Frequency identification of fractional systems based on gain and phase data

This paper presents a method dedicated to the modelling and the identification of fractional systems using frequency data such as gains and phases. The frequency characterization of fractional differential is defined first and a method to obtain the Bode plot of a fractional system is given. Then, minimization of the least-squares criterion according to the frequency data such as gains and phases is performed using Marquardt algorithm based on output errors. The advantage of this method is the abilities to estimate the order of the fractional system. At last a simulated example illustrates the validity of this methodology.