POD-Based Optimal Control of Current Profile in Tokamak Plasmas via Nonlinear Programming
C. Xu, J. Dalessio, Y. Ou, E. Schuster, T.C. Luce, J.R. Ferron, M.L. Walker and D.A. Humphreys
American Control Conference
Seattle, Washington, June 11-13, 2008
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 enabling high fusion gain and noninductive
sustainment of the plasma current for steady-state operation.
The evolution in time of the current profile is related to the
evolution of the spatial derivative of the poloidal flux profile,
which is modeled in normalized cylindrical coordinates using
a partial differential equation (PDE) usually referred to as
the magnetic diffusion equation. The dynamics of the plasma
poloidal flux profile can be modified by three actuators: the
total plasma current, the non-inductive power, and the average
plasma density. These three actuators, which are constrained
not only in value and rate but also in their initial and
final values, are used to drive the poloidal flux profile, or
equivalently the current profile, as close as possible to a desired
target profile at a specific final time. To solve this constrained
finite-time open-loop optimal control problem, model reduction
based on proper orthogonal decomposition (POD) is combined
with sequential quadratic programming (SQP) in an iterative
fashion. The use of a low dimensional dynamical model reduces
the computational effort, and therefore the time required to
solve the optimization problem, which is critical for a potential
implementation of a receding horizon control strategy.