Nonlinear control in fusion reactors

There is consensus in the fusion reactor community that active control will be one of the key enabling technologies. With further advancements in reduced-order fusion modeling, advances in control systems for fusion will continue, including vertical and shape control, kinetic and current profile control, MHD (magnetohydrodynamic) stabilization and plasma transport reduction. This dissertation addresses different control problems in tokamaks using as common denominator a nonlinear control approach. Contributions are made in the areas of kinetic control, magnetic control, and MHD flow control.; In the area of kinetic control, we approach the problem of nonlinear control of burn instability in fission reactors, where a lumped-parameter nonlinear model involving approximate conservation equations for the energy and the densities of the species is used to synthesize a nonlinear feedback controller (backstepping, feedback linearization, passivity and input to state stability) for stabilizing the thermally unstable burn condition of a fusion reactor. In addition, the problem of control of kinetic profiles in non-burning plasmas, where a set of nonlinear partial differential equations (PDE's) describing approximately the dynamics of the density and energy was considered as the plant model used to synthesize a boundary controller (infinite-dimensional nonlinear backstepping) whose goal was the control of the density and energy spatial distributions, is also considered.; In the area of magnetic control, the problem of plasma vertical position stabilization and shape control under actuation saturation in the DIII-D Tokamak at General Atomics is approached. In this case, modifications of the nominal control loops (nonlinear anti-windup augmentation) are proposed to ensure stability of the plant and good behavior of the nominal controller under the presence of voltage saturation in the coils that are used to vertically position and shape the plasma inside the tokamak.; In the area of MHD flow control, we consider the problem of mixing enhancement in an MHD liquid-metal blanket. A control law (nonlinear Lyapunov-based boundary control) is proposed for mixing enhancement in a magnetohydrodynamic (MHD) channel flow, also known as Hartmann flow. This flow is characterized by an electrically conducting fluid moving between parallel plates in presence of an externally imposed transverse magnetic field. The system is described by the MHD equations, a combination of the Navier-Stokes equation and the Maxwell equations under the so-called MHD approximation. Micro-jets and pressure and magnetic field sensors embedded into the walls of the flow domain are considered in this work to find a feedback control law that is optimal with respect to a cost functional related to mixing measure.