Current profile tracking for the DIII-D tokamak via LQI optimal control

In tokamak fusion plasmas, controlling the spatial distribution profile of the toroidal current is key to achieving advanced scenarios characterized by confinement improvement and possible steady-state operation. The dynamics of the current profile are nonlinear and coupled with other plasma parameters, motivating the use of model-based control strategies. In this work, we use a control-oriented model of the current profile evolution in DIII-D to design a feedback controller for regulating the profile around a desired trajectory. Without feedback, the response of the current profile to disturbances, model uncertainty, and perturbed initial conditions can be undesirable. To improve tracking performance of the system, a nonlinear input transformation is combined with a linear-quadratic-integral (LQI) optimal controller designed to minimize a weighted combination of the tracking error and controller effort. The resulting control law utilizes the total plasma current, total external heating power, and line averaged plasma density as actuators. We present simulation and experimental results showing successful rejection of perturbed initial conditions and input disturbances.