A tutorial on inversion-based shape control with design application to NSTX-U

Abstract

One of the most common designs for magnetic control in tokamaks is to ``linearize an equilibrium'' to obtain a sensitivity mapping, then invert this mapping in order to determine the feedback control currents or voltages. For this work, we refer to this broad class of methods as inversion-based shape control (IBSC). In this work we describe the IBSC framework in a comprehensive manner and show how variations such as using dynamic voltage mappings and quadratic-program constrained control fit naturally into the framework. Despite the prevalence of IBSC, some of these extensions and the challenges associated with specific variations of IBSC are less widely known. We pay special attention to the challenge of decoupling the interaction between shape control and vertical control, which was a source of degraded vertical control performance on NSTX-U. This work is intended to provide a systematic overview of IBSC, and to that end, we have provided background material, proposed design procedures, and tutorials on the magnetic control design process within the appendices. Applying the systematic design procedure to NSTX-U, we find that the vertical control bobble on NSTX-U can be removed via decoupling, and that the vertical control phase margin can be improved by 6 degrees just by including PF1A and PF2 as vertical actuators.