Frequency domain identification of fractional order time delay systems

The problem of identifying a fractional order transfer function with time delay from frequency response data is considered. A method combining harmony search and linear least squares technique is proposed to solve the frequency domain identification problem. The optimal fractional derivative order and the time delay of the transfer function model are found using harmony search, while the numerator and denominator coefficients are obtained by solving linear least squares problems for every fractional derivative order and time delay generated with harmony search. Linear least squares estimator is used to reduce the computational burden in the rough-tuning phase of harmony search. Iterative linear least squares estimator is used to improve the accuracy in the fine-tuning phase. A numerical example is given to demonstrate the effectiveness of the proposed identification method.