Design and Simulation of Extremum-Seeking Open-loop Optimal Control of Current Profile in the DIII-D Tokamak
Y. Ou, C. Xu, E. Schuster, T.C. Luce, J.R. Ferron, M.L.Walker and D.A. Humphreys
Plasma Physics and Controlled Fusion 50 (2008) 115001
Abstract
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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 rampup
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.