Model predictive control with integral action for the rotational transform profile tracking in NSTX-U

Active control of the toroidal current density profile is among those plasma control milestones that the National Spherical Tokamak eXperiment - Upgrade (NSTX-U) program must achieve to realize its next-step operational goals, which are characterized by high-performance, long-pulse, MHD-stable plasma operation with neutral beam heating. In this work, a previously developed physics-based control-oriented model is embedded in a feedback control scheme based on a model predictive control (MPC) strategy to track a desired current density profile evolution specified indirectly by a desired rotational transform profile. An integrator is embedded into the standard MPC formulation to account for various modeling uncertainties and external disturbances. The neutral beam powers, electron density, and total plasma current are used as actuators. The effectiveness of the proposed MPC strategy in regulating the current density profile in NSTX-U is demonstrated in closed-loop nonlinear simulations.