Fractional order systems in the electrical domain - Part 1: Background and introduction

In this first part, we present a background study of the fractional order system and the way to synthesize and implement those systems in the electrical domain by means of resistors and capacitors. The electrical test bench used to implement this fractional order system of the first kind is shown as well as two different arrangements. The first one is based on a fractional order system while the second one is made of an integer order systems. This part will be followed by a second one where the implementation results are shown as well as the systems robustness and the effects of some uncertainties related to the electrical domain. The results show that the fractional order system is robust and isn't affected by the components tolerance, which is not really the case for the integer order system.