Complete Parametric Identification of Fractional Order Hammerstein Systems

This paper discusses the parameter and differentiation order identification of continuous fractional order Hammerstein systems in ARX and OE forms. The least squares method is applied to the identification of nonlinear and linear parameters, in which the Grunwald-Letnikov definition and short memory principle are applied to compute the fractional order derivatives. A P-type order learning law is proposed to estimate the differentiation order iteratively and accurately. Particularly, a unique estimation result and a fast convergence speed can be arrived at by the order learning method. The proposed strategy can be successfully applied to the nonlinear systems with quasi-linear properties. The numerical simulations are shown to validate the concepts.