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.

In this paper, a system identification method for continuous fractional-order Hammerstein models is proposed. A block structured nonlinear system constituting a static nonlinear block followed by a fractional-order linear dynamic system is considered. The fractional differential operator is represented through the generalized operational matrix of block pulse functions to reduce computational complexity. A special test signal is developed to isolate the identification of the nonlinear static function from that of the fractional-order linear dynamic system. The merit of the proposed technique is indicated by concurrent identification of the fractional order with linear system coefficients, algebraic representation of the immeasurable nonlinear static function output, and permitting use of non-iterative procedures for identification of the nonlinearity. The efficacy of the proposed method is exhibited through simulation at various signal-to-noise ratios.

The identification of multi-input-multi-output process is always challenging due to significant loop interactions. This article proposes an identification technique for two-input-two-output processes with fractional order models via Haar wavelet feature. The presented technique can estimate independent four fractional single-pole time delay models without additional steps to decouple processes during identification. The method uses a well-known relay feedback test to produce the input-output data for measurements. Then, the Haar wavelet operational matrix based algebraic approach is utilised to identify the unknown process models with reduced complexity. Numerical analysis on various examples show the efficacy even in presence of noise and without additional filter or preprocessing of measured signals. The comparative study proves advantages of the presented approach.