Controller design techniques applied for a case of a linear fractional system

The purpose of this paper is to present tow methods to synthesize fractional order control for a given type of Fractional Order System FOS model. Two controllers are proposed for this class of FOS: Fractional Order Proportional Integrator (FO-PI) controller and Proportional Integrator PI. A practical and systematic tuning procedure has been developed for these controllers. In fact the paper presents an extension of some results developed in the simulation of integer order plants to FOS using the state representation; Computer simulation of the circuit model by Matlab was used to prove the relevance of our work and to show the effectiveness of the proposed controller design strategy and the robustness of the FO-PI controller compared to the classic PI under the same number of design parameters and the same specifications.