A novel method for approximating fractional order systems is presented. Vector fitting is involved in thismethod. As the basis of approximation of fractional order systems, approximation of fractional order operators ismostly achieved by curve fitting in frequency domain, such as the well-known Oustaloup’s method. However, thesemethods have several serious defects in principle. A new perspective based on system identification is adoptedto deal with approximation of fractional order operators in this paper. Moreover, nonzero initial condition forapproximating fractional order systems is considered. And the proposed assignment of initial values for the Caputocase offers an effective solution for the simulation with nonzero initial condition. Finally, numerical examples aregiven to verify the efficiency of the proposed method.
A novel method for approximating fractional order systems is presented. Vector fitting is involved in thismethod. As the basis of approximation of fractional order systems, approximation of fractional order operators ismostly achieved by curve fitting in frequency domain, such as the well-known Oustaloup’s method. However, thesemethods have several serious defects in principle. A new perspective based on system identification is adoptedto deal with approximation of fractional order operators in this paper. Moreover, nonzero initial condition forapproximating fractional order systems is considered. And the proposed assignment of initial values for the Caputocase offers an effective solution for the simulation with nonzero initial condition. Finally, numerical examples aregiven to verify the efficiency of the proposed method.