Closed-Loop System Identification and Controller Reconfiguration for EXTRAP T2R Reversed-Field Pinch

Abstract

We first briefly summarize a supposedly efficient novel method for measuring the external plasma response as applied to the inherently unstable reversed-field pinch EXTRAP T2R. Second, the set of parameters estimated with this particular method is harvested and fed as input to a discrete-time fixed-order fast-Fourier-transform-decoupled multi-input-multioutput controller synthesis. The thus reconfigured feedback system is implemented and experimentally tested on the real plant T2R. The recorded first-deployment results are encouraging. The overall methodology followed throughout this paper is emphasized and strongly exemplifies applied process control thinking for the stabilization of magnetically confined toroidal plasmas.Index Terms-Magnetic confinement fusion, plasma control, system identification. I. INTRODUCTORY OVERVIEWR OBUST CONTROLLER synthesis and simulations have been worked out for, e.g., the DIII-D Tokamak [1] in the case of resistive-wall modes (RWMs). Apparently, to do control system synthesis properly, the availability of some plant models is needed. Minimal requirements include (vague) bounds on important parameters in a plausible model structure. There are several studies of external plasma response measurements in the literature [2]-[6] and also computational results on the effect of 3-D external conducting structures on growth rates, eddies, and eigenmode geometry [7], [8]. Significant efforts and interest are spent on the topic of realistic experimentalcondition magnetohydrodynamics (MHD) and the associated control issues.Hosted by the Alfvén Laboratory at the Royal Institute of Technology (KTH) in Stockholm, Sweden, the reversed-field pinch (RFP) machine EXTRAP T2R is armed with dense arrays of saddle-shaped coils, both sensors and actuators. Basic parameters for T2R [9] are I p ∼ 100 kA, R = 124 cm, and a = 18 cm. Both sensor and actuator coil arrays are 4 × 32 sized, meaning that the poloidal angle is subdivided in four coil positions and the toroidal angle is subdivided in 32 coil positions. Currently, to save both analog and digital channels, as well as power supplies, the signals are respectively subtracted pairwise horizontally and vertically. This makes the sensor-array input and actuator output sizes equal to 64, but also renders even m mode numbers impossible to detect and affect. The unstable spectrum of T2R is constituted by m = 1 modes with small |n| (m is the poloidal mode-number, and n is the toroidal mode number).A specialty of T2R is the feedback control of MHD instabilities including the RWM. Theoretically, given the geometry and dimensions of T2R and the RFP equilibria, the normal-mode spectrum of magnetic perturbations express ∼15 unstable solutions [3], [10], [11]. Experimentally, they have all been shown to be simultaneously suppressible [12], [13]. More recently, the experimental verification of stabilized sustained nonaxisymmetrical perturbations to the plasma column has been produced [14] in essence by merely rehashing and refurbishing the classic active shell algorit...

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

“…If the reference signal of a harmonic resonant in the plasma is not zero, a RMP is generated. With the dither-injection capability [43], the user can work in the IS algorithm but simultaneously adding small amplitude random perturbations to the actuators. The dither injection is an essential tool for the data-driven system identification, as described later.…”

“…where τ m,n is the diffusion time through a passive resistive cylindrical shell, γm,n is the normalized growth rate and b app m,n represents the external perturbations applied by the actuators. Performing the discretization in time of equation ( 11) an expression for G m,n is obtained [43]:…”

“…Second, equation ( 4) is a MIMO system, while equation ( 13) is a SISO system having as input only I m,n and as output only b m,n . The controller matrix F dec is determined in order to minimize the variance of the output signal [43]…”

Tearing mode velocity braking due to resonant magnetic perturbations

“…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].…”