Abstract:
"It has been observed that many physical systems are well characterized by linear fractional
order models. Hence, their identification is attracting more and more interest of the scientific
community. However, they pose a more difficult identification problem than the integer order
systems because it requires not only the estimation of the model coefficients but also the
determination of the fractional orders with the tedious calculation of fractional order
derivatives. This thesis focuses on the identification in the time domain of the dynamic
fractional order systems described by linear fractional order differential equations. The
proposed identification method is based on the recursive least squares algorithm applied to an
ARX structure derived from the linear fractional order differential equation using a numerical
fractional differentiator of adjustable order. In the first place, this identification method has
been used to estimate the parameters with a prior knowledge of the fractional differentiation
orders of the fractional order linear differential equation representing the linear fractional order
system under investigation. Then, it has been used to estimate the parameters of a linear
fractional system of commensurate order without a prior knowledge of the commensurate
fractional order which is obtained among several values as the one when the square error
between the measured data and the estimated model is the smallest one. Finally, an extension of
the proposed identification method has been done to estimate the parameters and the order at
the same time of the fundamental linear fractional order system. Illustrative examples are also
presented to validate the usefulness of the proposed identification methods."
