La commande des systèmes d'ordre fractionnaire basé sur la fonction de transfert idéale de Bode

Abstract

The principal goal of this work is the fractional order control based on Bode’s ideal transfer function. The closed loop dynamic behaviour is exclusively linked to the open loop behaviour around the unity gain crossover frequency wu. Therefore, the motivation of the proposed controller in this context comes from the consideration of using the idea of ‘flat phase’ around the unity gain crossover frequency wu so that the closed loop system is robust to gain variations and the step response exhibit an iso-damping property, i. e. for different gain the step response present the same overshoot. To ensure similar frequency behaviour, in a frequency range of practical interest [hb,ωω] around a given unity gain crossover frequency wu, a controller have then been proposed based on fractional order systems which will guarantee that the open-loop transfer function of a unity feedback control will be the Bode’s ideal transfer function. Illustrative examples were made to show the effectiveness of the design and the results obtained have been also presented and discussed.