Application of Fractional Calculus for Parameter Estimation of Nonlinear Wiener Systems With Time Delay

Abstract

The parameter identification technique for a fractional-order Wiener system with time delay is proposed using the Haar wavelet operational matrices. The method is applicable to lower and higher-order Wiener systems, where the order could be an integer or fractional value. The proposed method accomplishes identification in two stages, whereby a special input signal is utilized to separate the identification of the nonlinearity from the linear dynamics. The graphical method is applied to the step responses to compute the static nonlinearity. Subsequently, the sinusoidal response is utilized along with the obtained nonlinearity parameters to identify the linear subsystem. The lower-order models of both subsystems are utilized for identification to reduce complexity. This operational matrix-based algebraic approach is simple yet accurate, and it is applicable to noisy data. Moreover, the proposed approach does not demand prior knowledge about the fractional order or time delay. This method is simulated and validated in MATLAB for various Wiener systems. Numerical results and comparisons with the existing methods illustrate the efficiency of the proposed method.