An Algebraic Approach for Identification of Linear Systems with Fractional Derivatives

TL;DR

This paper introduces an algebraic method using Mikusinski's operational calculus for exact identification of linear fractional order systems, estimating parameters and orders directly from input-output data without approximations.

Contribution

It presents a novel algebraic approach that enables simultaneous estimation of system parameters and fractional orders from data, avoiding the need for approximations.

Findings

Exact parameter and order estimation from convolutions of signals

Application demonstrated on a generalized Voigt model

Method does not require system approximations

Abstract

Identification of fractional order systems is considered from an algebraic point of view. It 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 Mikusinski's operational calculus, 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 is used to illustrate the approach.