Model-based Linear-Quadratic-Integral Controller for Simultaneous Regulation of the Current Profile and Normalized Beta in NSTX-U

H. Al Khawaldeh, B. Leard, S. T. Paruchuri, T. Rafiq, E. Schuster

11th ITER International School on “ITER Plasma Scenarios and Control”

San Diego, California, USA, July 25-29, 2022

Achieving advanced scenarios that are characterized by steady-state operation, stable plasma confinement, and high-performance plasmas is one of the primary objectives of National Spherical Tokamak eXperiment - Upgrade (NSTX-U). Attaining these objectives require active control of important plasma scalars and profiles. In particular, control algorithms that can optimize the tokamak performance to achieve the desired plasma profiles in any given scenario may be necessary. In this work, a model-based optimal control algorithm is developed for feedback control of the current profile in NSTX-U. A linear finite-dimensional control-oriented model is derived by discretizing and linearizing the magnetic diffusion equation in combination with empirical correlations used for electron density, electron temperature, and noninductive current drives. The linear time-variant model is then used for designing a linear-quadratic-integral (LQI) controller that is capable of regulating both the safety factor and the normalized beta around desired targets. The controller determines neutral beam injection (NBI) powers and the overall plasma current to achieve the desired current profile and normalized beta. The proposed controller is tested in higher-fidelity nonlinear simulations that employ 1D models for both current and temperature profiles using the Control Oriented Transport SIMulator (COTSIM). The closed-loop simulations show the effectiveness of the controller at shaping the safety factor in NSTX-U while achieving the desired normalized beta.

*Supported by the US DOE under DE-SC0021385.