Tokamak plasma models development for plasma magnetic control systems design by first principle equations and identification approach

摘要

To design plasma magnetic control systems in modern tokamaks one needs models of the plasma. These models are linear parameter varying (LPV) because of relatively small variations of outputs of the feedback loops around scenarios and may be obtained by first-principle equations, identification approach or by their combinations. The challenge of obtaining models of the plasma in the tokamak becomes more complicated by the existence of plasma position and poloidal field control loops with diagnostics and actuators which are needed as inner cascades for plasma current and shape control in particular on the Globus-M2 tokamak (Ioffe Inst., St. Petersburg, RF). The plasma equilibrium is reconstructed on the base of magnetic measurements outside the plasma by Picard iterations, moving filaments or neural networks, and linear plasma models are developed around the equilibrium with the help of the Kirchhoff’s law and force balance. In order to ensure the operability of plasma current and shape feedback control systems, the identification approach (controlled plant model design on the base of experimental input-output signals) is planned to be used. The basic methods of the identification are supposed to be applied as follows: subspaces, wavelets, linear matrix inequalities (LMIs), adaptive state observers, and dynamical neural networks which are able to automatically adjust their states to an unknown plant (elements of artificial intelligence). The solutions of the identification problem will be compared with the models obtained by the first principles with the aim to get the sufficient accuracy of coincidence. The approaches to be developed of getting tokamak plasma models may be applied to any vertically elongated (D-shaped) operating tokamak such as Globus-M2 (RF), D-IIID, NSTX (US), JET, ST40 (GB), ASDEX Upgrade (Germany), TCV (Switzerland), EAST (China), Damavand (Iran) etc.