Use of squared magnitude function in approximation and hardware implementation of SISO fractional order system

Abstract

This paper uses squared magnitude function and genetic algorithm (GA) to propose a generalized method for rational approximation of stable minimum phase fractional order transfer functions (FOTF). The unknown coefficients of an approximant are obtained by equating the squared magnitude of the approximant with that of the FOTF at frequency points (over a specified bandwidth) that are chosen optimally by using GA. Two FOTFs have been approximated by using the proposed method and one of the approximants has been realized in hardware using available discrete circuit components. The results of approximation and circuit realization strongly demonstrate the application of this work in approximation and/or realization of fractional order systems specifically, fractional order controller and filter of higher order.