First-principles-driven model-based optimal control of the current profile in NSTX-U

Regulation in time of the toroidal current profile is one of the main challenges toward the realization of the next-step operational goals for the National Spherical Tokamak eXperiment - Upgrade (NSTX-U). In this work, a nonlinear, control-oriented, physics-based model describing the temporal evolution of the current profile is first obtained by combining the magnetic diffusion equation with empirical correlations obtained for the electron density, electron temperature, and non-inductive current drives in NSTX-U. The proposed model is then embedded into the control design process to synthesize a time-variant, linear-quadratic-integral, optimal controller capable of regulating the safety factor profile around a desired target profile while rejecting disturbances. Neutral beam injectors, electron density, and the total plasma current are used as actuators to shape the current profile. The effectiveness of the proposed controller in regulating the safety factor profile in NSTX-U is demonstrated in closed-loop nonlinear simulations.