Model-Based Robust Control of Resistive Wall Modes via Synthesis

In this work, synthesis is employed to stabilize a model of the resistive wall mode (RWM) instability in the DIII-D tokamak. The General Atomics/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 c_pp, which is related to the RWM growth rate . 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, demonstrating significant performance increase over the classical proportional-derivative 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 varies over time during the discharge because of changes in the operating conditions such as pressure and rotation. In terms of robust stability, this method eliminates the need for growth-rate online identification and controller scheduling.

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