A Modified Approximation Method of Fractional Order System

Abstract

Many real world systems, including smart mechatronics systems, can be better characterized by dynamic systems of non-integer order. Using non-integer order or fractional order calculus, fractional order systems can be modeled more authentically. Due to the nature of the infinite dimensional model, proper approximations to fractional order differentiator (s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sup> , alpha isin Ropf) are fundamentally important. This paper contributed a new approximation scheme which is an extension of the well-established Oustaloup's approximation method. The benefits from using the proposed scheme are illustrated by numerical examples in both time and frequency domains