Extremum-Seeking Finite-Time Optimal Control of Plasma Current Profile at the DIII-D Tokamak

In a magnetic fusion reactor, the achievement of a certain type of plasma current profiles, which are compatible with magnetohydrodynamic (MHD) stability at high plasma pressure, is key to enable high fusion gain and noninductive sustainment of the plasma current for steady-state operation. The approach taken toward establishing such plasma current profiles at the DIII-D tokamak is to create the desired profile during the plasma current ramp-up and early flattop phases. The evolution in time of the current profile is related to the evolution of the poloidal flux, which is modeled in normalized cylindrical coordinates using a partial differential equation (PDE) usually referred to as the magnetic diffusion equation. The control problem is formulated as an open-loop, finite-time, optimal control problem for a nonlinear distributed parameter system, and is approached using extremum seeking. Simulation results, which demonstrate the accuracy of the considered model and the efficiency of the proposed controller, are presented.