Space-State Modeling and Control of Tokamak Reactors

Abstract Nuclear fusion has the potential to produce unlimited, clean energy, which presents itself as a reliable energy supply but it also helps to stop the threat of climate change that faces the world nowadays. However, to sustain the pulse duration long enough to produce the necessary energy, new controls have to be developed, composing a new application area of Control Engineering, with new and interesting challenges for the control community. In this sense, this paper deals with the modeling of tokamak nuclear fusion reactors. In order to control the creation of unstable modes in fusion processes, it is necessary to derive numerical models suitable for control strategies. The model presented in this paper addresses flux and energy conservation issues, discussing the mechanisms behind the creation of uncontrollable modes. The dynamics of the system is given by means of the energy functions which are solved for the currents in the structure, plasma current and plasma position. Thus, the equations for the state variables are derived based on the Hamiltonian equation of motion. In order to solve this system numerically, this model is linearized around an operation point by taking a Newton-Raphson step. Besides, the system output is completed by considering the equations for the flux and the poloidal field. Finally, the resulting low-order linear model is modified so as to obtain the corresponding state-space model which is verified by means of numerical experiments.

[1]  J. B. Lister,et al.  Comparing DINA code simulations with TCV experimental plasma equilibrium responses , 2001 .

[2]  G. Ambrosino,et al.  Magnetic control of plasma current, position, and shape in Tokamaks: a survey or modeling and control approaches , 2005, IEEE Control Systems.

[3]  R. R. Khayrutdinov,et al.  Studies of plasma equilibrium and transport in a Tokamak fusion device with the inverse-variable technique , 1993 .

[4]  D. Bonvin,et al.  A globally stabilising controller under saturated input for linear planar systems with one unstable pole , 2004, Proceedings of the 2004 American Control Conference.

[5]  J. B. Lister,et al.  The separatrix response of diverted TCV plasmas compared with the predictions of the CREATE-L model , 1998 .

[6]  M. Walker,et al.  Control of tokamak plasmas: introduction to a special section , 2005, IEEE Control Systems.

[7]  J. Lister,et al.  Measurement of the open loop plasma equilibrium response in TCV , 1999 .

[8]  J. B. Lister,et al.  Improving tokamak vertical position control in the presence of power supply voltage saturation , 2005 .

[9]  J. Lister,et al.  Comparing TCV experimental VDE responses with DINA code simulations , 2002 .

[10]  A. Pironti,et al.  Control of tokamak plasmas. II , 2006, IEEE Control Systems.

[11]  L. Zakharov,et al.  Equilibrium of Current-Carrying Plasmas in Toroidal Configurations , 1986 .

[12]  J. M. de la Cruz,et al.  Real time current profile control at JET , 1998 .

[13]  L. L. Lao,et al.  Experimental study of the vertical stability of high decay index plasmas in the DIII-D tokamak , 1990 .

[14]  P. L. Mondino,et al.  The JET magnet power supplies and plasma control systems , 1987 .

[15]  Aitor J. Garrido,et al.  Linear models for plasma current control , 2007 .

[16]  Aitor J. Garrido,et al.  A SURVEY ON CONTROL-ORIENTED PLASMA PHYSICS IN TOKAMAK REACTORS , 2007 .

[17]  J. B. Lister,et al.  Control of the vertical instability in tokamaks , 1990 .

[18]  S. I. Braginskii.  Transport Processes in a Plasma , 1965 .