Estimating the fractional order of orthogonal rational functions used in the identification

This paper deals with the identification of fractional order systems via orthogonal rational functions. These functions have widely been used in system identification of classical integer order systems. It has been shown that due to some properties such as the presence of non-exponentional aperiodic multimodes in the fractional order systems, it is much better to use fractional orthogonal rational functions in approximation of these systems. One problem which arises in this area is the estimation of fractional order of these orthogonal rational functions. In the existing methods, these parameters have been found by trial and error which requires a large amount of calculations. To reduce the computational effort, a new strategy is suggested in the present work to estimate the fractional order. The proposed strategy is constructed based on pre-processing the step response of the system in hand.