Closed-loop tracking control of poloidal magnetic flux profile in tokamaks

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 reactor. The time evolution of the toroidal current profile is related to the poloidal magnetic flux profile evolution, which is modeled in cylindrical coordinates using a nonlinear partial differential equation (PDE) usually referred to as the magnetic diffusion equation. In this paper, we propose a framework to solve a closed-loop, finite-time, optimal tracking control problem for the poloidal magnetic flux profile via diffusivity, interior, and boundary actuation. The proposed approach is based on reduced order modeling via proper orthogonal decomposition (POD) and successive optimal control computation for a bilinear system. Simulation results illustrate the performance of the proposed controller.