PI Regulation of a Reaction-Diffusion Equation with Delayed Boundary Control

التفاصيل البيبلوغرافية
العنوان: PI Regulation of a Reaction-Diffusion Equation with Delayed Boundary Control
المؤلفون: Christophe Prieur, Hugo Lhachemi, Emmanuel Trélat
المساهمون: University College Dublin [Dublin] (UCD), GIPSA - Infinite Dimensional Dynamics (GIPSA-INFINITY), GIPSA Pôle Automatique et Diagnostic (GIPSA-PAD), Grenoble Images Parole Signal Automatique (GIPSA-lab), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Grenoble Alpes (UGA), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), This publication has emanated from research supported in part by a research grant from Science Foundation Ireland (SFI) under grant number 16/RC/3872 and is co-funded under the European Regional Development Fund and byI-Form industry partners., Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
المصدر: IEEE Transactions on Automatic Control
IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2021, 66 (4), pp.1573-1587. ⟨10.1109/TAC.2020.2996598⟩
IEEE Transactions on Automatic Control, 2021, 66 (4), pp.1573-1587. ⟨10.1109/TAC.2020.2996598⟩
بيانات النشر: HAL CCSD, 2021.
سنة النشر: 2021
مصطلحات موضوعية: Lyapunov function, 0209 industrial biotechnology, 1-D reaction-diffusion equation, Partial Differential Equations (PDEs), 1-D Reaction-diffusion equation, PID controller, Boundary (topology), 02 engineering and technology, Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, Setpoint, Tracking error, symbols.namesake, 020901 industrial engineering & automation, Control theory, Neumann trace, Reaction–diffusion system, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], Electrical and Electronic Engineering, Mathematics - Optimization and Control, Delay boundary control, Mathematics, Computer Science Applications, PI regulation control, Control and Systems Engineering, Optimization and Control (math.OC), Time derivative, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Numerical stability
الوصف: The general context of this work is the feedback control of an infinite-dimensional system so that the closed-loop system satisfies a fading-memory property and achieves the setpoint tracking of a given reference signal. More specifically, this paper is concerned with 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. In this setting, the studied reaction-diffusion equation might be either open-loop stable or unstable. The proposed control strategy goes as follows. First, a finite-dimensional truncated model that captures the unstable dynamics of the original infinite-dimensional system is obtained via spectral decomposition. The truncated model is then augmented by an integral component on the tracking error of the left Neumann trace. After resorting to the Artstein transformation to handle the control input delay, the PI controller is designed by pole shifting. Stability of the resulting closed-loop infinite-dimensional system, consisting of the original reaction-diffusion equation with the PI controller, is then established thanks to an adequate Lyapunov function. In the case of a time-varying reference input and a time-varying distributed disturbance, our stability result takes the form of an exponential Input-to-State Stability (ISS) estimate with fading memory. Finally, another exponential ISS estimate with fading memory is established for the tracking performance of the reference signal by the system output. In particular, these results assess the setpoint regulation of the left Neumann trace in the presence of distributed perturbations that converge to a steady-state value and with a time-derivative that converges to zero. Numerical simulations are carried out to illustrate the efficiency of our control strategy.
Comment: Preprint
اللغة: English
تدمد: 0018-9286
DOI: 10.1109/TAC.2020.2996598⟩
URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dcb0b959107aea966f27b06e29c4acda
https://hal.archives-ouvertes.fr/hal-02294321/document
Rights: OPEN
رقم الانضمام: edsair.doi.dedup.....dcb0b959107aea966f27b06e29c4acda
قاعدة البيانات: OpenAIRE
الوصف
تدمد:00189286
DOI:10.1109/TAC.2020.2996598⟩