Rational approximation of fractional order systems by vector fitting method

Abstract

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