Spectrum-based stability analysis for fractional-order delayed resonator with order scheduling

We consider the stability analysis and controller design for a novel active vibration suppression technique, what we call the fractional-order delayed resonator (FODR), to suppress the oscillations from a single-degree-of-freedom mechanical structure. The parameterized control formulas for the associated gain and delay are firstly proposed. Then, an analytical procedure is presented to perform the complete stability analysis for the FODR alone and the coupled system. For practical implementation, the fractional feedback controller is realized by an integer-order approximate transfer function. Then, we introduce a novel control strategy named “order scheduling”, which treats the order as a tunable parameter, to enhance the control flexibility. The results show that this powerful technique can widen the feasible frequency band, improve the vibration control speed, and enhance the stability robustness of the system. Finally, three numerical cases show the viability of the proposed scheme.