Optimization of the Current Ramp-up Phase in \mbox{DIII-D} via Physics-model-based Control of Plasma Safety Factor Profile Dynamics

Simulations and experimental results in DIII-D are presented to demonstrate the potential of physics-model-based control of the $q$ profile to improve the reproducibility of plasma startup conditions by achieving a specified target $q$ profile at the end of the current ramp-up. Three different $q$ profiles ($q_{min}$ of 1.3, 1.65, 2.1 and $q_{95}$ of 4.4, 5.0, 6.2, respectively) were specified as targets. A feedforward + feedback scheme is utilized to control the $q$ profile and is constructed by embedding a nonlinear, physics-based model of the $q$ profile dynamics into the control design process. A unique characteristic of the feedforward trajectories obtained by solving the optimization problem is the regulation of the plasma current ramp-up rate to achieve the target $q$ profiles. The feedback controller is employed to add robustness to the control scheme and account for drifts due to external plasma disturbances.