Combined Current Profile and $\beta_N$ Control to Facilitate Accessibility and Reproducibility Testing of High-qmin Steady-State Scenarios

The capability of combined current profile and $\beta_N$ control to enable access and repeatability of steady-state scenarios for high $q_{min}>1.5$ discharges is studied in both nonlinear simulations and experiments. The presentation focuses on model-predicted $q$-profile+$\beta_N$ control, which numerically solves successive optimal control problems over a receding time horizon by exploiting efficiently solvable quadratic programming techniques. One of the key advantages of this control approach is that it allows for explicit incorporation of state/input constraints to prevent the controller from driving the plasma outside of stability/performance limits and obtain, as closely as possible, steady state conditions in the $q$ profile. To characterize the $q$ profile+$\beta_N$ response, empirical correlations are combined with first-principles laws to arrive at a control-oriented model, which captures the dominant physics that is necessary for model-based optimal control design.