Robust adaptive control of the sawtooth instability in nuclear fusion

The sawtooth instability is a repetitive phenomenon occurring in plasmas of tokamak nuclear fusion reactors. Experimental studies of these instabilities and the effect they have on the plasma (notably the drive of secondary instabilities and consequent performance reduction) for a wide variety of plasma conditions is an important line of study in nuclear fusion research. Variations in the plasma conditions have a significant influence on the dynamical behavior of the sawtooth instability. Therefore, this paper presents the design of a sawtooth period controller which is robust against such variations. The controller is from a class of adaptive controllers better known as extremum seekers. In this technique, a cost function in terms of the desired sawtooth period is optimized on-line. The Extremum Seeking Controller (ESC) is model-free and is therefore inherently robust against model uncertainty. Simulations show that the controller is robust against variations in plasma parameters, delay in the sawtooth crash detection, and noise on the in- and outputs of the process. Because of its robustness, ESC is a promising candidate strategy for a wide range of fusion-related control problems with high model uncertainty.