Approximation and order reduction of fractional order SISO system

It this paper approximation of fractional-order systems into 2nd order integer-order state-space models is presented. The operation is performed it two steps, in first step integer order approximation of fractional order system is done using oustaloup's approximation algorithm and then, the approximated system is realized in a state-space form using MATLAB and dimension of the resulting integer-order model is be reduced using efficient Balanced realization based Techniques namely Balanced Truncation (BT), Singular Purturbation Approximation (SPA), Hankel Norm Approximation (HNA), Hankel Norm Approximation with reduced DC-gain or Modified Hankel Norm Approximation (MHNA) fallowed by steady state reduction by dc-gain. Three SISO fractional order problems have also been discussed to show the performance of the suggested technique.