An Algebraic Approach to the Identification of Linear Systems with Fractional Derivatives

Abstract

Identification of fractional-order systems is considered from an algebraic point of view. The approach presented allows for a simultaneous estimation of model parameters and fractional (or integer) orders from input and output data. It is exact in that no approximations are required. Using the Laplace transform, algebraic manipulations are performed on the operational representation of the system. The unknown parameters and fractional orders are calculated solely from convolutions of known signals. A generalized Voigt model describing a viscoelastic material and a diffusion-wave equation representing a fractional partial differential equation are used to illustrate the approach.