Nonlinear control and online optimization of the burn condition in ITER via heating, isotopic fueling and impurity injection

Abstract

The ITER tokamak, the next experimental step toward the development of nuclear fusion reactors, will explore the burning plasma regime in which the plasma temperature is sustained mostly by fusion heating. Regulation of the fusion power through modulation of fueling and external heating sources, referred to as burn control, is one of the fundamental problems in burning plasma research. Active control will be essential for achieving and maintaining desired operating points, responding to changing power demands, and ensuring stable operation. Most existing burn control efforts use either non-model-based control techniques or designs based on linearized models. These approaches must be designed for particular operating points and break down for large perturbations. In this work, we utilize a spatially averaged (zero-dimensional) nonlinear model to synthesize a multi-variable nonlinear burn control strategy that can reject large perturbations and move between operating points. The controller uses all of the available actuation techniques in tandem to ensure good performance, even if one or more of the actuators saturate. Adaptive parameter estimation is used to improve the model parameter estimates used by the feedback controller in real-time and ensure asymptotic tracking of the desired operating point. In addition, we propose the use of a model-based online optimization algorithm to drive the system to a state that minimizes a given cost function, while respecting input and state constraints. A zero-dimensional simulation study is presented to show the performance of the adaptive control scheme and the optimization scheme with a cost function weighting the fusion power and temperature tracking errors.

Nonlinear burn condition control in tokamaks using isotopic fuel tailoring

“…The controller handles both thermal excursions and quenches and depends parametrically on the equilibrium point, allowing it to be used to drive the system from one equilibrium point to another. The coupling of such a scheme with adaptive control techniques and a real-time optimization algorithm was studied in [32]. In this work, a zero-dimensional simulation study compares the performance of the actively controlled system to the open loop system when switching between operating points, showing a significant improvement in performance.…”

“…The selection of the controller gains K E , K n , γ K , and K I , is a trade-off between the robustness of the scheme to these uncertainties and the sensitivity of the controller to noise. In order to handle the the uncertainties in a parametric way, a nonlinear adaptive control law can be synthesized as an augmentation [32] of the proposed controller. A real-time optimization algorithm for updating the choice of operating point parameters Ē , n, and γ¯ in response to changes in impurity content or confinement parameters can also be included.…”

“…A real-time optimization algorithm for updating the choice of operating point parameters Ē , n, and γ¯ in response to changes in impurity content or confinement parameters can also be included. Such an algorithm, like the preliminary version reported in [32], could be used to optimize the response of parameters like the fusion power and the divertor heat load, while maintaining the stability properties of the controller proposed in this work. Finally, simulation of the proposed scheme using more complex integrated modeling codes, such as TRANSP, CORSICA, or CRONOS, will be used to assess robustness to unmodeled complexities, e.g.…”

“…In this work, the choice of the desired equilibrium point is considered to be made offline prior to the discharge, however, a real-time optimization algorithm could be used to determine the equilibrium that best achieves some predetermined goal, e.g. to maximize fusion gain [32].…”

Nonlinear burn control in ITER using adaptive allocation of actuators with uncertain dynamics

“…The regulation of temperature and density in a fusionproducing (burning) plasma in ITER will require the use of nonlinear burn control algorithms [1][2][3][4] that request the correct amounts of external heating and fueling for equilibrium stabilization [5]. Because the fast ions introduced from neutral beam injection (NBI) and fusion reactions, as well as the heating by other auxiliary sources, unevenly heat the plasma ion and electron populations [6,7], the ion and electron temperatures will not be necessarily coupled.…”