Generalization of Reset Controllers to Fractional Orders

Henrique Paz and Duarte Valério ()
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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

Mathematics, 2022, vol. 10, issue 24, 1-18

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.

Keywords: fractional calculus; nonlinear control; reset control; impulsive systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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