Impulse Response Invariant Discretization of Complex Fractional Order Integrator

TL;DR

This paper introduces an impulse response invariant discretization method for complex fractional order integrators, enabling accurate digital implementation of these systems with verified effectiveness through frequency and impulse response comparisons.

Contribution

It proposes a novel IRID approach specifically for CFOIs, including derivation, MATLAB implementation, and validation against continuous models.

Findings

The IRID method accurately approximates CFOIs in both time and frequency domains.

Comparisons show the discretized CFOI closely matches the original continuous response.

The method provides a reliable way to implement CFOIs digitally.

Abstract

When the order of an integrator is a complex number, the integrator is called a complex fractional order integrator (CFOI). The impulse response invariant discretization (IRID) method is proposed to approximately discretize the CFOI. The definition of the CFOI is introduced firstly, and the real and imaginary parts of the CFOI in frequency-domain responses are derived. The code of IRID for the CFOI based on the MATLAB language is explained. The comparisons of the impulse responses and frequency-domain responses between the CFOI and the approximate discrete/continuous transfer functions are presented to illustrate the effectiveness and correctness of the proposed discretization method. This paper offers a reliable method to implement the CFOI.