Computation of Orders of a Commensurable Fractional Order Model

This paper deals with the calculation of the system order and the determination of the input order of a commensurable fractional order model. The system and input orders are equal to the number of system and input parameters, respectively. The benefit of the proposed method is that no search algorithms or over-parameterized equations have to be used. Instead, the calculation of the system order is reduced to fractional integration and the determination of the correct rank of the fractional Gramian of a model-based replacement system. The input order is determined by detecting when a matrix similar to the fractional Gramian of the model based replacement system loses full rank. This model-based replacement system can be derived by applying the modulating function method to the original fractional order model. A view on practical implementation is given and a numerical example completes this paper.