Optimal Current Profile Control for Enhanced Repeatability of L-mode and H-mode Discharges in DIII-D
W.P. Wehner, J.E. Barton, E. Schuster, C.T. Holcomb, T.C. Luce, J.R. Ferron, M.L. Walker, D.A. Humphreys, B.G. Penaflor, R.D. Johnson
Symposium on Fusion Technology
Prague, Czech Republic, September 5-9, 2016
Abstract
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To collect meaningful experimental data, it is necessary to maintain
consistent operating conditions in the tokamak plasma across repeated
discharges. Presently, the desired plasma formation conditions, such
as the shape of the plasma current profile, are achieved in a trial
and error fashion, which can be a lengthy, wasteful process. In this
work, model-based control techniques including optimal feedforward
control and linearized feedback control are used to obtain a desired
current profile at a specified time in low-confinement-mode (L-mode)
as well as high-confinement-mode (H-mode) discharges. The evolution of
the current profile is closely related to the evolution of the poloidal
magnetic flux profile, which can be properly modeled in a
first-principles manner by a nonlinear partial differential equation
(PDE) referred to as the magnetic flux diffusion equation (MDE).
Simplified, control-oriented formulations of the magnetic diffusion
equation have already been developed for the DIII-D tokamak for both
L-mode and H-mode discharges. In both cases, the control-oriented models
combine the MDE with physics-based correlations for the electron
temperature, plasma resistivity, and non-inductive current drive sources
including neutral beam injection (NBI), electron cyclotron current
drive (ECCD), and bootstrap current drive. With the use of these models,
an open-loop control problem, i.e. an actuator trajectory optimization
problem, is formulated to find a feasible path from the expected initial
condition to the desired target. The result comprises a sequence of
feedforward (open-loop) control requests and a corresponding state
evolution from the initial condition to the desired target. On top of
this optimal feedforward control sequence an optimal state feedback
(closed-loop) controller based on a linearized model is added to track
the desired state evolution. Experimental evidence of the effectiveness
of the control approach in reaching the targets and facilitating
repeatability between discharges is presented.