Robust sawtooth period control based on adaptive online optimization

The systematic design of a robust adaptive control strategy for the sawtooth period using electron cyclotron current drive (ECCD) is presented. Recent developments in extremum seeking control (ESC) are employed to derive an optimized controller structure and offer practical tuning guidelines for its parameters. In this technique a cost function in terms of the desired sawtooth period is optimized online by changing the ECCD deposition location based on online estimations of the gradient of the cost function. The controller design does not require a detailed model of the sawtooth instability. Therefore, the proposed ESC is widely applicable to any sawtoothing plasma or plasma simulation and is inherently robust against uncertainties or plasma variations. Moreover, it can handle a broad class of disturbances. This is demonstrated by time-domain simulations, which show successful tracking of time-varying sawtooth period references throughout the whole operating space, even in the presence of variations in plasma parameters, disturbances and slow launcher mirror dynamics. Due to its simplicity and robustness the proposed ESC is a valuable sawtooth control candidate for any experimental tokamak plasma, and may even be applicable to other fusion-related control problems.