Nonlinear Sliding Mode Control of the Current Density Profile in Tokamaks
M. Lauret, E. Schuster
Symposium on Fusion Technology
Prague, Czech Republic, September 5-9, 2016
Abstract
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Research on fusion plasmas in tokamaks has led to the insight that the
poloidal magnetic- flux distribution within the plasma has a crucial
impact on its performance. Achieving certain types of poloidal
magnetic-flux profiles, or alternatively certain types of q profiles,
leads to resilience against undesirable instabilities and to higher
bootstrap- current fractions, which in turns favor steady-state
operation. To reliably and repeatedly achieve a desired q profile,
feedback control is needed. Extensive work has been recently going on
towards the development of q-profile feedback controllers. The
nonlinearity of the plasma and the coupling between magnetic and
kinetic variables demand a model- based control approach based on the
magnetic-flux diffusion equation (MDE). The MDE is a nonlinear partial
differential equation (PDE) modeling the time evolution of the poloidal
magnetic-flux profile, and therefore of the q profile. Due to the
complexity of the MDE, much of the previous work in this area used a
linearized version of it for control design. While linear control
approaches proved themselves effective in experiments, there is
potential for improved performance by avoiding linearization and using
the knowledge embedded in the nonlinear model to its fullest extent.
One of the challenges associated with the design of model-based nonlinear
q-profile feedback controllers arises from the fact that the model is
non-affine in control, i.e. the q-profile dynamics depend nonlinearly
on the control inputs (e.g., total plasma current and H&CD powers). In
this work, we develop and test in simulations a nonlinear sliding mode
controller for q-profile regulation that takes into account all the
nonlinearities of the model. Assessment of the robustness of the proposed
controller against unmodeled dynamics and perturbations, which is in
general an advantageous characteristic of sliding mode controllers, is
also part of this work.