A New Multimodel Representation of Fractional-Order Systems in Both Time and Frequency Domains

In order to deal with some difficult problems in fractional-order systems, like high computational load of fractional-order operator, fractional-order transfer function is commonly approximated by an integer order model. However, the dimension of this model increases with its accuracy, which can make the design of a controller more difficult. In this paper, a new approach for modelling of fractional-order systems is investigated. Exploiting the multimodel technique, the suggested method replaces the unique fractional-order model by a set of simpler integer order models. The determination of the different models is based on an approximation of the fractional-order derivative operator sα. Then the global model is obtained through a fusion of the simple models weighted by their respective relevance degrees calculated by optimizing a constrained least squares problem. The resulting final model can represent adequately the fractional-order systems both in time and in frequency domains. Simulations and comparative studies carried out on academic examples indicate the interest, the clarity and the improvement in accuracy in both time and frequency domains of the proposed modelling method, compared to modelling by a single model based on the approximation of Oustaloup.