Physics-model-based nonlinear actuator trajectory optimization and safety factor profile feedback control for advanced scenario development in DIII-D

Abstract

DIII-D experimental results are reported to demonstrate the potential of physics-model-based safety factor profile control for robust and reproducible sustainment of advanced scenarios. In the absence of feedback control, variability in wall conditions and plasma impurities, as well as drifts due to external disturbances, can limit the reproducibility of discharges with simple preprogrammed scenario trajectories. The control architecture utilized is a feedforward + feedback scheme where the feedforward commands are computed off-line and the feedback commands are computed on-line. In this work, a first-principles-driven (FPD), physics-based model of the q profile and normalized beta (β N) dynamics is first embedded into a numerical optimization algorithm to design feedforward actuator trajectories that steer the plasma through the tokamak operating space to reach a desired stationary target state that is characterized by the achieved q profile and β N. Good agreement between experimental results and simulations demonstrates the accuracy of the models employed for physics-model-based control design. Second, a feedback algorithm for q profile control is designed following an FPD approach, and the ability of the controller to achieve and maintain a target q profile evolution is tested in DIII-D high confinement (H-mode) experiments. The controller is shown to be able to effectively control the q profile when β N is relatively close to the target, indicating the need for integrated q profile and β N control to further enhance the ability to achieve robust scenario execution. The ability of an integrated q profile + β N feedback controller to track a desired target is demonstrated through simulation.

Enhanced reproducibility of L-mode plasma discharges via physics-model-basedq-profile feedback control in DIII-D

“…The feedforward control law needs to be complemented by a feedback control law in order to mitigate deviations from the desired state reference trajectory due to perturbations in the initial condition, external disturbances, and unmodeled dynamics. Three feedback control algorithms were employed in these experiments, which were designed based on optimal control [8,21], robust control [1,9,10], and backstepping control [11] design techniques. The feedback portion of the controller was interfaced with the real-time EFIT (rtEFIT) equilibrium reconstruction code [22].…”

“…The achieved feedback-controlled profiles (dashed red lines) are compared with the targets in both figures 4 and 6, showing a significant and consistent matching improvement. To allow for a better comparison, all the shots presented in this section were achieved using the same type of robust-control algorithm [1,9,10]. Figures 4(a) and (b) show how the combined feedforward + feedback controller is capable of repeatedly achieving Target 1 at the predefined time of approximately 1.5 s in shots #157950 and #157951.…”

“…In the absence of feedback control, variability in wall conditions and plasma impurities, as well as drifts due to external plasma disturbances, can limit the reproducibility of discharges attained with simple pre-programmed scenario trajectories. A combined feedforward + feedback control scheme [1] has been employed to optimize the current ramp-up phase by consistently achieving target q profiles at prescribed times in L-mode discharges. The scheme incorporates the physics of the to-be-controlled system by embedding a control-oriented plasma-response model in the control design.…”

First demonstration of real-time kinetic equilibrium reconstruction on TCV by coupling LIUQE and RAPTOR

“…via parallelization and use of GPUs [29,30]. For the transport equations instead, efforts are made to reduce the complexity of the modeling while retaining the most relevant features [19,31,32], as well as using machine learning techniques to emulate the solutions of the most computational expensive part of the model [33][34][35][36][37]. Another approach is to entirely substitute physics-based models with data driven models trained on databases of previous experiments [38].…”

Multi-experiment state-space identification of coupled magnetic and kinetic parameters in tokamak plasmas

“…A method for profile control of the electron temperature and the safety factor based on a real-time estimation of linearized static plasma profiles is explored in [15]. First principle model-based control for the current profile and the electron temperature profile is used in [16] and physics-based control of the plasma safety factor profile and stored energy is used in [17,18].…”