Robust Control of the Poloidal Magnetic Flux Profile in the Presence of Unmodeled Dynamics
Y. Ou, C. Xu, E. Schuster
Symposium on Fusion Engineering
San Diego, CA, May 31-June 5, 2009
Abstract
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The potential operation of a tokamak fusion reactor in a
highly-efficient, steady-state mode is directly related to the
achievement of certain types of radial profiles for the current
flowing toroidally in the device. The evolution in time of the
toroidal current profile in tokamaks is related to the evolution of
the poloidal magnetic flux profile, which is modeled in normalized
cylindrical coordinates using a nonlinear partial differential
equation (PDE) usually referred to as the magnetic diffusion equation.
We propose a robust control scheme to regulate the poloidal magnetic
flux profile in tokamaks in the presence of model uncertainties. These
uncertainties come mainly from the resistivity term of the magnetic
diffusion equation. First we either simulate the magnetic diffusion
equation or carry out experiments to generate data ensembles, from
which we then extract the most energetic modes to obtain a reduced
order model based on proper orthogonal decomposition (POD) and
Galerkin projection. The obtained reduced-order model corresponds to a
linear state space representation with uncertainty. Taking advantage
of the structure of the state matrices, the reduced order model is
reformulated into a robust control framework, with the resistivity
term as an uncertain parameter. An H∞ controller is designed to
minimize the regulation/tracking error. Finally, the synthesized
model-based robust controller is tested in simulations.