IDA-PBC control for the coupled plasma poloidal magnetic flux and heat radial diffusion equations in tokamaks

The IDA-PBC control of plasma dynamics in a tokamak is investigated. It is based on a model made of the two coupled PDEs of resistive diffusion for the magnetic poloidal flux and of radial thermal diffusion. The used Thermal-Magneto-Hydro-Dynamics (TMHD) couplings are the Lorentz forces (with non-uniform resistivity) and the bootstrap current. The control model is obtained with the coupling of the two finite dimensional approximations obtained from the two diffusion models, using two geometric reduction schemes. A feedforward control is used to ensure the compatibility with the actuator physical ability. Then, an IDA-PBC (Interconnection and Damping Assignment - Passivity Based Control) controller is proposed for the coupled model to improve the system stabilization and convergence speed. The obtained numerical results are validated against the simulation data obtained from the RAPTOR (RApid Plasma Transport simulatOR) code for the TCV (Tokamak of Configuration Variable at CRPP, EPFL, Lausanne, Switzerland) tokamak real-time control system.