Fractional Digital Control of a Heat Solid: Experimental Results

The purpose of this paper is to make a contribution for solving one of the major drawbacks for using fractional controllers: the controller implementation. In digital form, this is usually done by using a truncated version of the Grundwald-Letnikov formula for fractional derivative. In this work, experimental results are given comparing this method for digital implementation of a fractional PD controller, with the alternative method resulting from the use of the trapezoidal rule and the continued fraction expansion for obtaining the discrete transfer function of the controller. From the results an interesting conclusion can be stated: the second method, which gives a controller in the form of a digital IIR filter, allows the use of lower order approximations of the fractional differential operator, that is, it reduces the memory and speed requirements of the digital system in which the controller is implemented.