Stability analysis and model-based control in EXTRAP-T2R with time-delay compensation

Olofsson, Erik; Witrant, Emmanuel; Briat, Corentin; Niculescu, Silviu‐Iulian; Brunsell, Per R.

doi:10.1109/cdc.2008.4738882

Cited by 7 publications

(7 citation statements)

References 16 publications

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“…Notably, the matrix weight V (i) z implies direct-outputvariance minimization, which is, in essence, an IS equivalent [14], [15], [32], [33], whereas the weight V (ii) z of (8) is analogous to the ideas of clean-mode control (CMC), as inaugurated in [34]. This can be understood as follows.…”

Section: A Closed-loop System Performancementioning

confidence: 98%

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: A Closed-loop System Performancementioning

confidence: 98%

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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“…Notably, the matrix weight V (i) z implies direct output variance minimization, in essence an intelligent-shell (IS) equivalent [15], [14], [29], [30], whereas weight V (ii) z of (7) is analogous to the ideas of clean-mode control (CMC) as inaugurated in [31].…”

Section: Static Decoupling Discrete-time Fixed-order Controller mentioning

confidence: 99%

Closed-loop identification and controller reconfiguration for EXTRAP T2R reversed-field pinch

Olofsson¹,

Brunsell²

2009

2009 23rd IEEE/NPSS Symposium on Fusion Engineering

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We briefly summarize a supposedly efficient novel method for measuring the external plasma response as applied to the inherently unstable reversed-field pinch EXTRAP T2R. The set of parameters estimated with this particular method is then harvested and fed as input to a discrete-time fixed-order fast fourier transform decoupled multi-input-multi-output controller synthesis. The thus reconfigured feedback system is implemented and experimentally tested on the real plant T2R. A particular and intended behaviour is observed, it seems, from these firstdeployment results. I. INTRODUCTORYOVERVIEW Robust controller synthesis and simulations have been worked out for e.g. the DIII-D Tokamak [1] in the case of RWMs. Apparently, to properly do control system synthesis availability of some plant model 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], [3], [4], [5], [6], and also computational results on the effect of 3D external conducting structures on growth-rates, eddies and eigenmode geometry [7], [8]. Significant efforts and interest is spent on the topic of realistic experimental-conditions MHD dynamics 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. Typical parameters for T2R [9] are I p = 100 kA, R = 124 cm and a = 18 cm. A speciality of T2R is feedback control of magnetohydrodynamic (MHD) instabilities including the resistive-wall mode (RWM). Theoretically, given the geometry and dimensions of T2R and the RFP equilibria, the normalmodes spectrum of magnetic perturbations express ∼ 15 unstable solutions [10], [11], [3]. Experimentally, they have all been shown to be simultaneously suppressable [12], [13]. More recently, 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 algorithm of [15], [16].The role of this particular work is to carefully develop a fourier mode decoupled plasma control system, yet another recycling of the mode-controller (MC) concept, in a partially automated manner.MHD control research at T2R strives to generate results not only relevant to RFPs, but also to macroscopic plasma dynamics in general with particular focus on Tokamaks. For example, RWMs in Tokamaks are typically more involved than the nonresonant RWM perturbation in RFPs, which for the latter is current-driven and present for all β. Tokamak RWMs in contrast, are resonant and grows while rotating with respect to the vessel, as well as being pressure-driven, i.e. triggered by high-β. Although different in detail RFP and Tokamak RWMs are basically different instances of the same underlying physical principles and T2R is a highly versa...

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“…Additionally, F P ID (s) is a diagonal proportional-integral-derivative (PID) [18] controller; tuned [3], symptomatically, without knowledge of the experimental plasma response. The study [19] also had this weakness: no available experimental values for plasma growth-rates, albeit the theoretical shape of the RFP spectrum was considered in this design. In principle the counterworking actuator response could be improved by harnessing knowledge of the spatial structure of the perturbation.…”

Section: Background and Setting: The Intelligent-shell And Mode-controlmentioning

confidence: 99%

“…are derived from (5), (6) and (7). System F is constructed by zero-order-hold discretization F (z) of the continuous-time representation of the bundled amplifier plus coil model F (s) = kF τF s+1 , where k F = 4.1 and τ F = 1.1 × 10 −3 s. A onesample delay augmentation to account for computational latency [19,7] then defines actuation-block F (z) = z −1 F (z). The state space equivalent of F (z) is (A F , B F , C F ).…”

Section: Instantiation Of System Matrices For T2rmentioning

confidence: 99%

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

Olofsson¹,

Brunsell²,

Witrant³

et al. 2010

Plasma Phys. Control. Fusion

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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.

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Stability analysis and model-based control in EXTRAP-T2R with time-delay compensation

Cited by 7 publications

References 16 publications

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

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

Closed-loop identification and controller reconfiguration for EXTRAP T2R reversed-field pinch

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

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