A Fractional-Order Control Approach to Ramp Tracking with Memory-Efficient Implementation

We investigate the fractional-order (FO) control of arbitrary order LTI systems. We show that, for ramp tracking or input disturbance rejection, it is advantageous to include an FO integrator to the open-loop if we have to increase the order of integration further than one. With the lower phase-loss of the FO integrator it is easier to guarantee a desired phase margin. Furthermore the flat phase response around the crossover-frequency (iso-damping property) can be achieved for a wider frequency range such that the closed-loop is more robust wrt. amplitude and phase margins. The drawback of the FO approach is the increased implementation effort and the algebraic decay, which slows down the transient response for larger times. The algebraic decay can be reduced by placing the fractional closed-loop poles to the corresponding integer-order poles. The remaining FO transfer zeros are compensated by an additional filter. We acheieve a more efficient implementation by reducing the memory needed by a direct discretization of the Grunwald-Letnikov definition. As the controller design is done in the frequency domain, we investigate the effect of the different memory truncations. All strategies are demonstrated by simulation.