Rational Approximation and Analog Realization of Fractional Order Transfer Function with Multiple Fractional Powered Terms

The concept of model order reduction of high integer order systems using approximate moment matching has been generalized and extended to rational approximation of fractional order transfer function (FOTF). This approximation method converts an FOTF into characteristic numeric values and thus can be applied to rational approximation of FOTF, irrespective of its form of representation. This is very effective when FOTF has multiple fractional powered terms. Two circuit configurations for analog realization of FOTF through rational approximation are discussed and have been shown to be useful in hardware implementation. As a case study, a half order differentiator has been implemented in hardware and can be extended to any FOTF.