Development of data-driven plasma parameters estimators for adaptive model-free plasma vertical stabilization.
Different model-based approaches have been proposed in literature to solve the vertical stabilization problem in a robust fashion. In many cases the adopted control approach has been tailored taking into account the features of the specific experimental device, as in the case of the JET tokamak VS system or of the DIII-D tokamak . Such a customization is needed since the performance of any existing VS system strongly depends on the growth rate gamma of the instability, usually defined as the unstable eigenvalue of the linearized plasma response model obtained around the considered configuration. The eigenvector associated to gamma describes the behaviour of the plasma and of the currents in the passive structures along the unstable direction.
A possible VS control approach could be to adapt the control gains as function of gamma. However, the estimation of the unstable eigenvalue is based on the real-time reconstruction of the plasma equilibrium, which is still a computationally demanding task, if compared with the time scale the VS system should react in.
One possibility to achieve robust performance in present tokamaks is to adapt the VS parameters according to an empirical relationship between gamma and some measurements.
One possible control strategy to guarantee the level of robustness required for plasma magnetic control is to resort to model-free approaches that do not heavily rely on the knowledge of a plant model. To this aim the TRAINER team members have introduced a possible approach to solve problem that exploits the Extremum Seeking (ES) algorithm originally proposed. Indeed, the authors have shown that it is possible to stabilize on average an unstable plant by minimizing a properly chosen candidate Lyapunov function of the plant state with a suitable choice of the control action.
The TRAINER members have developed a VS system based on ES that exploits the knowledge of the plasma behaviour to design a Kalman Filter (KF) that estimates the dynamic of the plant along the unstable mode gamma, given a reference plasma linear model. Such an estimate is then used to compute a candidate Lyapunov function to be minimized by the ES control algorithm, hence achieving overall stabilization. In [R16] it has been proved that a limited knowledge of the plasma behaviour (i.e. a single and reduced order linear model) is sufficient to design a VS algorithm that works for the entire flattop, despite the variation of plasma shape and current density distribution. However, this WP aims at improving both the robustness and the performance of such a model-free approach by developing a data-driven estimator for the plasma growth rate to be used to schedule different pre-computed KFs during the evolution of the plasma discharge.
The main idea is to develop a plasma classifier which is based on plasma profile parameters (e.g. poloidal beta and internal inductance) and shape parameters (e.g. major radius, elongation, triangularity). A parameter space clustering associates each plasma to a given cluster providing a linear model with similar growth rate and sensitivity of the vertical position to the current that flow in the VS circuit (VS3 in the ITER jargon). The association of the measured/estimated plasma parameters to the cluster is obtained via a Support Vector Machine. The linear model can be obtained in a very short time and can be used both for adaptive Kalman Filtering and for adapting VS controller parameters.
This WP includes two tasks:
[T2.1] – Development of the data-driven estimator of the plasma growth rate
[T2.2] – Development of an Extremum-seeking based Vertical Stabilization (VS) system and assess the possibility to integrate it with the growth rate estimator developed by [T2.1]
The following deliverables are expected as outcomes of [WP2]:
[D3] – Delivery of a data-driven estimator for the plasma growth rate
[D6] – Extremum-seeking based Vertical Stabilization system