Robust Control Design for the Poloidal Magnetic Flux Profile Evolution in the Presence of Model Uncertainties
Y. Ou, C. Xu and E. Schuster
IEEE Transactions on Plasma Science, vol. 38, no. 3, pp. 375-382, March 2010
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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 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 de- composition 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_{\inf} controller is designed to minimize the regulation/tracking
error. Finally, the synthesized model-based robust controller is tested in simulations.
