Online Parameter Identification of a Fractional Order Model

This paper deals with the parameter identification of a fractional order model using modulating function method. The novelty is that the system has not to be at rest at the beginning of the parameter identification. That means, regarding fractional calculus, the initialization function must be considered. In the paper, it is stated that if a modulating function has a particular property the initialization function can be neglected. In this paper, it is also shown that the spline-type modulating function fulfills this property. Before the property can be stated, the used fundamentals of fractional calculus are given and the modulating function method is provided. Due to the property of this method, a fractional order differential equation is converted into an algebraic one. By shifting the modulating function, a system of linear equations is generated and a least squares algorithm in matrix form is applied to estimate the parameters. An error analysis and a numerical example complete this paper.