Non Integer Model from Modal Decomposition for Time Domain System Identification

Abstract

This article deals with modeling and identification of non integer systems in the time domain. An identification method is developed providing estimation of both model coefficients and differentiation orders. The non integer state-space representation is defined, and a modal decomposition of non integer systems is given. From the modal decomposition, also called developed modal form, a new identification model is defined. This model is parametrized by eigenmode parameters, three for each mode: the modal coefficient, the eigenvalue and the differentiation order which is common to all modes. These parameters are then estimated by an output error identification method using the Marquardt algorithm. Two examples illustrate this identification method: a simulated noised non integer system identification, and a real thermal system identification. In each case, the system is accurately identified by a three eigen mode non integer model. An integer ARX model with the same number of parameters, used for the identification of the real thermal system, gives unsatisfactory results.