Burn Control in Fusion Reactors Using Simultaneous Boundary and Distributed Actuation
M. D. Boyer and E. Schuster
52nd IEEE Conference on Decision and Control
Florence, Italy, December 10-13, 2013
Abstract
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The control of the plasma density and temperature profiles is one of
the fundamental problems in nuclear fusion reactors. During reactor
operation, the spatial profiles of deuterium-tritium fuel, alpha
particles generated by fusion reactions, and energy must be precisely
regulated. In this work we combine distributed actuation with a
backstepping boundary control law to stabilize an unstable equilibrium
in a burning plasma. Disturbance estimation update laws are included
to improve disturbance rejection and tracking. A one-dimensional
approximation of the transport equation for energy, as well as for the
densities of deuterium-tritium fuel ions and alpha particles, is
represented in cylindrical coordinates by a system of partial
differential equations (PDEs). 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 a
particular target system chosen to facilitate the use of additional
actuators distributed throughout the plasma. Numerical simulations
show that a controller designed on a very coarse grid can stabilize
the system and that distributed actuation improves the system response.