Model-predictive kinetic control with data-driven models on EAST
Authors: Moreau D. , Wang S. , Qian J.P. , Yuan Q. , Huang Y. , Li Y. , Ding S. , Du H. , Gong X. , Li M. , Liu H. , Luo Z. , Zeng L. , Olofsson E. , Sammuli B. , Artaud J.F. , Ekedahl A. , Witrant E. 
Published: October 2024

Abstract
In this work, model-predictive control (MPC) was combined for the first time with singular perturbation theory, and an original plasma kinetic control method based on extremely simple data-driven models and a two-time-scale MPC algorithm has been developed. A comprehensive review is presented in this paper. Slow and fast semi-empirical models are identified from data, by considering the fast kinetic plasma dynamics as a singular perturbation of a quasi-static equilibrium, which itself is governed, on the slow time scale, by the flux diffusion equation. This control technique takes advantage of the large ratio between the time scales involved in magnetic and kinetic plasma transport. It is applied here to the simultaneous control of the safety factor profile, q(𝑥), and of several kinetic variables, such as the poloidal beta parameter, βp
, and the internal inductance parameter, li
, on the EAST tokamak. In the experiments, the available control actuators were lower hybrid current drive (LHCD) and co-current neutral beam injection (NBI) from different sources. Ion cyclotron resonant heating (ICRH) and electron cyclotron resonant heating (ECRH) are used as additional actuators in control simulations. In the controller design, an observer provides, in real time, an estimate of the system states and of the mismatch between measured and predicted outputs, which ensures robustness to model errors and offset-free control. Based on the observer information, the controller predicts the behavior of the system over a given time horizon and computes the optimal actuation by solving a quadratic programming optimization problem that takes the actuator constraints into account. A number of control applications are described in the paper, either in nonlinear simulations with EAST-like parameters or in real experiments on EAST. The simulations were performed with a fast plasma simulator (METIS) using either two control actuators (LHCD and ICRH) in a low density scenario, or up to four actuators at higher density: LHCD, ECRH, and two NBI systems driven in a on/off pulse-width-modulation (PWM) mode, with different injection angles. The control models are identified with the prediction-error method, using datasets obtained from open loop simulations in which the actuators are modulated with pseudo-random binary sequences. The simulations with two actuators show that various q(𝑥) profiles and βp
waveforms can be tracked without offset, within times that are consistent with the resistive and thermal diffusion time scales, respectively. In simulations with four actuators, simultaneous tracking of time-dependent targets is shown for q(𝑥) at two normalized radii, 𝑥 = 0 and 𝑥 = 0.4, and for βp
. Due to the inherent mismatch between the optimal NBI power request and the delivered PWM power, the kinetic controller performs with reduced accuracy compared with simulations that do not use the NBI/PWM actuators. The first experimental tests using this new control algorithm were performed on EAST when the only available actuator was the LHCD system at 4.6 GHz. The algorithm was thus used in its simplest single-input-single-output version to track time-dependent targets for the central safety factor, q0
, or for βp
. In the closed loop control experiments, the q0
targets were tracked in about one second, consistently with the plasma resistive time constant. Excellent tracking of a piecewise linear βp
target waveform was also achieved. When the NBI system became controllable in real time by the EAST plasma control system, new experiments were dedicated to multiple-input-multiple-output MPC control with three actuators: LHCD and two NBI actuators using the PWM algorithm. Given that the minimum time allowed between NBI on/off switching was 0.1 s, i.e. larger than the characteristic time of the fast plasma dynamics, a reduced version of the MPC controller based only on the slow model was used. Various controller configurations were tested during a single experimental session, with up to three controlled variables chosen among q
0 = q(𝑥= 0), q
1 = q(𝑥= 0.5), βp
and li
. The main difficulty encountered during this session was the unavailability of the full baseline ICRH and ECRH powers that were used in the reference scenario, and from which the plasma model was identified. This often led to the saturation of one or several actuators, which prevented some targets selected in advance from being accessible. Nevertheless, in cases that were free from actuator saturation, q
0 and q
1 targets were successfully reached, in a time that is consistent with the resistive diffusion time of the model and with small oscillations that are characteristic of the PWM operation of the neutral beams. During the simultaneous control of q
0 and βp
, the ICRH power was too low and, in addition, the plasma density was much larger than the reference one. The q
0 targets were not accessible in this high-density/low-power case, but βp
control was successful. Finally, the simultaneous control of q
0 and li
was satisfactory and, during the simultaneous control of, q
0, βp
and li
, the tracking of βp
and li
was satisfactory but q0
was too large due to the lack of ICRH power and to NBI saturation. In conclusion, the extensive nonlinear simulations described in this paper have demonstrated the relevance of combining MPC, data-driven models and singular perturbation methods for plasma kinetic control. This technique was also assessed experimentally on EAST, although some tests were perturbed by undesired parameter changes with respect to the reference scenario.