A unified approach for reduced order modeling of fractional order system in delta domain

A unified approach for reduced order modelling of fractional order system in the delta domain is presented in this paper. The delta operator modelling of Fractional Order System converges to its continuous-time counterparts as the sampling time approaches close to zero. A fractional order differentiator is approximated to a higher order rational transfer function using the method of Oustaloup approximation. This approximated higher order continuous-time transfer function is then discretized to obtain the corresponding transfer function in the complex delta domain. An approximate frequency fitting (AFF) method is used to obtain a reduced order model of the fractional order system. Using AFF, the reduced model is obtained by matching a number of frequency points of the higher order system. The reduction mechanism is a variant of Padé type approximation in which least square technique is utilized. Model order reduction is normally resorted to reduce the dimension of the higher order system to a manageable size without compromising to the time and frequency domain properties of the original higher order system. The computational algorithm of the AFF technique is implemented using Matlab simulation. An example is taken to exhibit the efficiency of the proposed method in developing a unified framework in reduced order modeling of fractional order system.