An IDA-PBC approach for the control of 1D plasma profile in tokamaks

In this paper, a PCH model obtained from the spatial reduction of a thermo-magneto-hydrodynamics model for plasma dynamics in tokamaks is used to design an optimal IDA-PBC (Interconnection and Damping Assignment - Passivity Based Control) controller of the magnetic field profile. Due to the actuator constraints which imply to have a finite dimensional base of physically feasible current profile deposits, the controller inputs/outputs are reduced to be compatible with the system limitations. The loop voltage at the plasma boundary and the total external heating source power are considered as controller outputs. Reference on the total plasma current and the central safety factor value is given to compute the magnetic field profile reference. Bootstrap current and non-linearity of plasma resistivity or external current deposit scaling laws are taken into account. Simulation results based on Tore Supra WEST tokamak (a project of Tore Supra upgrade) are provided to illustrate the effectiveness of the method.