Poloidal Magnetic Flux Profile Control in Tokamaks via Normalized Coprime Factorization Robust Control
J. Barton, Y. Ou, C. Xu, E. Schuster and M. L. Walker
IEEE Multi-conference on Systems and Control
Denver, Colorado, September 28-30, 2011
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Abstract
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The potential steady-state operation of a fusion tokamak, with good
confinement and a high fusion gain, is related to setting up a
suitable current density profile in the device. Experiments at the
DIII-D tokamak focus on creating the desired current profile during
the plasma current ramp-up and early flat-top phases of the discharge
with the aim of maintaining this target profile throughout the
subsequent phases of the discharge. The time evolution of the current
density profile in a tokamak is related to the time evolution of the
poloidal magnetic flux profile, which is modeled in normalized
cylindrical coordinates by a partial differential equation referred to
as the magnetic diffusion equation. Extremum seeking and nonlinear
programming techniques have been employed to find optimal open-loop
(feedforward) solutions to the finite time control problem during the
ramp-up and early flat-top phases. In order to reject the effects of
external disturbances to the system, we propose an optimal H∞ feedback
control input that is added to the optimal feedforward control input
to regulate the poloidal flux profile around the desired reference
trajectories of the system. The combined feedforward + feedback,
model-based controller is then tested through simulation.
