Abstract
The q-profile control problem in the ramp-up phase of plasma discharges is considered in this work. The magnetic diffusion partial differential equation (PDE) models the dynamics of the poloidal magnetic flux profile, which is used in this work to formulate a PDE-constrained optimization problem under a quasi-static assumption. The minimum surface theory and constrained numeric optimization are then applied to achieve suboptimal solutions. Since the transient dynamics is pre-given by the minimum surface theory, then this method can dramatically accelerate the solution process. In order to be robust under external uncertainties in real implementations, PID (proportional-integral-derivative) controllers are used to force the actuators to follow the computational input trajectories. It has the potential to implement in real-time for long time discharges by combining this method with the magnetic equilibrium update.