Robust control of the poloidal magnetic flux profile in the presence of unmodeled dynamics

Abstract

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.