Parameter and differentiation order estimation in fractional models

This paper deals with continuous-time system identification using fractional differentiation models. An adapted version of the simplified refined instrumental variable method is first proposed to estimate the parameters of the fractional model when all the differentiation orders are assumed known. Then, an optimization approach based on the use of the developed instrumental variable estimator is presented. Two variants of the algorithm are proposed. Either, all differentiation orders are set as integral multiples of a commensurate order which is estimated, or all differentiation orders are estimated. The former variant allows to reduce the number of parameters and can be used as a good initial hit for the latter variant. The performances of the proposed approaches are evaluated by Monte Carlo simulation analysis. Finally, the proposed identification algorithms are used to identify thermal diffusion in an experimental setup.