Optimal and Constrained Magnetic Control for Tokamak Early Operations and Commissioning

Nuclear fusion is projected to be the future clean and sustainable source of energy. The research is intense and has broken several records in terms of the power and length of fusion reactions. This dissertation is centered on tokamaks, toroidal-shaped devices developed to confine the high-temperature and energy plasma (a perfectly ionized gas) exploiting magnetic fields. In tokamaks, the necessity to have a stable, high performing plasma leads to a high interest in plasma control, in particular in plasma magnetic control, that needs to control the plasma shape and/or centroid position, plasma current, and to guarantee plasma vertical stability. The future reactors are expected to be much larger than the current ones, making necessary careful planning and testing of capability to lower the risk of accidents that could lead to serious damage of the machine and delays. The preparatory work consists in developing and testing all the plant functionality using engineering designed code: to model plasma scenario, the simultaneous solution of the Grad-Shafranov equations and the time evolution of the plasma kinetic profiles is needed. To achieve the desired plasma evolution during ramp-up while staying within safe operational limits (such as the reduced active current and voltage limits typically applied during commissioning phases), a combination of feedforward and feedback control actions is essential. In this thesis, the development of a new model-based procedure for the constrained optimization of plasma ramp-up, called the CREATE-ILC code (an enhancement of the CREATE-BD code), is presented. This tool formulates a constrained quadratic programming problem and employs a linear time-varying electromagnetic model to generate active currents and voltages that ensure the desired breakdown and ramp-up phases, while adhering to the imposed constraints. Given that model-based approaches are sensitive to uncertainties and disturbances, an Iterative Learning Control (ILC) strategy is incorporated to handle discrepancies between the desired and experimental behaviors. The CREATE-ILC’s ability to optimize ramp-up currents is anticipated to be validated during the MAST-U tokamak RT-04 experimental campaign. Although the nominal scenario can be programmed to respect current and voltage saturation limits, the feedback control architecture, which compensates for model uncertainties and disturbances, may inadvertently cause active currents to exceed these limits. To mitigate this risk, three Current Limit Avoidance (CLA) algorithms, designed for integration within the magnetic control architecture, are proposed. These algorithms replace any currents that exceed saturation limits with a pattern that minimizes performance degradation. The CLA based on a quadratic programming algorithm has already been experimentally validated during the TCV tokamak RT-04 experimental campaign. When designing a scenario, the plasma evolution must also account for the heat fluxes impacting the machine, as the distribution of these fluxes on the first wall is closely tied to the plasma's magnetic characteristics. The thermal model used to numerically program the scenario is subject to modeling errors, and it is expected that these will be better characterized during the early stages of commissioning. This introduces the risk that pre-programmed scenarios could surpass the desired temperature, necessitating scenario adjustments to meet specifications. To address this, we propose a first wall temperature controller, consisting of an outer loop integrated with the classical magnetic control architecture, which applies limited plasma shape and active current variations to reduce heat fluxes as needed. This approach, with limited online plasma corrections, could prevent delays due to scenario re-tuning. Additionally, the control strategy can be applied during full-power plasma operation, where plasma power and heat fluxes are expected to be significantly higher.