Backstepping Control of Density and Energy Profiles in a Burning Tokamak Plasma
M.D. Boyer and E. Schuster
50th IEEE Conference on Decision and Control
Orlando, Florida, December 12-15, 2011
Abstract
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The control of plasma density profiles is one of the most fundamental
problems in fusion reactors. During reactor operation, the spatial
profiles of deuterium-tritium fuel, alpha-particles generated by f
usion reactions, and energy must be precisely regulated. Here we apply
a backstepping boundary control technique to stabilize an unstable
equilibrium in a burning plasma. A one-dimensional approximation of
the transport equation for energy as well as the density of
deuterium-tritium fuel ions and alpha-particles is represented in
cylindrical coordinates by a system of partial differential equations
(PDEs). To control the ion and energy density profiles, the PDE system
is discretized in space using a finite difference method and a
backstepping design is applied to obtain a discrete transformation
from the original system into an asymptotically stable target system.
Numerical simulations of the resulting boundary control law show that
the profiles can be successfully controlled with just one step of
backstepping.