Parameter Identification of Fractional-Order LTI Systems using Modulating Functions with Memory Reduction

Abstract

The parameter estimation problem of a linear time-invariant fractional-order system is investigated by means of the modulating function method. Based on the assumption of known model structure and derivative orders, the modulating function method can be generalized to the fractional-order case in three different ways. We show that two approaches are identical for linear systems. This facilitates the computation of the fractional-order derivatives of modulating functions. The second part includes the initialization of the fractional-order system. We show that the spline type modulating function is capable of reducing the effect of the memory on the parameter estimation. However, it is not possible to compensate the initialization completely. In contrast to these tuning principles also the robustness against measurement noise must be considered. For this purpose we decouple the memory and noise compensation. The adjusted spline-type modulating functions reduce the initialization effect and the recursive least square estimation provides the possibility to increase the numbers of equations such that the effect of the noise is reduced.