Comparison of the electronic realization of the fractional-order system and its model

Real objects in general are fractional-order (FO) systems, although in some types of systems the order is very close to an integer order. Also application of FO models is more adequate for the description of dynamical systems than integer-order models. This paper is devoted to the analogue electronic realization of the FO systems, e.g. controlled objects and/or controllers whose mathematical models are FO differential equations. The electronic realization is based on FO differentiator and FO integrator where operational amplifiers are connected with appropriate impedance or in our realization with so called Fractional Order Element (FOE) or Constant Phase Element (CPE). Presented network model in spite of its simplicity approximates quite well the properties of the ideal FO system compared with e.g. domino ladder networks. Also presented, along with the mathematical description, are simulation and measurement results.