New perspectives of analog and digital simulations of fractional order systems
Résumé
In the recent decades, fractional order systems have been found to be useful in many areasof physics and engineering. Hence, their efficient and accurate analog and digital simulationsand numerical calculations have become very important especially in the fields of fractionalcontrol, fractional signal processing and fractional system identification. In this article, newanalog and digital simulations and numerical calculations perspectives of fractional systems areconsidered. The main feature of this work is the introduction of an adjustable fractional orderstructure of the fractional integrator to facilitate and improve the simulations of the fractionalorder systems as well as the numerical resolution of the linear fractional order differential equations.First, the basic ideas of the proposed adjustable fractional order structure of the fractionalintegrator are presented. Then, the analog and digital simulations techniques of the fractionalorder systems and the numerical resolution of the linear fractional order differential equationare exposed. Illustrative examples of each step of this work are presented to show the effectivenessand the efficiency of the proposed fractional order systems analog and digital simulationsand implementations techniques.