Contribution a l’analyse des systemes d'ordre fractionnaire

Abstract

Fractional order systems have received a considerable interest in numerous domains of applied sciences and engineering. These systems are generally described by fractional order differential equations. In the frequency domain, they are represented by irrational transfer functions. Because of these irrational functions, fractional order systems have been marginally studied. Since they do not have exact analytical solutions, digital and approximation techniques are widely used for their resolution, analysis and implementation. In this thesis resolution, analog implementation and analysis techniques of fundamental fractional order systems based on rational function approximations of their irrational transfer functions are presented. Derivation and analysis of the frequency and temporal characteristics have also been done. To show the efficiency and exactitude of the proposed methods, illustrative examples have been presented. The obtained simulation results were satisfactory. They have been compared to some of the recent resolution methods in the literature.Comparisons of the obtained characteristics with those of a regular second system have been also done.