Synthesis and operation of an FFT-decoupled fixed-order reversed-field pinch plasma control system based on identification data

Abstract

Recent developments and applications of system identification methods for the reversed-field pinch (RFP) machine EXTRAP T2R have yielded plasma response parameters for decoupled dynamics. These datasets are the fundament for a real-time implementable fast fourier transform (FFT) decoupled discrete-time fixed-order strongly-stabilizing synthesis as described in this work. Robustness is assessed over the dataset by bootstrap calculation of the sensitivity transfer function worst-case H∞-gain distribution. Output-tracking and magnetohydrodynamic (MHD) mode m = 1-tracking is considered in the same framework simply as two distinct weighted traces of a performance channel output-covariance matrix as derived from the closed-loop discrete-time Lyapunov equation. The behaviour of the resulting multivariable controller is investigated with dedicated T2R experiments.

Tearing mode velocity braking due to resonant magnetic perturbations

“…In EXTRAP T2R, the shell behaves almost like an ideal wall due to the fast TM rotation and the amplitude of the radial component of the core TMs is very small at the shell. In figures 1(a) and (b) respectively the time evolution of the plasma current and of the radial component of the magnetic perturbations is shown for a shot with no external perturbation applied but in which the feedback works with the revised intelligent shell algorithm [26] to suppress all the RWMs and error fields. With no feedback, all the harmonics corresponding to the RWMs and to the error fields grow up to 0.2-0.3 mT leading to the termination of the discharge at approximately 15 ms [22].…”

“…Some RFP devices [22,23] are equipped with a large number of active coils that allow the generation of external perturbations with a well defined and clean spectrum that make them useful machines for the study of tokamak-relevant underlying physics related to resonant and non-resonant perturbations [24]. Feedback algorithms based on modern control theory recently implemented on the EXTRAP T2R RFP allow the suppression of RWMs and error fields and the simultaneous application of a selected external magnetic perturbation harmonic [25][26][27][28]. The user can decide the desired spectrum of the external perturbations (both amplitude and phase time evolution) and the feedback will reproduce these reference signals at the plasma boundary [24].…”

Implementation of advanced feedback control algorithms for controlled resonant magnetic perturbation physics studies on EXTRAP T2R

“…Hereafter W DFT represents the matrix that performs the linear FFT. The FFT-decoupled control system considered here is [33…”

“…In this paper we will describe from a physics perspective two new feedback algorithms implemented in EXTRAP T2R that allow the suppression of RWMs and error fields and allow the simultaneous application of any selected external magnetic perturbation harmonic in a controlled fashion. These algorithms are described from a control theory point of view in [32,33]. With these new tools, the user will decide the desired spectrum of the external perturbations (both amplitude and phase time evolution) and the feedback will be able to reproduce these reference signals at the plasma boundary.…”

Braking due to non-resonant magnetic perturbations and comparison with neoclassical toroidal viscosity torque in EXTRAP T2R

“…EXTRAP T2R [25] is equipped with an array of control coils [26,27] that allow the suppression of RWMs and error fields. The system can generate an external magnetic perturbation with a single (m,n) harmonic [27][28][29], i.e. with negligible sideband components (m and n are the poloidal and toroidal mode number respectively).…”