Model Reduction for Axisymmetric Tokamak Control

Abstract

We deal with the problem of reducing a complicated electromagnetic passive structure model coupled to a linear plasma response model to a size that allows rapid calculations of gains for plasma position and shape control. We find that model reduction through eigenmode decomposition does not reproduce the input-to-output relationship of the system, unless one has a good idea of which eigenmodes are important. Hankel singular mode decomposition, on the other hand, provides an orthogonal basis for the system response, where the modes are ordered by their importance to the input-to-output relationship. A perturbed equilibrium plasma response model is used together with an electromagnetic model of the Alcator C-MOD passive structure to assess the performance of different model reduction schemes. We find that between 10 and 20 modes are required to give an adequate representation of the passive system. Emphasis is placed on keeping the reduction process independent of the parameters of the plasma we are trying to control.