On-line identification of temperature-dependent thermal conductivity

Vergnaud, Alban; Beaugrand, Guerric; Gaye, Oumar; Perez, Laetitia; Lucidarme, Philippe; Autrique, Laurent

doi:10.1109/ecc.2014.6862267

Cited by 8 publications

(5 citation statements)

References 11 publications

(7 reference statements)

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“…This method is based on the Conjugate Gradient Method (CGM) which acts as an iterative regularization method (convergence of this well-known minimization method is discussed for linear systems in [15], [16] and for specific non-linear system in [17], [18]). Examples of numerical implementation for identification purposes in a thermal context are given in [19], [20] or [21]. However, in the works cited above, the authors never broached the question of control.…”

Section: Ihcp Resolutionmentioning

confidence: 99%

Quasi-Online Disturbance Rejection for Nonlinear Parabolic PDE using a Receding Time Horizon Control

Azar¹,

Perez²,

Prieur

et al. 2021

2021 European Control Conference (ECC)

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Null controllability of nonlinear partial differential equation is a very complex challenge. The context underlying this study is to improve the behavior of the plasma in a tokamak reactor in order to lengthen the duration of the nuclear fusion process. Considering the class of a specific parabolic PDE, the well known heat equation is nonlinear if thermal properties are temperature dependent. In such a context a numerical method based on the resolution of inverse heat conduction problem is proposed. It aims to provide identified control laws quasi-online in order to guarantee that the thermal state is kept close to its equilibrium state at zero. The iterative conjugate gradient method is implemented in order to control the temperature in the one-dimensional spatial domain despite several disturbances (time-dependent or thermo-dependent). The proposed strategy is based on successive numerical resolutions of ill-posed inverse problem on receding time horizons which are adapted considering the previous evolution of the system. Numerical results in the investigated configuration highlight that identified control laws are able to reject disturbances and to ensure null controllability.

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Section: Ihcp Resolutionmentioning

confidence: 99%

Quasi-Online Disturbance Rejection for Nonlinear Parabolic PDE using a Receding Time Horizon Control

Azar¹,

Perez²,

Prieur

et al. 2021

2021 European Control Conference (ECC)

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“…We will extend the CCBM to the free model situation in the future. Moreover, it is not difficult to derive a similar regularization method for solving corresponding inverse problems in the transport-dispersive model [15] in chromatography and other similar inverse problems [20,28,34]. …”

Section: Discussionmentioning

confidence: 99%

A modified coupled complex boundary method for an inverse chromatography problem

Cheng

Lin

Zhang

et al. 2017

Journal of Inverse and Ill-Posed Problems

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Adsorption isotherms are the most important parameters in rigorous models of chromatographic processes. In this paper, in order to recover adsorption isotherms, we consider a coupled complex boundary method (CCBM), which was previously proposed for solving an inverse source problem [2]. With CCBM, the original boundary fitting problem is transferred to a domain fitting problem. Thus, this method has advantages regarding robustness and computation in reconstruction. In contrast to the traditional CCBM, for the sake of the reduction of computational complexity and computational cost, the recovered adsorption isotherm only corresponds to the real part of the solution of a forward complex initial boundary value problem. Furthermore, we take into account the position of the profiles and apply the momentum criterion to improve the optimization progress. Using Tikhonov regularization, the well-posedness, convergence properties and regularization parameter selection methods are studied. Based on an adjoint technique, we derive the exact Jacobian of the objective function and give an algorithm to reconstruct the adsorption isotherm. Finally, numerical simulations are given to show the feasibility and efficiency of the proposed regularization method.

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“…CGM is a descent method that solves the problem of parametric identification by stopping the minimization when a relevant threshold J stop is obtained. Such method has been developed for thermal applications in [14][15][16][17][18]. At each iteration k of the algorithm, three well-posed problems have to be solved:…”

Section: Inverse Problemmentioning

confidence: 99%

“…In the framework of thermal properties identification, the iterative regularization method based on the CGM has been developed in [14]. In recent works, authors have proposed new developments for mobile heating source tracking in 2D and 3D geometries [15][16][17] and for quasi online identification of a temperature dependent characteristics in [18].…”

Section: Introductionmentioning

confidence: 99%

Stabilization Using In-domain Actuator: A Numerical Method for a Non Linear Parabolic Partial Differential Equation

Azar¹,

Perez²,

Prieur³

et al. 2020

Lecture Notes in Electrical Engineering

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This paper deals with the problem of null controllability for an unstable nonlinear parabolic partial differential equation (PDE) system considering in-domain actuator. The main objective of this communication is to provide an efficient control law in order to stabilize the system state close to zero in a desired time whatever the initial state is. A numerical approach is developed and in order to highlight the relevance of the proposed control strategy, a realistic physical problem is investigated. Thermal evolution of a thin rod with homogeneous Dirichlet boundaries conditions is considered. Thermal state is described by the heat equation and assuming that thermal conductivity is temperature dependent, a nonlinear mathematical model has to be taken into account. Considering that all the model inputs are known, a direct problem is numerically solved (regarding a finite element method) in order to estimate the temperature at each point of the 1D geometry and at each instant. Then an inverse problem is formulated in such a way as to determine the in-domain control which ensures a final temperature close to zero. An iterative regularization method based on the conjugate gradient method (CGM) is developed for the minimization of a quadratic cost function (output error). Several numerical experimentations are provided in order to discuss the numerical approach attractiveness.

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On-line identification of temperature-dependent thermal conductivity

Cited by 8 publications

References 11 publications

Quasi-Online Disturbance Rejection for Nonlinear Parabolic PDE using a Receding Time Horizon Control

Quasi-Online Disturbance Rejection for Nonlinear Parabolic PDE using a Receding Time Horizon Control

A modified coupled complex boundary method for an inverse chromatography problem

Stabilization Using In-domain Actuator: A Numerical Method for a Non Linear Parabolic Partial Differential Equation

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