Poloidal magnetic flux profile control in tokamaks via normalized coprime factorization robust control

The potential steady-state operation of a fusion tokamak, with good confinement and a high fusion gain, is related to setting up a suitable current density profile in the device. Experiments at the DIII-D tokamak focus on creating the desired current profile during the plasma current ramp-up and early flat-top phases of the discharge with the aim of maintaining this target profile throughout the subsequent phases of the discharge. The time evolution of the current density profile in a tokamak is related to the time evolution of the poloidal magnetic flux profile, which is modeled in normalized cylindrical coordinates by a partial differential equation referred to as the magnetic diffusion equation. Extremum seeking and nonlinear programming techniques have been employed to find optimal open-loop (feedforward) solutions to the finite time control problem during the ramp-up and early flat-top phases. In order to reject the effects of external disturbances to the system, we propose an optimal H_∞ feedback control input that is added to the optimal feedforward control input to regulate the poloidal flux profile around the desired reference trajectories of the system. The combined feedforward + feedback, model-based controller is then tested through simulation.