H∞H∞ stabilization of the current profile in tokamak plasmas via an LMI approach

This paper deals with the H"~ stabilization of the spatial distribution of the current profile of tokamak plasmas using a Linear Matrix Inequality (LMI) approach. The control design is based on the one dimensional resistive diffusion equation of the magnetic flux that governs the plasma current profile evolution. The feedback control law is derived in the infinite dimensional setting without spatial discretization. The proposed distributed control is based on a proportional-integral state feedback taking into account both interior and boundary engineering actuators. Supporting numerical simulations are presented and tuning of the controller parameters attenuating uncertain disturbances is discussed.

[1]  E. Joffrin,et al.  The CRONOS suite of codes for integrated tokamak modelling , 2010 .

[2]  Didier Mazon,et al.  Feedback control of the lower hybrid power deposition profile on Tore Supra , 2007 .

[3]  J. M. Ball,et al.  GEOMETRIC THEORY OF SEMILINEAR PARABOLIC EQUATIONS (Lecture Notes in Mathematics, 840) , 1982 .

[4]  Yuri V. Orlov,et al.  Discontinuous unit feedback control of uncertain infinite-dimensional systems , 2000, IEEE Trans. Autom. Control..

[5]  Sylvain Brémond,et al.  Polytopic Control of the Magnetic Flux Profile in a Tokamak Plasma , 2011 .

[6]  Andrey Smyshlyaev,et al.  Adaptive Control of Parabolic PDEs , 2010 .

[7]  Richard E. Grandy,et al.  Orlando, Florida, USA , 2011 .

[8]  Eugenio Schuster,et al.  Optimal Tracking Control of Current Profile in Tokamaks , 2011, IEEE Transactions on Control Systems Technology.

[9]  Jacques Blum.  Numerical simulation and optimal control in plasma physics : with applications to Tokamaks , 1989 .

[10]  B. Saoutic,et al.  Tore Supra: Toward Steady State in a Superconducting Tokamak , 2009 .

[11]  Emilia Fridman,et al.  An LMI approach to Hinfinity boundary control of semilinear parabolic and hyperbolic systems , 2009, Autom..

[12]  Didier Georges,et al.  Model-based control of the magnetic flux profile in a Tokamak plasma , 2010, 49th IEEE Conference on Decision and Control (CDC).

[13]  X. Litaudon,et al.  Feedback control of the current profile on Tore Supra , 1997 .

[14]  C. D. Challis,et al.  The use of internal transport barriers in tokamak plasmas , 2004 .

[15]  Yury Orlov,et al.  Sliding mode stabilization of the current profile in Tokamak plasmas , 2011, IEEE Conference on Decision and Control and European Control Conference.

[16]  Sylvain Brémond,et al.  Validation of plasma current profile model predictive control in tokamaks via simulations , 2011 .

[17]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[18]  Sylvain Brémond,et al.  Plasma Control in Tore Supra , 2009 .

[19]  Jet Efda Contributors,et al.  A two-time-scale dynamic-model approach for magnetic and kinetic profile control in advanced tokamak scenarios on JET , 2008 .

[20]  Vilmos Komornik,et al.  Fourier Series in Control Theory , 2005 .

[21]  Rafael Castro-Linares,et al.  Trajectory tracking for non-holonomic cars: A linear approach to controlled leader-follower formation , 2010, 49th IEEE Conference on Decision and Control (CDC).

[22]  Eugenio Schuster,et al.  Sequential linear quadratic control of bilinear parabolic PDEs based on POD model reduction , 2011, Autom..

[23]  X. Litaudon,et al.  Steady state long pulse tokamak operation using Lower Hybrid Current Drive , 2011 .

[24]  R. J. La Haye,et al.  Plasma models for real-time control of advanced tokamak scenarios , 2011 .

[25]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[26]  D. A. Humphreys,et al.  Receding-horizon optimal control of the current profile evolution during the ramp-up phase of a tokamak discharge , 2011 .

[27]  Lihua Xie,et al.  H[∞] control and filtering of two-dimensional systems , 2002 .

[28]  Christophe Prieur,et al.  A Strict Control Lyapunov Function for a Diffusion Equation With Time-Varying Distributed Coefficients , 2013, IEEE Transactions on Automatic Control.

[29]  Sylvain Brémond,et al.  Real-time control of the safety factor profile diagnosed by magneto-hydrodynamic activity on the Tore Supra tokamak , 2011 .

[30]  E. Joffrin,et al.  A control-oriented model of the current profile in tokamak plasma , 2007 .

[31]  Lars-Erik Persson,et al.  Weighted Inequalities of Hardy Type , 2003 .

[32]  Steven Paul Hirshman,et al.  Finite‐aspect‐ratio effects on the bootstrap current in tokamaks , 1988 .