sampled input-output signals. It is recognised that there is no universal model parameter estimation method which would be suitable for all types of nonlinear system models. In this work, two parameter estimation methods, targeting specific nonlinear model structures, have been developed.

    The first proposed parameter estimation method is based on an extension of the simplified and refined instrumental variable method for identification of integer-order continuous-time linear transfer function models. The proposed extended method is able to estimate parameters of fractional-order continuous-time Hammerstein–Wiener (HWFC) models, where the case of estimation of linear, Hammerstein (HFC), and Wiener (WFC) models is considered as a special case. It is also possible to estimate the classical integer-order model counterparts as a special case. Subsequently, the proposed extension to the simplified and refined instrumental variable methods for HWFC model estimation is abbreviated to HWSRIVCF and HWRIVCF, respectively. The refined version, HWRIVCF, considers the noise model to be of Box-Jenkins type, while the simplified version, HWRIVCF, assumes an output error measurement noise scenario. The advantage of this novel extension, compared to published methods, is that the output static nonlinearity of the Wiener model part does not need to be invertible.

    The second proposed fractional-order parameter estimation method is based on an existing delayed integer-order state variable filtering technique. In general, the developed method is able to estimate parameters of continuous-time fractional-order nonlinear models, when formulated in input-output form. The individual elements of the input-output equation (regression model) comprises of higher order time derivatives, signal powers, and products between the input and output signals and their powers. In this thesis, the focus is on a special model subclass, namely, a class of bilinear system models due mainly to its previous use in control engineering applications.

    A comprehensive case study, presenting the full system identification cycle, is also given. In this study, fractional-order continuous-time transfer function model of a 1D linear solid a diffusion process has been identified from sampled input-output data. The data was generated from a governing diffusion equation solved by the finite volume method.
    Date of Award2015
    Original languageEnglish
    Awarding Institution
    • Coventry University
    SupervisorIvan Zajic (Supervisor)

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