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Multidimensional system of cascaded control of plasma form and current in tokamak with channel decoupling and H ∞-controller

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Abstract

Consideration was given to the development and numerical modeling of the multidimensional cascaded system with H ∞-controller in the external cascade for control of the plasma form and current in tokamak. For controller design, the problem of mixed sensitivity was solved by selecting the weight functions in the composite matrix of the performance criterion. The internal loop was intended for decoupling the current control channels in the magnetic coils of the tokamak poloidal fields and following the given scenario currents. Linearized models obtained from the nonlinear plasma-physical DINA code by linearizing the ITER scenario at different points were used to design the controllers. The robust stability margin was estimated in the frequency domain using singular numbers of the matrix transfer functions of the closed-loop control system. The designed cascaded system was modeled in the DINA code.

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References

  1. Ariola, M. and Pironti, A., Magnetic Control of Tokamak Plasmas, London: Springer, 2008.

    MATH  Google Scholar 

  2. Lukash, V.E., Dokuka, V.N., and Khairutdinov, R.R., Software Complex DINA in the MATLAB System for Problems of Plasma Control in Tokamak, Vopr. Atom. Nauk. Tekh., Termoyadernyi Sintez, 2004, no. 1, pp. 40–49.

  3. Mitrishkin, Y.V., Korostelev, A.Y., Dokuka, V.N., et al., Design and Modeling of ITER Plasma Magnetic Control System in Plasma Current Ramp-Up Phase on DINA Code, Proc. 48 IEEE Conf. Decision Control, Shanghai, 2009, pp. 1354–1359.

  4. Kuznetsov, E.A. and Mitrishkin, Yu.V., Self-oscillating System for Stabilization of Unstable Vertical Position of Plasma of the GLOBUS-M Spherical Tokamak, Preprint of Trapeznikov Inst. of Control Sci., Russ. Acad. Sci., Moscow, 2005.

  5. Moriyama, S., Nakamura, K., Nakamura, Y., et al., Analysis of Optimal Feedback Control of Vertical Plasma Position in a Tokamak System, Jpn. J. Appl. Phys., 1985, vol. 24, no. 7, pp. 849–855.

    Article  Google Scholar 

  6. Mitrishkin, Y. and Kimura, H., Plasma Vertical Speed Robust Control in Fusion Energy Advanced Tokamak, Proc. 40 IEEE Conf. Decision Control, Orlando, 2001, pp. 1292–1297.

  7. Kadurin, A.V. and Mitrishkin, Yu.V., Robust H ∞-System for Stabilization of the Speed of Vertical Position of Plasma in Tokamaks Relative to the Zero Value, Proc. XLVIII Conf. “Current Problems of Fundamental and Applied Sciences,” Moscow: Mosk. Fiz. Tekhn. Inst., 2005, part 3, pp. 207–209.

    Google Scholar 

  8. Mitrishkin, Yu.V., Sushin, I.S., and Korostelev, A.Ya., Stabilization of Unstable Vertical Position of Plasma in Tokomak with Input Saturation, Proc. XLIX Conf. “Current Problems of Fundamental and Applied Sciences,” Moscow: Mosk. Fiz. Tekhn. Inst., 2006, part 3, pp. 247–248.

    Google Scholar 

  9. Schuster, E., Walker, M.L., Humphreys, D.A., et al., Plasma Vertical Stabilization in the Presence of Coil Voltage Saturation in the DIII-D Tokamak, in Am. Control Conf., Denver, 2003, vol. 3, pp. 2323–2328.

    Google Scholar 

  10. Albanese, R. and Villone, F., The Linearized CREATE-L Plasma Response Model for the Control of Current, Position and Shape in Tokamaks, Nucl. Fusion, 1998, vol. 38, no. 5, pp. 723–738.

    Article  Google Scholar 

  11. Albanese, R., Ambrosino, G., Coccorese, E., et al., Plasma Current, Shape, and Position Control in ITER, Fusion Technol., 1996, vol. 30, no. 2, pp. 167–183.

    Google Scholar 

  12. Ambrosino, G., Ariola, M., Mitrishkin, Y., et al., Plasma Current and Shape Control in Tokamaks Using H ∞ and µ-synthesis, Proc. 36 IEEE Conf. Decision Control, San Diego, 1997, pp. 3697–3702.

  13. Ariola, M., Ambrosino, G., Lister, J.B., et al., AModern Plasma Controller Tested on the TCV Tokamak, Fusion Technol., 1999, vol. 36, no. 2, pp. 126–138.

    Google Scholar 

  14. Ariola, M. and Pironti, A., Plasma Shape Control for the JET Tokamak. An Optimal Output Regulation Approach, IEEE Control Syst. Mag., 2005, vol. 5, pp. 65–75.

    Article  Google Scholar 

  15. Mitrishkin, Y.V., Kurachi, K., and Kimura, H., PlasmaMultivariable Robust Control System Design and Simulation for a Thermonuclear Tokamak-Reactor, Int. J. Control, 2003, vol. 76, no. 13, pp. 1358–1374.

    Article  MathSciNet  MATH  Google Scholar 

  16. Belyakov, V., Kavin, A., Kharitonov, V., et al., Linear Quadratic Gaussian Controller Design for Plasma Current, Position and Shape Control System in ITER, Fusion Eng. Design, 1999, vol. 45, pp. 55–64.

    Article  Google Scholar 

  17. Skogestad, S. and Postlethwaite, I., Multivariable Feedback Control. Analysis and Design, Hoboken: Wiley, 2005, 2nd ed.

    Google Scholar 

  18. Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.

    Google Scholar 

  19. Plasma Performance Assessment (ITER D 22HGQ7), September 24, 2009.

  20. Khayrutdinov, R.R. and Lukash, V.E., Studies of Plasma Equilibrium and Transport in a Tokamak Fusion Device with the Inverse-Variable Technique, J. Comp. Physics, 1993, vol. 109, no. 2, pp. 193–201.

    Article  MATH  Google Scholar 

  21. Wesson, J., Tokamaks, Oxford: Clarendon, 1997.

    Google Scholar 

  22. Dokuka, V.N., Kadurin, A.V., Mitrishkin, Yu.V., and Khayrutdinov, R.R., Synthesis and Modeling of the H ∞-System of Magnetic Control of the Plasmain the Tokamak-Reactor, Autom. Remote Control, 2007, vol. 68, no. 8, pp. 1410–1428.

    Article  MATH  Google Scholar 

  23. Mitrishkin, Y., Korostelev, A., Kartsev, N., et al., Synthesis and Modeling of Plasma Vertical Speed, Shape, and Current Profile Control Systems in Tokamak, Proc. Int. Workshop “Control for Nuclear Fusion,” Eindhoven Univ. Technol., The Netherlands, 2008, www.wtb.tue.nl/cnf/program.php.

    Google Scholar 

  24. Mitrishkin, Yu.V. and Korostelev, A.Ya., Cascaded System for Tracking the Plasma Current and Form in Tokamak with Control Channel Decoupling, Vest. Bauman MGTU, Priborostroenie, 2010, no. 2, pp. 21–38.

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  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    A. V. Kadurin & Yu. V. Mitrishkin

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  1. A. V. Kadurin
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  2. Yu. V. Mitrishkin
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Original Russian Text © A.V. Kadurin, Yu.V. Mitrishkin, 2011, published in Avtomatika i Telemekhanika, 2011, No. 10, pp. 52–71.

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Kadurin, A.V., Mitrishkin, Y.V. Multidimensional system of cascaded control of plasma form and current in tokamak with channel decoupling and H ∞-controller. Autom Remote Control 72, 2053–2070 (2011). https://doi.org/10.1134/S0005117911100067

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