Comparison between different continuous-time realizations based on the tau method of a nonlinear repetitive control scheme - LAAS - Laboratoire d'Analyse et d'Architecture des Systèmes
Conference Papers Year : 2023

Comparison between different continuous-time realizations based on the tau method of a nonlinear repetitive control scheme

Abstract

This paper presents a new framework to study a continuous-time finite-dimensional approximation of a repetitive control scheme for minimum-phase nonlinear systems. Based on the tau method, three state matrices are proposed to approximate the transport equation, namely tau-Fourier, tau-Legendre and tau-Chebyshev models. Then, the forwarding approach allows us to set up three finite dimensional controllers whose structure is derived from these tau models. In all three cases, we prove that a smooth steady state is reached and that the output converges to zero as the order increases. We also show that, for a fixed order, the tau-Fourier controller leads to the smallest output. Lastly, numerical comparisons are discussed and emphasize our theoretical expectations.
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Dates and versions

hal-04178964 , version 1 (08-08-2023)

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Cite

Mathieu Bajodek, Daniele Astolfi. Comparison between different continuous-time realizations based on the tau method of a nonlinear repetitive control scheme. 62nd IEEE Conference on Decision and Control (CDC 2023), Dec 2023, Singapour, Singapore. ⟨10.1109/CDC49753.2023.10384072⟩. ⟨hal-04178964⟩
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