Optimal Tracking Control of Current Profile in Tokamaks
Y. Ou, C. Xu, E. Schuster, T.C. Luce, J.R. Ferron, M.L. Walker and D.A. Humphreys
IEEE Transactions on Control Systems Technology, vol. 19, no. 2, pp. 432-441, March 2011
Abstract
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Setting up a suitable current spatial profile in tokamak plasmas has been demonstrated to be a key condition for one possible
advanced scenario with improved confinement and possible steady-state operation. Experiments at the DIII-D tokamak focus on
creating the desired current profile during the plasma current ramp-up and early flattop phases with the aim of maintaining
this target profile during the subsequent phases of the discharge. The evolution in time of the current profile is related to
the evolution of the poloidal magnetic flux, which is modeled in normalized cylindrical coordinates using a parabolic partial
differential equation (PDE) usually referred to as the magnetic diffusion equation. We propose a framework to solve a
finite-time, optimal tracking control problem for the current profile evolution via diffusivity, interior, and boundary
actuation during the ramp-up and early flattop phases of the discharge. The proposed approach is based on reduced order modeling
via proper orthogonal decomposition (POD) and successive optimal control computation for a bilinear system. Simulation results
illustrate the performance of the proposed controller.