Data-driven Robust Control of the Plasma Rotational Transform Profile and Normalized Beta Dynamics for Advanced Tokamak Scenarios in DIII-D
W. Shi, W. Wehner, J. Barton, M.D. Boyer, E. Schuster, D. Moreau, M.L. Walker, J.R. Ferron, T.C. Luce, D.A. Humphreys, B.G. Penaflor and R.D. Johnson
Fusion Engineering and Design, 117 (2017) 39–57
Abstract
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A control-oriented, two-timescale, linear, dynamic, response model of
the rotational transform profile and the normalized beta is proposed
based on experimental data from the DIII-D tokamak. Dedicated
system-identification experiments without feedback control have been
carried out to generate data for the development of this model. The
data-driven dynamic model, which is both device-specific and
scenario-specific, represents the response of the iota profile and the
normalized beta to the electric field due to induction as well as to
the heating and current drive (H&CD) systems during the flat-top phase
of an H-mode discharge in DIII-D. The control goal is to use both
induction and the H&CD systems to locally regulate the plasma iota
profile and the normalized beta around particular target values close
to the reference state used for system identification. A singular
value decomposition (SVD) of the plasma model at steady state is
carried out to decouple the system and identify the most relevant
control channels. A mixed-sensitivity robust control design problem is
formulated based on the dynamic model to synthesize a stabilizing
feedback controller without input constraints that minimizes the
reference tracking error and rejects external disturbances with minimal
control energy. The feedback controller is then augmented with an
anti-windup compensator, which keeps the given controller well-behaved
in the presence of magnitude constraints in the actuators and leaves
the nominal closed-loop system unmodified when no saturation is present.
The proposed controller represents one of the first feedback profile
controllers integrating magnetic and kinetic variables ever implemented
and experimentally tested in DIII-D. The preliminary experimental
results presented in this work, although limited in number and
constrained by actuator problems and design limitations, as it will be
reported, show good progress towards routine current profile control
in DIII-D and leave valuable lessons for further advancements in the
field.