Extremum-Seeking-Based Receding-Horizon Optimal Control of Plasma Current Profile at the DIII-D Tokamak

Y. Ou, C. Xu, E. Schuster, T. C. Luce, J. R. Ferron, M. L. Walker and D. A. Humphreys

IFAC World Congress on Automatic Control

Seoul, Korea, July 6-11, 2008

Abstract

A key goal in the control of a magnetic fusion reactor is to maintain current profiles that are compatible with a high fraction of self-generated non-inductive current as well as with magnetohydrodynamic (MHD) stability at high plasma pressure. This enables high fusion gain and noninductive sustainment of 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 nonlinear partial differential equation (PDE) usually referred to as the magnetic diffusion equation. We propose, and test in simulations, an extremum-seeking-based, receding-horizon, diffusivity-interior-boundary control scheme designed to match as close as possible a desired current profile within a prespecified time interval.