Backstepping control of the plasma current profile in the DIII-D tokamak

Control of the spatial profile of plasma current in tokamak plasmas has been demonstrated to be a key condition for achieving advanced scenarios with improved confinement and possible steady-state operation. The dynamics of the current profile are nonlinear and coupled with several other plasma parameters, motivating the design of model-based controllers that can account for these complexities. In this work, we consider a control-oriented model of the current profile evolution in DIII-D and the problem of regulating the current profile around a desired feed-forward trajectory. In open-loop, the response of the system to disturbances and perturbed initial conditions may be undesirable. To improve the performance of the system, the PDE model is discretized in space using a finite difference method and a backstepping design is applied to obtain a discrete transformation from the original system into an asymptotically stable target system with desirable properties. Through a nonlinear transformation, the resulting boundary control law utilizes the total plasma current, total power, and line averaged density as actuators. A Simserver simulation study is done to test the controller´s performance and its implementation in the DIII-D plasma control system. Finally, experimental results showing the ability of the controller to reject input disturbances and perturbations in initial conditions are presented.