Filter approximation and model reduction comparison for fractional order systems

This paper presents a comparison study for filter approximations and model reduction techniques for control systems of fractional orders. Oustaloup´s recursive filter and a refined Oustaloup´s filter are represented to obtain higher integer order approximations of fractional order systems. Then these higher integer order systems are exposed to model reduction with some existing techniques preserving some of the dominant eigenvalues. Original system and reduced order systems are compared on a Bode diagram and average errors of the reduced systems are computed. Then, a Matlab toolbox is developed which one can easily enter the fractional order system and apply filter approximations and model reductions. Average errors of each technique for desired fractional order system can be computed using the toolbox. Thus, this study is thought to be useful for the related area of research.