Approximation of high order integer systems by fractional order reduced-parameters models

The approximation of a fractional system, characterized by a long memory, by an integer order transfer function, requires the use of a very high number of parameters. This characteristic is used in this paper to deal with the approximation of large order systems using a high number of parameters fractional models, but using only few parameters. Contrary to the traditional system order reduction methods which, because of reducing the system order, also reduce the number of its parameters, the use of fractional models leads to models using only very few parameters, but of infinite dimension, because of their “long memory” characteristics. This new use of fractional derivative is therefore named reduced-parameters modeling or model compression and is attractive for the analysis and design of large dynamical systems.