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  • © 2014

Safety Factor Profile Control in a Tokamak

  • Complete study of the safety factor profile control in a tokamak provides a single reference for the reader

  • Use of several well-established control techniques and comparison of these enabling the reader to select the most appropriate

  • Written by experts in the field

  • Includes supplementary material: sn.pub/extras

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

Part of the book sub series: SpringerBriefs in Control, Automation and Robotics (BRIEFSCONTROL)

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eBook USD 39.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-01958-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
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  • Tax calculation will be finalised during checkout
Softcover Book USD 54.99
Price excludes VAT (USA)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xi
  2. Introduction

    • Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur
    Pages 1-10
  3. Mathematical Model of the Safety Factor and Control Problem Formulation

    • Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur
    Pages 11-22
  4. A Polytopic LPV Approach for Finite-Dimensional Control

    • Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur
    Pages 23-32
  5. Infinite-Dimensional Control-Lyapunov Function

    • Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur
    Pages 33-59
  6. Controller Implementation

    • Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur
    Pages 61-84
  7. Conclusion

    • Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur
    Pages 85-86
  8. Back Matter

    Pages 87-96

About this book

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

  • GIPSA-lab, Dept. of Automatic Control Grenoble Campus, University of Grenoble, Saint Martin d'Hères, France

    Federico Bribiesca Argomedo

  • GIPSA-lab, Dept of Automatic Control Grenoble Campus, University of Grenoble, Saint Martin d'Hères, France

    Emmanuel Witrant, Christophe Prieur

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-01958-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 54.99
Price excludes VAT (USA)