Fractional-Order Memory-Reset Hybrid Integrator-Gain System - Part I
Frequency Domain Properties
C. Weise (Ilmenau University of Technology)
K. Wulff (Ilmenau University of Technology)
S. A. Hosseini (TU Delft - Mechatronic Systems Design)
M. B. Kaczmarek (TU Delft - Mechatronic Systems Design)
S. Hassan HosseinNia (TU Delft - Mechatronic Systems Design)
J. Reger (Ilmenau University of Technology)
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Abstract
We introduce a fractional-order generalization of the hybrid integrator-gain system (HIGS) with memory reset of the fractional-order operator when re-enter the integration mode. We compute the describing function for rational orders in terms of Mittag-Leffler functions. The concepts also allow for the evaluation of the higher-order harmonics. For the implementation we represent higher-order approximations by combining first-order reset elements with an integrator. The fractional-order extension without memory reset can also be approximated using the same framework. Finally we show how the approximation affects the describing function.
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