Time-dependent SOLPS-ITER simulations of the tokamak plasma boundary for model predictive control using SINDy

Abstract

Time-dependent SOLPS-ITER simulations have been used to identify reduced models with the sparse identification of nonlinear dynamics (SINDy) method and develop model-predictive control of the boundary plasma state using main ion gas puff actuation. A series of gas actuation sequences are input into SOLPS-ITER to produce a dynamic response in upstream and divertor plasma quantities. The SINDy method is applied to identify reduced linear and nonlinear models for the electron density at the outboard midplane $n_\mathrm{e,sep}^\mathrm{OMP}$ and the electron temperature at the outer divertor $T_\mathrm{e,sep}^{\,\mathrm{div}}$ . Note that $T_\mathrm{e,sep}^{\,\mathrm{div}}$ is not necessarily the peak value of T _e along the divertor. The identified reduced models are interpretable by construction (i.e. not black box), and have the form of coupled ordinary differential equations. Despite significant noise in $T_\mathrm{e,sep}^{\,\mathrm{div}}$ , the reduced models can be used to predict the response over a range of actuation levels to a maximum deviation of 0.5% in $n_\mathrm{e,sep}^\mathrm{OMP}$ and 5%–10% in $T_\mathrm{e,sep}^{\,\mathrm{div}}$ for the cases considered. Model retraining using time history data triggered by a preset error threshold is also demonstrated. A model predictive control strategy for nonlinear models is developed and used to perform feedback control of a SOLPS-ITER simulation to produce a setpoint trajectory in $n_\mathrm{e,sep}^\mathrm{OMP}$ using the integrated plasma simulator framework. The developed techniques are general and can be applied to time-dependent data from other boundary simulations or experimental data. Ongoing work is extending the approach to model identification and control for divertor detachment, which will present transient nonlinear behavior from impurity seeding, including realistic latency and synthetic diagnostic signals derived from the full SOLPS-ITER output.

Keywords

• SOLPS-ITER
• model based control
• detachment