Robust numeric implementation of the fractional-order element.

The fractional-order (FO) element has recently been included in the integer-order Robust Control Framework (RCF) through an infinite impulse response approximation. The primary focus of the previous results has been only on the robustness of its integer-order approximation. This paper proposes an end-to-end approach to design and numerically implement a fractional-order controller to ensure robustness during the entire flow, without commensurability assumptions. The robustness is ensured using the structured singular value (SSV) semi-metric at each step of the proposed approach. First, the design step ensures that both the fractional-order controller and its integer-order representation meet robustness criteria. Afterwards, the resulting high-order representation is simplified using a three-step order reduction procedure, without losing robustness, as detailed in the paper. Finally, the controller is numerically implemented using a sampling rate and a uniform quantization step computed for minimum transient and steady-state performance degradation. The end-to-end workflow is presented in a toolbox-oriented manner on a benchmark system. [ABSTRACT FROM AUTHOR]