Optimal Rational Function Approximation for Fractional Integral and Differential Operators

Bode diagram based rational function approximation method for fractional integral and differential operators are analyzed in detail. For the approximation rational function orders is the lowest under satisfying approximation accuracy in the approximation frequency interval, two steps are proposed: 1) Choose reasonable initial and terminal frequency of rational function logarithmic amplitude-frequency characteristic. 2) Set approximation error of logarithmic amplitude-frequency characteristic by taking the error between asymptote and exact value into account. Computation examples demonstrate the validity of this method.