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
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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.