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A structured control model for the thermo-magneto-hydrodynamics of plasmas in tokamaks

MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL systems 2016年第3期22卷 181-206页

作者： Ngoc Minh Trang Vu Lefevre, Laurent Maschke, Bernhard CEA IRFM St Paul Les Durance France Univ Grenoble Alpes LCIS Valence France Univ Lyon 1 Lab Automat & Genie Proc F-69365 Lyon France

A thermo-magneto-hydrodynamics port-Hamiltonian model is derived for the plasmas in tokamaks. Electromagnetic field and material domain balance equations are expressed in covariant forms, together with the magneto-hydrodynamics interconnection structure connecting them together. The balance equations for the entropy, mass and momentum, as well as closure equations in the material domain, are derived from the Boltzmann equation (kinetic theory). The Gibbs-Duhem equation is used to compute the irreversible entropy source term and to define the interdomain R-field of the model. All derived interdomain couplings in the material domain are represented using Dirac and Stokes-Dirac structures and the resistivity R-field structure. The complete model is summarized in a Bond Graph.

关键词： plasma dynamics Port-Hamiltonian systems thermo-magneto-hydrodynamics kinetic theory distributed parameters systems

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Multi-Agent Model Predictive Control for Transport Phenomena Processes

Multi-Agent Model Predictive Control for Transport Phenomena...

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作者： Sergio Jorge Pereira da Costa NOVA University of Lisbon

学位级别：博士

Throughout the last decades, control systems theory has thrived, promoting new areas of development, especially for chemical and biological process engineering. Production processes are becoming more and more complex and researchers, academics and industry professionals dedicate more time in order to keep up-to-date with the increasing complex- ity and nonlinearity. Developing control architectures and incorporating novel control techniques as a way to overcome optimization problems is the main focus for all people involved. Nonlinear Model Predictive Control (NMPC) has been one of the main responses from academia for the exponential growth of process complexity and fast growing scale. Prediction algorithms are the response to manage closed-loop stability and optimize results. Adaptation mechanisms are nowadays seen as a natural extension of prediction methodologies in order to tackle uncertainty in distributed parameter systems (DPS), governed by partial differential equations (PDE). parameters observers and Lyapunov adaptation laws are also tools for the systems in study. Stability and stabilization conditions, being implicitly or explicitly incorporated in the NMPC formulation, by means of pointwise min-norm techniques, are also being used and combined as a way to improve control performance, robustness and reduce computational effort or maintain it low, without degrading control action. With the above assumptions, centralized (or single agent) or decentralized and dis- tributed Model Predictive Control (MPC) architectures (also called multi-agent) have been applied to a series of nonlinear distributed parameters systems with transport phenomena, such as bioreactors, water delivery canals and heat exchangers to show the importance and success of these control techniques.

关键词： distributed parameters systems nonlinear model predictive control multi-agent control stability adaptation pointwise min-norm control

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distributed and backstepping boundary controls to achieve IDA-PBC design 8

Distributed and backstepping boundary controls to achieve ID...

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8th Vienna International Conference on Mathematical Modelling

作者： Vu, N. M. Tsang Lefevre, L. Nouailletas, R. Univ Grenoble Alpes LCIS F-26902 Grenoble France CEA Cadarache CEA DSM IRFM STEP Cadarache France

An IDA-PBC-like control synthesis for infinite dimensional port Hamiltonian systems is investigated. As for the finite dimensional case, a feedback control transforms the original model into a closed loop target Hamiltonian model. Both distributed control and boundary control are used. The finite rank distributed control is determined to solve an average IDA-PBC matching equation. A backstepping boundary control is used to stabilize the matching error. The control model chosen to illustrate the approach is the so-called resistive diffusion equation for the radial diffusion of the poloidal magnetic flux. (C) 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： distributed parameters systems port-Hamiltonian systems IDA-PBC control back-stepping control plasma control

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The piston problem in a port-Hamiltonian formalism 5

The piston problem in a port-Hamiltonian formalism

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5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control

作者： Lequeurre, Julien Tucsnak, Marius Univ Lorraine IECL Site MetzBatiment A F-57045 Metz 1 France Univ Lorraine IECL F-54506 Vandoeuvre Les Nancy France

The aim of this paper is to write two simple fluid-structure interaction coupled systems as wellposed port Hamiltonian systems. Moreover, we investigate the stabilization of the system Burgers/piston Otanks to a very simple feedback law. (C) 2015, ILAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： distributed parameters systems port-Hamiltonian systems

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The piston problem in a port-Hamiltonian formalism ∗

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IFAC-PapersOnLine 2015年第13期48卷 212-216页

作者： Julien Lequeurre Marius Tucsnak Université de Lorraine IECL Site de Metz Bâtiment A Ile du Saulcy F-57045 Metz Cedex 1 France Université de Lorraine IECL Site de Nancy B.P. 70239 F-54506 Vandoeuvre-lès-Nancy Cedex France

The aim of this paper is to write two simple fluid-structure interaction coupled systems as wellposed port-Hamiltonian systems. Moreover, we investigate the stabilization of the system Burgers/piston thanks to a very ... 详细信息

关键词： distributed parameters systems port-Hamiltonian systems

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IDA-PBC control for the coupled plasma poloidal magnetic flux and heat radial diffusion equations in tokamaks 19

IDA-PBC control for the coupled plasma poloidal magnetic flu...

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19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014

作者： Trang Vu, N.M. Nouailletas, R. Lefèvre, L. Brémond, S. Felici, F. Univ. Grenoble Alpes LCIS France Laboratoire CEA/DSM/IRFM/STEP CEA Cadarache France TU Eindhoven Mechanical Engineering Control Systems Technology Group P.O. Box 513 Eindhoven Netherlands

ISBN: (纸本)9783902823625

The IDA-PBC control of plasma dynamics in a tokamak is investigated. It is based on a model made of the two coupled PDEs of resistive diffusion for the magnetic poloidal flux and of radial thermal diffusion. The used Thermal-Magneto-Hydro-Dynamics (TMHD) couplings are the Lorentz forces (with non-uniform resistivity) and the bootstrap current. The control model is obtained with the coupling of the two finite dimensional approximations obtained from the two diffusion models, using two geometric reduction schemes. A feedforward control is used to ensure the compatibility with the actuator physical ability. Then, an IDA-PBC (Interconnection and Damping Assignment - Passivity Based Control) controller is proposed for the coupled model to improve the system stabilization and convergence speed. The obtained numerical results are validated against the simulation data obtained from the RAPTOR (RApid Plasma Transport simulatOR) code for the TCV (Tokamak of Configuration Variable at CRPP, EPFL, Lausanne, Switzerland) tokamak real-time control system. © IFAC.

关键词： distributed parameters systems IDA-PBC control Plasma control Port-controlled Hamiltonian systems Tokamak

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IDA-PBC control for the coupled plasma poloidal magnetic flux and heat radial diffusion equations in tokamaks

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IFAC Proceedings Volumes 2014年第3期47卷 11398-11403页

作者： N.M. Trang VU R. NOUAILLETAS L. LEFÈVRE S. BRÉMOND F. FELICI Univ. Grenoble Alpes LCIS F-26902 France Laboratoire CEA/DSM/IRFM/STEP CEA Cadarache France TU Eindhoven Mechanical Engineering Control Systems Technology Group P.O. Box 513 5600 Eindhoven The Netherlands

关键词： distributed parameters systems plasma control Tokamak Port-Controlled Hamiltonian systems IDA-PBC control

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Stabilization of a System of n+1 Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2013年第12期58卷 3097-3111页

作者： Di Meglio, Florent Vazquez, Rafael Krstic, Miroslav Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA Univ Seville Dept Aerosp Engn Seville 41092 Spain

We solve the problem of stabilization of a class of linear first-order hyperbolic systems featuring n rightward convecting transport PDEs and one leftward convecting transport PDE. We design a controller, which requires a single control input applied on the leftward convecting PDE's right boundary, and an observer, which employs a single sensor on the same PDE's left boundary. We prove exponential stability of the origin of the resulting plant-observer-controller system in the spatial L-2-sense.

关键词： Control design distributed parameters systems observers

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Geometric discretization for a plasma control model

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IFAC Proceedings Volumes 2013年第2期46卷 755-760页

作者： N.M.T. VU L. LEFEVRE R. NOUAILLETAS S. BREMOND Laboratoire de Conception et d'Intégration des Systèmes Institut Polytechnique de Grenoble Valence France Laboratoire CEA/DSM/IRFM/STEP CEA Cadarache France

we define a family of geometric discretization methods for the reduction of a 1D distributed parameters systems of conservation laws and apply these methods to the reduction of plasma control model written in Port-Controlled Hamiltonian (PCH) form. In these discrete schemes, variables are projected into appropriate bases in order to perform exact spatial differentiation. We show that some spectral and energetical properties are therefore preserved. A geometric (symplectic) collocation scheme using Lagrange polynomials is investigated. Numerical results show oscillations in the transient response in case of non homogeneous boundary conditions or sharp distributed control. A second symplectic spectral scheme using Bessel conjugated bases is then derived which allows a more accurate approximation of eigenfunctions and reduces the unwanted numerical oscillations. Finally, the proposed numerical integration of the control model is validated against experimental data from the tokamak Tore Supra.

关键词： geometric discretization symplectic methods pseudo-spectral methods distributed parameters systems plasma control Port-Controlled Hamiltonian systems

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Material balance and closure equations for plasmas in Tokamaks

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IFAC Proceedings Volumes 2013年第14期46卷 60-65页

作者： Ngoc Minh Trang Vu Laurent Lefèvre Laboratoire de Conception et d'Intégration des Systèmes Institut Polytechnique de Grenoble BP54 26902 VALENCE Cedex 09 France

A port-Hamiltonian model is derived for the thermo-magneto-hydrodynamics (TMHD) of plasma in tokamaks. This paper focuses on the balance and closure equations in the material domain. First a kinetic theory point of view is adopted and transport equations are derived from the Boltzmann equation. Then material derivatives are introduced to derive macroscopic balance equations of the TMHD fluid model from these kinetic transport equations. Finally, the Gibbs-Duhem equation is used to compute the irreversible entropy source term and to define the interdomain ℛ - field of the model.

关键词： plasma dynamics port Hamiltonian systems thermo-magneto-hydrodynamics distributed parameters systems kinetic theory thermodynamics

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