NONLINEAR BACKSTEPPING CONTROL FOR THE FUEL DIFFUSION LAG IN FUSION REACTORS

Abstract

Control of plasma density and temperature magnitudes, as well as their profiles, are among the most fundamental problems in fusion reactors. Existing efforts use control techniques based on linearized models. In this work, a zero-dimensional nonlinear model involving approximate conservation equations for the energy and the densities of the species was used to synthesize a nonlinear feedback controller for stabilizing the burn condition of a fusion reactor. The model addresses the issue of the lag due to the finite time for the fresh fuel to diffuse into the plasma center. Nonlinear backstepping is used to deal with this imposed lag. In this way we make our control system independent of the fueling system and the reactor can be fed either by pellet injection or by gas puffing. The controller exhibits excellent properties of robustness and the boundness of the state variables is guaranteed for a large set of values of the lag constant. In addition the nonlinear controller proposed guarantees a much larger region of attraction than the previous linear controllers, it is capable of rejecting perturbations in initial conditions leading to both thermal excursion and quenching, and its effectiveness does not depend on whether the operating point is an ignition or a subignition point.