Model-based Optimization and Feedback Control of the Current Density Profile Evolution in NSTX-U

Unlike nuclear fission in present nuclear power plants, where energy is generated by splitting heavy atoms like uranium, nuclear fusion generates energy by fusing light nuclei like hydrogen isotopes under high-temperature and high-pressure conditions, at which the reactants (hydrogen isotopes) separate from their electrons and form an ionized gas called plasma, which is considered as the fourth state of matter. Contrary to fission, fusion provides more energy density, poses almost no risk of a catastrophic nuclear accident, and produces mostly short-term, low-level radioactive waste.The main difficulty in maintaining fusion reactions is the development of a device that can confine the hot plasma for sufficiently long time while preventing it from hitting the walls of the confining device. Among several techniques, magnetic confinement appears as the most promising approach. In particular, the tokamak device is a toroidal device surrounded by large magnetic coils responsible for the magnetic fields that confine the plasma. A spherical tokamak, or a spherical torus (ST), is a variation of the conventional tokamak concept. Compared to a standard tokamak, the ST device extrapolates to a more compact, potentially lower-cost reactor with higher efficiency of confinement. Nuclear fusion research is a highly challenging, multidisciplinary field seeking contributions from both plasma physics and multiple engineering areas. As an application of plasma control engineering, this dissertation mainly explores methods to control the current density profile evolution within the National Spherical Torus eXperiment-Upgrade (NSTX-U), which is a substantial upgrade based on the NSTX device, which is located in Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ. Active control of the toroidal current density profile is among those plasma control milestones that the 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. Therefore, the aim of this work is to develop model-based, feedforward and feedback controllers that can enable time regulation of the current density profile in NSTX-U by actuating the total plasma current, electron density, and the powers of the individual neutral beam injectors.Motivated by the coupled, nonlinear, multivariable, distributed-parameter plasma dynamics, the first step towards control design is the development of a physics-based, control-oriented model for the current profile evolution in NSTX-U in response to non-inductive current drives and heating systems. Numerical simulations of the proposed control-oriented model show qualitative agreement with the high-fidelity physics code TRANSP. The next step is to utilize the proposed control-oriented model to design an open-loop actuator trajectory optimizer. Given a desired operating state, the optimizer produces the actuator trajectories that can steer the plasma to such state. The objective of the feedforward control design is to provide a more systematic approach to advanced scenario planning in NSTX-U since the development of such scenarios is conventionally carried out experimentally by modifying the tokamak’s actuator trajectories and analyzing the resulting plasma evolution.Finally, the proposed control-oriented model is embedded in feedback control schemes based on optimal control and Model Predictive Control (MPC) approaches. Integrators are added to the standard Linear Quadratic Gaussian (LQG) and MPC formulations to provide robustness against various modeling uncertainties and external disturbances. The effectiveness of the proposed feedback controllers in regulating the current density profile in NSTX-U is demonstrated in closed-loop nonlinear simulations. Moreover, the optimal feedback control algorithm has been implemented successfully in closed-loop control simulations within TRANSP through the recently developed Expert routine