Vector dither experiment design and direct parametric identification of reversed-field pinch normal modes

Olofsson, Erik; Hjalmarsson, Håkan; Rojas, Cristian R.; Brunsell, Per R.; Drake, James R.

doi:10.1109/cdc.2009.5400016

Cited by 12 publications

(20 citation statements)

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“…Specifically, this paper continues the results from [14], [17], and [18] as follows. The retooled controller of [14] is used to run the experiments described in [17] and [18]. Data from [17] and [18] have not been previously used for improved control design.…”

Section: Introductory Overviewmentioning

confidence: 86%

“…The superscript r betokens the radial magnetic-field component, and B r,ext m,n is a driving term typically dichotomized B r,ext m,n = B r,err m,n + B r,app m,n , i.e., the separation of error-field effects and externally applied (known, originating from actuator saddle coils) field. The idea in [17] and [18] is to assume that B r,err m,n is a low-frequency term that is absorbed by the integrator in the controller [14]. Identification data are then acquired from a situation where B r,ext m,n ≈ 0 since B r,app m,n becomes a superposition of a zero-mean dithering signal and a relatively static component ≈ −B r,err m,n .…”

Section: Closed-loop Direct Parametric System Identificationmentioning

confidence: 99%

“…The retooled controller of [14] is used to run the experiments described in [17] and [18]. Data from [17] and [18] have not been previously used for improved control design. This important connecting step is taken here.…”

Section: Introductory Overviewmentioning

confidence: 99%

“…Thus, modeling ends at an expression of the superimposed sum of independent dynamical systems for each spatial array signal Fourier component. After modeling, the best experimental parameters for this model are obtained by novel MHD measurements utilizing weak perturbations on all eigenmodes concurrently [17], [18]. At this stage, a bundle of linear models (with some parameter spread) is acquired for which feedback controllers are designed.…”

Section: Introductory Overviewmentioning

confidence: 99%

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

Erik

Olofsson

Brunsell

2010

IEEE Trans. Plasma Sci.

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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...

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Section: Introductory Overviewmentioning

confidence: 86%

Section: Closed-loop Direct Parametric System Identificationmentioning

confidence: 99%

Section: Introductory Overviewmentioning

confidence: 99%

Section: Introductory Overviewmentioning

confidence: 99%

See 2 more Smart Citations

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

Erik

Olofsson

Brunsell

2010

IEEE Trans. Plasma Sci.

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“…Spearheaded by [13] already 25 years ago, there has been a clear shift from general purpose design criteria such as Doptimal and E-optimal design to applications oriented design criteria [4]; there are for example methods emerging for as diverse applications as deconvolution [14], fusion reactors [15], magnetic resonance imaging, and MPC [16].…”

Section: Introductionmentioning

confidence: 99%

Input design using cylindrical algebraic decomposition

Hjalmarsson

Egebrand

2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract-Experiment design for system identification has seen significant progress in the last decade. One contribution has been to derive convex relaxations of such problems. Consider that only a scalar function of the system parameters is of interest. A standard step in such a case is to first linearize this function with respect to the estimated parameters. The objective of this contribution is twofold: firstly, to examine if there are cases where the linearized approximation is inadequate, and secondly to explore how to improve upon this approximation. By way of examples we show that it is not difficult to construct examples where linearization is insufficient. Furthermore, we introduce the use of higher order approximations and we formally show that this leads to polynomial optimization problems under Gaussian assumptions. We propose the use of cylindrical algebraic decomposition as a method to obtain exact solutions for this type of problems. Numerical examples are provided.

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