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Generalization of Reset Controllers to Fractional Orders

Author

Listed:
  • Henrique Paz

    (IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal)

  • Duarte Valério

    (IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal)

Abstract

Reset control is a simple non-linear control technique that can help overcome the structural limitations of linear control. Fractional control uses the concept of fractional derivatives to expand the range of possibilities when modeling a controller, making it more robust. Fractional reset control merges the advantages of both areas and is the object of this paper. Fractional-order versions of different reset controllers were implemented, namely a fractional Clegg integrator, a fractional generalized first-order reset element, a fractional generalized second-order reset element, and fractional “constant in gain lead in phase” controllers with first- and second-order reset elements. These were computed directly from a numerical implementation of the Grünwald–Letnikov definition of fractional derivatives, and their performances were analyzed.

Suggested Citation

  • Henrique Paz & Duarte Valério, 2022. "Generalization of Reset Controllers to Fractional Orders," Mathematics, MDPI, vol. 10(24), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4630-:d:996121
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    References listed on IDEAS

    as
    1. Duarte Valério & Manuel D. Ortigueira & António M. Lopes, 2022. "How Many Fractional Derivatives Are There?," Mathematics, MDPI, vol. 10(5), pages 1-18, February.
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