Tuning of Fractional Controllers Minimising H2 and H∞ Norms

H2 and H∞ controllers minimise the H2 or the H∞ norm of a suitable loop transferfunction involving the plant to control and some weighing transfer functions chosen to fulfilperformance specifications. In this paper this type of controllers is developed for the casewhen the plant and / or the weighing transfer functions are of fractional (commensurate)order. Since no analytical results similar to those existing for the integer case have beenfound, a genetic algorithm is used to minimise the desired norm. An application totemperature control is used to illustrate the method.