Low-Order Representation of Robust Fractional-Order Controllers for Fractional-Order Interval Plants

The fractional-order (FO) element has been recently integrated into the generalized Robust Control Framework using the Oustaloup method. As such, the parametric uncertainties from fractional-order interval plants can now be treated using the structured singular value framework. Moreover, the resulting infinite impulse response approximation manages to satisfy the robust stability and the robust performance criteria according to the given uncertainty block. However, the recommended approximation order for each fractional-order element is equal to the number of decades of the frequency range where the approximation is valid, which can lead to a high-order controller representation. The aim of this paper is to present two methods for the order reduction without losing the robustness properties, followed by an optimization problem whose solution is a low-order approximation of a fractional-order controller which maintains the robust stability and robust performance as well. A finite commensurate order interval plant has been used as a numerical example to illustrate the effectiveness of the proposed method.