Modeling of fractional-order integrators and differentiators using tustin-based approximations and model order reduction techniques

Abstract

This paper presents a set of low-order approximators/dis-cretizers of fractional order derivative and integrator. The approximations are obtained using the Frequency Weighted (FW) reduction method applied to a high order Tustin–Muir based model of fractional-order derivative and integrator. Simulation examples confirm high accuracy of the models both in frequency and time domains. This illustrates the usefulness of the introduced methodology, which can be applied to selection of a set of relatively low order discrete-time approximators of fractional-order derivative and integrator.