A unified approach for digital realization of fractional order operator in delta domain

Abstract

The fractional order operator (s?a,0 < a <1) plays the pivotal role for the realization of fractional orders systems (FOS). For the realization of the FOS, fractional order operator (FOO) needs to be realized either in discrete or continuous time domain. Discrete time rational approximation of FOO in the z -domain fails to provide meaningful information at fast sampling interval. Moreover, z domain rational transfer function becomes highly sensitive with respect to its coefficients variation resulting to the poor finite word length effects for digital realization. In the other hand delta operator parameterized system allows to develop unification of continuous and discrete time formulations leading to the development of a unified framework for digital realization at fast sampling interval. The discrete time approximation of the FOO in delta domain is found to be robust to its coefficient variation in comparison to the shift operator based discretization of FOO. In this paper, discrete d -operator parameterization is proposed for the digital realization using direct discretization of FOO. As a result, superior finite word length effect is observed for the realization of the FOO in discrete delta domain. Fractional order operator with different orders (a ) are considered for the realization purpose using the proposed method and the results obtained using MATLare presented for validation.