Toroidal Current Profile Control During Low Confinement Mode Plasma Discharges in DIII-D via First-Principles-Driven Model-based Robust Control Synthesis
J. Barton, M.D. Boyer, W. Shi, E. Schuster, T.C. Luce, J.R. Ferron, M.L. Walker, D.A. Humphreys, B.G. Penaflor and R.D. Johnson
Nuclear Fusion 52 (2012) 123018 (24pp)
Abstract
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In order for ITER to be capable of operating in advanced tokamak operating regimes, characterized by a high fusion
gain, good plasma confinement, magnetohydrodynamic stability, and a non-inductively driven plasma current, for
extended periods of time, several challenging plasma control problems still need to be solved. Setting up a suitable
toroidal current density profile in the tokamak is key for one possible advanced operating scenario characterized by
non-inductive sustainment of the plasma current. At the DIII-D tokamak the goal is to create the desired current
profile during the ramp-up and early flat-top phases of the plasma discharge and then actively maintain this target
profile for the remainder of the discharge. The evolution in time of the toroidal current profile in tokamaks is
related to the evolution of the poloidal magnetic flux profile, which is modeled in normalized cylindrical
coordinates using a first-principles, nonlinear, dynamic partial differential equation (PDE) referred to as the
magnetic diffusion equation. The magnetic diffusion equation is combined with empirical correlations developed from
physical observations and experimental data from DIII-D for the electron temperature, the plasma resistivity, and
the non-inductive current drive to develop a simplified, control-oriented, nonlinear, dynamic PDE model of the
poloidal flux profile evolution valid for low confinement mode discharges. In this work, we synthesize a robust
feedback controller to reject disturbances and track a desired reference trajectory of the poloidal magnetic flux
gradient profile by employing the control-oriented model of the system. A singular value decomposition of the static
gain matrix of the plant model is utilized to identify the most relevant control channels and is combined with the
dynamic response of system around a given operating trajectory to design the feedback controller. A general framework
for real-time feedforward + feedback control of magnetic and kinetic plasma profiles was implemented in the DIII-D
Plasma Control System and was used to demonstrate the ability of the feedback controller to control the toroidal
current profile evolution in the DIII- D tokamak. These experiments constitute the first time ever a
first-principles-driven, model-based, closed-loop magnetic profile controller was successfully implemented and
tested in a tokamak device.