The fractional order lead compensator

In this paper the fractional order lead compensator (FOLC) is discussed, which, with respect to the traditional lead compensator, introduces a new parameter, alpha, the fractional order of the structure. Two methods are proposed for the design, one of them analytical and the other graphical. The analytical one forces the condition that the compensator gives its maximum phase, phi_m at the gain crossover frequency, omega _m The graphical one allows the use of a graphical criterion for the obtaining of the parameters of the FOLC. This criterion is based on the lead regions defined for the compensator in the complex plane, depending on the value of alpha. This second method allows a flexible and direct selection of the parameters of the fractional structure, taking into account considerations of robustness and overphase. An illustrative example of application is presented and simulation results show the effectiveness of the proposed methods of design