Enhancing the control of tokamaks via a continuous nonlinear control law

The control of the current, position and shape of an elongated cross-section tokamak plasma is complicated by the instability of the plasma vertical position. In this case the control becomes a significant problem when saturation of the power supplies is considered. Current saturation is relatively benign due to the integrating nature of the tokamak, resulting in a reasonable time horizon for strategically handling this problem. On the other hand, voltage saturation is produced by the feedback controller itself, with no intrinsic delay. In practice, during large plasma disturbances, such as sawteeth, ELMs and minor disruptions, voltage saturation of the power supply can occur and as a consequence the vertical position control can be lost. If such a loss of control happens the plasma displaces vertically and hits the wall of the vessel, which can cause damage to the tokamak. The consideration and study of voltage saturation is especially important for ITER. Due to the size and therefore the cost of ITER, there will naturally be smaller margins in the Poloidal Field coil power supplies implying that the feedback will experience actuator saturation during large transients due to a variety of plasma disturbances. The next generation of tokamaks under construction will require vertical position and active shape control and will be fully superconducting. When the magnetic transverse field in superconducting magnets changes, the magnet generates two types of heat loss, the so-called coupling loss and the so-called hysteresis loss, grouped together as AC losses. Superconducting coils possess superconducting properties only below a critical temperature around a few K. AC losses are detrimental since they heat up the superconducting material. Thus, if AC losses are too large, the cryogenic plant can no longer hold the required temperature to maintain the superconductivity properties. Once the superconductivity is lost, the electric currents in the coils produce an enormous heat loss due to the ohmic resistivity, which can lead to a possible damage to the coils. In general, the coils are designed with enough margin to absorb all likely losses. A possible loss reduction could allow us to downsize the superconducting cross section in the cables, reducing the overall cost, or simply increase the operational cooling margin for given coils. In this thesis we have tried to take into consideration these two major problems. The thesis is therefore focused on the following main objectives: i) the stability analysis of the tokamak considering voltage saturation of the power supplies and ii) the proposition of a new controller which enhances the stability properties of the tokamak under voltage saturation and iii) the proposition of a controller which takes into consideration the problem of reducing the AC losses. The subject of the thesis is therefore situated in an interdisciplinary framework and as a result the thesis is subdivided into two principal parts. The fir