Model-based Robust Control of Resistive Wall Modes via mu-synthesis

J. Dalessio, E. Schuster, D. Humphreys, M. Walker, Y. In and J.S. Kim

Fusion Science and Technology, v 55, n 2, February, 2009, p 163-179

Abstract

In this work, mu-synthesis is employed to stabilize a model of the resistive wall mode (RWM) instability in the DIII-D tokamak. The GA/Far-Tech DIII-D RWM model, which replaces the spatial perturbation of the plasma with an equivalent perturbation of surface current on a spatially fixed plasma boundary, is used to derive a linear state space representation of the mode dynamics. The spatial and current perturbations are equivalent in the sense that they both produce the same magnetic field perturbation at surrounding conductors. The key term in the model characterizing the magnitude of the instability is the time-varying uncertain parameter cpp, which is related to the RWM growth rate gamma. Taking advantage of the structure of the state matrices, the model is reformulated into a robust control framework, with the growth rate of the RWM modeled as an uncertain parameter. A robust controller that stabilizes the system for a range of practical growth rates is proposed. The controller is tested through simulations, which demonstrates significant performance increase over the classical PD controller, extending the RWM growth rate range for which the system is stable and satisfies predefined performance constraints, and increasing the level of tolerable measurement noise. The simulation study shows that the proposed model-based DK controllers can successfully stabilize the mode when the growth rate vary over time during the discharge due to changes in the operating conditions such as pressure and rotation. In terms of robust stability, this method eliminates the need of growth rate online identification and controller scheduling.