Fractional-Order Memory-Reset Hybrid Integrator-Gain System - Part I: Frequency Domain Properties

C. Weise; K. Wulff; S. A. Hosseini; M. B. Kaczmarek; S. Hassan HosseinNia; J. Reger

doi:10.1016/j.ifacol.2025.10.116

Fractional-Order Memory-Reset Hybrid Integrator-Gain System - Part I: Frequency Domain Properties

C. Weise, K. Wulff, S. A. Hosseini, M. B. Kaczmarek, S. Hassan HosseinNia , J. Reger^*

^*Corresponding author for this work

Mechatronic Systems Design

Research output: Contribution to journal › Conference article › Scientific › peer-review

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.

Original language	English
Pages (from-to)	277-282
Number of pages	6
Journal	IFAC-PapersOnline
Volume	59
Issue number	16
DOIs	https://doi.org/10.1016/j.ifacol.2025.10.116
Publication status	Published - 2025
Event	11th IFAC Symposium on Robust Control Design, ROCOND 2025 - Porto, Portugal Duration: 2 Jul 2025 → 4 Jul 2025

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10.1016/j.ifacol.2025.10.116

1-s2.0-S2405896325015034-mainFinal published version, 1.09 MBLicence: CC BY-NC-ND

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title = "Fractional-Order Memory-Reset Hybrid Integrator-Gain System - Part I: Frequency Domain Properties",

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.",

author = "C. Weise and K. Wulff and Hosseini, {S. A.} and Kaczmarek, {M. B.} and {Hassan HosseinNia}, S. and J. Reger",

year = "2025",

doi = "10.1016/j.ifacol.2025.10.116",

language = "English",

volume = "59",

pages = "277--282",

journal = "IFAC-PapersOnline",

issn = "2405-8971",

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note = "11th IFAC Symposium on Robust Control Design, ROCOND 2025 ; Conference date: 02-07-2025 Through 04-07-2025",

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T1 - Fractional-Order Memory-Reset Hybrid Integrator-Gain System - Part I

T2 - 11th IFAC Symposium on Robust Control Design, ROCOND 2025

AU - Weise, C.

AU - Wulff, K.

AU - Hosseini, S. A.

AU - Kaczmarek, M. B.

AU - Hassan HosseinNia , S.

AU - Reger, J.

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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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U2 - 10.1016/j.ifacol.2025.10.116

DO - 10.1016/j.ifacol.2025.10.116

M3 - Conference article

AN - SCOPUS:105021824765

SN - 2405-8971

VL - 59

SP - 277

EP - 282

JO - IFAC-PapersOnline

JF - IFAC-PapersOnline

IS - 16

Y2 - 2 July 2025 through 4 July 2025

ER -

Fractional-Order Memory-Reset Hybrid Integrator-Gain System - Part I: Frequency Domain Properties

Abstract

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