Approximation of High-Order Lumped Systems by Using non Interger Order Trasfer Functions

Non-integer order systems have been studied by several authors to model particular physical systems (electrical, biological etc.). In particular it can be shown that a non integer order system is equivalent to an infinite order LTI system. This feature can be useful considered for model order reduction purposes . The main aim of this paper is to show the mathematical background of this new approximation theory, the criteria for selecting the order of a non-integer order model which behaves as the original integer order ones and the quality indexes that can be considered for assessing the goodness of the approximated model. The introduction of non integer order systems resulted to be an efficient way to compress frequency response information usually intrinsic in an high number of poles and zeros. The comparison with a traditional method of model order reduction proved that a reduced model with the same number of parameters is not able to get the same good performance in the frequency domain. To this aim, some examples and simulations are reported.