First-principles model-based robust control of the current profile evolution in the DIII-D tokamak

Setting up a suitable toroidal current profile in a fusion tokamak reactor is vital to the eventual realization of a commercial nuclear fusion power plant. Creating the desired current profile during the ramp-up and early flat-top phases of the plasma discharge and then actively maintaining this target profile for the remainder of the discharge is the goal at the DIII-D tokamak. The evolution of the toroidal current profile in toka-maks is related to the evolution of the poloidal magnetic flux profile, which is modeled by the magnetic diffusion equation. A simplified first-principles-driven, nonlinear, dynamic, control-oriented, partial differential equation model of the poloidal flux profile evolution is obtained by combining the magnetic diffusion equation with empirical correlations obtained from experimental data at DIII-D and is used to synthesize a robust H
_∞
feedback controller to track a desired reference trajectory of the poloidal magnetic flux gradient profile. We employ a singular value decomposition of the static gain matrix of the plant model to identify the most relevant channels which we control with the feedback controller. A framework for real-time feedforward + feedback control was implemented in the DIII-D Plasma Control System and experimental results in the DIII-D tokamak are presented to illustrate the capabilities of the feedback controller. These experiments mark the first time ever a first-principles-driven model-based magnetic profile controller was successfully implemented and tested in a tokamak device.