Coefficients and Delay Estimation of the General Form of Fractional Order Systems Using Non-Ideal Step Inputs

Abstract

This paper proposes a novel method for the simultaneous estimation of the coefficients and the delay term of a delayed fractional order system. Because of the practicality aspect of the non-ideal step inputs, such inputs are used in this paper for the first time to identify a fractional order system. To this end, the proposed identification procedure is separately described for two types of fractional order systems, i.e., including both non-delayed and delayed systems. For the non-delayed system, a fractional order integral approach is developed, and for the delayed system, a filtering approach is investigated to make the delay term to be explicitly appeared in the parameters vector. In simulation results, some illustrative examples, covering both non-delayed and delayed systems, are given to demonstrate the validity of the proposed method.