Simultaneous feedback control of toroidal magnetic field and plasma current on MST using advanced programmable power supplies

Programmable control of the inductive electric field enables advanced operations of reversed-field pinch (RFP) plasmas in the Madison Symmetric Torus (MST) device and further develops the technical basis for ohmically heated fusion RFP plasmas. MST's poloidal and toroidal magnetic fields ($B_\text{p}$ and $B_\text{t}$) can be sourced by programmable power supplies (PPSs) based on integrated-gate bipolar transistors (IGBT). In order to provide real-time simultaneous control of both $B_\text{p}$ and $B_\text{t}$ circuits, a time-independent integrated model is developed. The actuators considered for the control are the $B_\text{p}$ and $B_\text{t}$ primary currents produced by the PPSs. The control system goal will be tracking two particular demand quantities that can be measured at the plasma surface ($r=a$): the plasma current, $I_\text{p} \sim B_\text{p}(a)$, and the RFP reversal parameter, $F\sim B_\text{t}(a)/\Phi$, where $\Phi$ is the toroidal flux in the plasma. The edge safety factor, $q(a)\propto B_t(a)$, tends to track $F$ but not identically. To understand the responses of $I_\text{p}$ and $F$ to the actuators and to enable systematic design of control algorithms, dedicated experiments are run in which the actuators are modulated, and a linearized dynamic data-driven model is generated using a system identification method. We perform a series of initial real-time experiments to test the designed feedback controllers and validate the derived model predictions. The feedback controllers show systematic improvements over simpler feedforward controllers.