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Communication Dans Un Congrès Année : 2020

Neumann trace tracking of a constant reference input for 1-D boundary controlled heat-like equations with delay

Hugo Lhachemi
Emmanuel Trélat

Résumé

This paper discusses the Proportional Integral (PI) regulation control of the left Neumann trace of a one-dimensional reaction-diffusion equation with a delayed right Dirichlet boundary control. Specifically, a PI controller is designed based on a finite-dimensional truncated model that captures the unstable dynamics of the original infinite-dimensional system. In this setting, the control input delay is handled by resorting to the Artstein transformation. The stability of the resulting infinite-dimensional system, as well as the tracking of a constant reference signal in the presence of a constant distributed perturbation, is assessed based on the introduction of an adequate Lyapunov function. The theoretical results are illustrated with numerical simulations.
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Dates et versions

hal-02958099 , version 1 (05-10-2020)

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Hugo Lhachemi, Christophe Prieur, Emmanuel Trélat. Neumann trace tracking of a constant reference input for 1-D boundary controlled heat-like equations with delay. IFAC WC 2020 - 21st IFAC World Congress, Jul 2020, Berlin (virtual), Germany. pp.7716-7721, ⟨10.1016/j.ifacol.2020.12.1517⟩. ⟨hal-02958099⟩
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