Generalization of order distribution concept use in the fractional order system identification

In this paper, the order distribution concept in the frequency domain identification has been extended to include fractional order systems having poles and zeros simultaneously. The existing nonlinear optimization problem appeared when both poles and zeros, is are changed to a quadratic problem that can be solved using least squares algorithms. To collect the required data, system is excited by a multi sine input signal with appropriately selected frequencies. Then a nonparametric identification in frequency domain is accomplished to calculate the empirical transfer function estimate (ETFE). This estimate is then used to implement the frequency domain identification on all defined members of the model set to estimate the model parameters in noise free and disturbed cases.