Safety Factor Profile Control in a Tokamak

  • Federico Bribiesca Argomedo
  • Emmanuel Witrant
  • Christophe Prieur

Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)

Also part of the SpringerBriefs in Control, Automation and Robotics book sub series (BRIEFSCONTROL)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur
    Pages 1-10
  3. Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur
    Pages 11-22
  4. Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur
    Pages 23-32
  5. Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur
    Pages 33-59
  6. Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur
    Pages 61-84
  7. Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur
    Pages 85-86
  8. Back Matter
    Pages 87-96

About this book

Introduction

Control of the Safety Factor Profile in a Tokamak uses Lyapunov techniques to address a challenging problem for which even the simplest physically relevant models are represented by nonlinear, time-dependent, partial differential equations (PDEs). This is because of the  spatiotemporal dynamics of transport phenomena (magnetic flux, heat, densities, etc.) in the anisotropic plasma medium. Robustness considerations are ubiquitous in the analysis and control design since direct measurements on the magnetic flux are impossible (its estimation relies on virtual sensors) and large uncertainties remain in the coupling between the plasma particles and the radio-frequency waves (distributed inputs).

The Brief begins with a presentation of the reference dynamical model and continues by developing a Lyapunov function for the discretized system (in a polytopic linear-parameter-varying formulation). The limitations of this finite-dimensional approach motivate new developments in the infinite-dimensional framework. The text then tackles the construction of an input-to-state-stabilityLyapunov function for the infinite-dimensional system that handles the medium anisotropy and provides a common basis for analytical robustness results. This function is used as a control-Lyapunov function and allows the amplitude and nonlinear shape constraints in the control action to be dealt with.

Finally, the Brief addresses important application- and implementation-specific concerns. In particular, the coupling of the PDE and the finite-dimensional subsystem representing the evolution of the boundary condition (magnetic coils) and the introduction of profile-reconstruction delays in the control loop (induced by solving a 2-D inverse problem for computing the magnetic flux) is analyzed. Simulation results are presented for various operation scenarios on Tore Supra (simulated with METIS) and on TCV (simulated with RAPTOR).

Control of the Safety Factor Profile in a Tokamak will be of interest to both academic and industrially-based researchers interested in nuclear energy and plasma-containment control systems, and graduate students in nuclear and control engineering.

     

Keywords

Boundary Control Control Problems Infinite-dimensional Systems Nuclear Fusion Tokamak

Authors and affiliations

  • Federico Bribiesca Argomedo
    • 1
  • Emmanuel Witrant
    • 2
  • Christophe Prieur
    • 3
  1. 1.GIPSA-lab, Dept. of Automatic Control Grenoble CampusUniversity of GrenobleSaint Martin d'HèresFrance
  2. 2.GIPSA-lab, Dept of Automatic Control Grenoble CampusUniversity of GrenobleSaint Martin d'HèresFrance
  3. 3.GIPSA-lab, Dept of Automatic Control Grenoble CampusUniversity of GrenobleSaint Martin d'HèresFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-01958-1
  • Copyright Information The Author(s) 2014
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-01957-4
  • Online ISBN 978-3-319-01958-1
  • Series Print ISSN 2191-8112
  • Series Online ISSN 2191-8120
  • About this book
Industry Sectors
Automotive
Chemical Manufacturing
Electronics
Energy, Utilities & Environment
Aerospace
Oil, Gas & Geosciences
Engineering