"Control of the Safety Factor Profile in a Tokamak" uses
Lyapunov techniques to address a challenging problem for which even
the simplest physically relevant models are represented by
nonlinear, time-dependent, partial differential equations (PDEs).
This is because of thespatiotemporal dynamics of transport
phenomena (magnetic flux, heat, densities, etc.) in the anisotropic
plasma medium.
Robustness considerations are ubiquitous in the analysis and
control design since direct measurements on the magnetic flux are
impossible (its estimation relies on virtual sensors) and large
uncertainties remain in the coupling between the plasma particles
and the radio-frequency waves (distributed inputs).
The Brief begins with a presentation of the reference dynamical
model and continues by developing a Lyapunov function for the
discretized system (in a polytopic linear-parameter-varying
formulation). The limitations of this finite-dimensional approach
motivate new developments in the infinite-dimensional framework.
The text then tackles the construction of an
input-to-state-stability Lyapunov function for the
infinite-dimensional system that handles the medium anisotropy and
provides a common basis for analytical robustness results. This
function is used as a control-Lyapunov function and allows the
amplitude and nonlinear shape constraints in the control action to
be dealt with.
Finally, the Brief addresses important application- and
implementation-specific concerns. In particular, the coupling of
the PDE and the finite-dimensional subsystem representing the
evolution of the boundary condition (magnetic coils) and the
introduction of profile-reconstruction delays in the control loop
(induced by solving a 2-D inverse problem for computing the
magnetic flux) is analyzed. Simulation results are presented for
various operation scenarios on Tore Supra (simulated with METIS)
and on TCV (simulated with RAPTOR).
"Control of the Safety Factor Profile in a Tokamak" will be of
interest to both academic and industrially-based researchers
interested in nuclear energy and plasma-containment control
systems, and graduate students in nuclear and control
engineering."
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