Valério, D, Ortigueira MD, da Costa JSá.
2008.
Identifying a Transfer Function From a Frequency Response, April. Journal of Computational and Nonlinear Dynamics. 3:021207., Number 2
AbstractIn this paper, the classic Levy identification method is reviewed and reformulated using a complex representation. This new formulation addresses the well known bias of the classic method at low frequencies. The formulation is generic, coping with both integer order and fractional order transfer functions. A new algorithm based on a stacked matrix and its pseudoinverse is proposed to accommodate the data over a wide range of frequencies. Several simulation results are presented, together with a real system identification. This system is the Archimedes Wave Swing, a prototype of a device to convert the energy of sea waves into electricity.
Ortigueira, MD.
2008.
An introduction to the fractional continuous-time linear systems: the 21st century systems. IEEE Circuits and Systems Magazine. 8:19–26., Number 3: IEEE
AbstractA brief introduction to the fractional continuous-time linear systems is presented. It will be done without needing a deep study of the fractional derivatives. We will show that the computation of the impulse and step responses is very similar to the classic. The main difference lies in the substitution of the exponential by the Mittag-Leffler function. We will present also the main formulae defining the fractional derivatives.