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Fusion Engineering and Design 88 (2013) 1091– 1096

Contents lists available at ScienceDirect

Fusion Engineering and Design

journa l h om epa ge: www.elsev ier .com/ locat e/ fusengdes

inearized models for a new magnetic control in MAST

. Artasersea,∗, F. Mavigliab, R. Albaneseb, G.J. McArdlec, L. Pangionec

Associazione Euratom-ENEA sulla Fusione, Via Enrico Fermi 45, I-00044 Frascati (RM), ItalyAssociazione Euratom-ENEA-CREATE sulla Fusione, Via Claudio 21, I-80125 Napoli, ItalyEURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK

i g h l i g h t s

We applied linearized models for a new magnetic control on MAST tokamak.A suite of procedures, conceived to be machine independent, have been used.We carried out model-based simulations, taking into account eddy currents effects.Comparison with the EFIT flux maps and the experimental magnetic signals are shown.A current driven model for the dynamic simulations of the experimental data have been performed.

r t i c l e i n f o

rticle history:vailable online 4 February 2013

eywords:AST

inearized modelokamakagnetic control

quilibriumtate space model

a b s t r a c t

The aim of this work is to provide reliable linearized models for the design and assessment of a newmagnetic control system for MAST (Mega Ampère Spherical Tokamak) using rtEFIT, which can easilybe exported to MAST Upgrade. Linearized models for magnetic control have been obtained using the 2Daxisymmetric finite element code CREATE L. MAST linearized models include equivalent 2D axisymmetricschematization of poloidal field (PF) coils, vacuum vessel, and other conducting structures. A plasmalessand a double null configuration have been chosen as benchmark cases for the comparison with experi-mental data and EFIT reconstructions. Good agreement has been found with the EFIT flux map and theexperimental signals coming from magnetic probes with only few mismatches probably due to brokensensors.

A suite of procedures (equipped with a user friendly interface to be run even remotely) to provide

linearized models for magnetic control is now available on the MAST linux machines.

A new current driven model has been used to obtain a state space model having the PF coil currentsas inputs. Dynamic simulations of experimental data have been carried out using linearized models,including modelling of the effects of the passive structures, showing a fair agreement. The modellingactivity has been useful also to reproduce accurately the interaction between plasma current and radial

position control loops.

. Introduction

MAST is a spherical tokamak (ST), which presents a compactcored apple” shape and a lower aspect ratio, up down symmet-ic usually operating in a double null divertor (DND) magneticonfiguration. Plasmas with elongated cross section are verticallynstable hence subjected to vertical displacement events (VDEs)hich affecting the tokamaks operation [1,2]. MAST is equippedith extensive and advanced diagnostics, with a digital control sys-

em which includes density feedback control and a novel opticalystem for plasma radial position control. Real time equilibriumeconstruction, based on rtEFIT [3], has been deployed in the

∗ Corresponding author. Tel.: +39 06 9400 5906; fax: +39 06 9400 5735.E-mail address: giovanni.artaserse@enea.it (G. Artaserse).

920-3796/$ – see front matter © 2013 Euratom-ENEA Association sulla Fusione. Publishedttp://dx.doi.org/10.1016/j.fusengdes.2012.12.033

© 2013 Euratom-ENEA Association sulla Fusione. Published by Elsevier B.V. All rights reserved.

control system. Reliable linearized models are necessary for thedesign and assessment of a new magnetic control system for MASTusing rtEFIT, which can easily be exported to MAST Upgrade.

In Section 2 of this paper the MAST machine modelling activityis introduced. The porting of the XSCTools to MAST is treated inSection 3. Benchmark cases are analyzed in Section 4 with dynamicsimulations including eddy currents, comparing the model predic-tions with flux map reconstructions and experimental magneticsignals. Summary and conclusions are given in Section 5.

2. MAST modelling

MAST has a central solenoid (P1), which provides the magneticflux used to control the plasma current, and a set of up downsymmetric PF coil sets (as shown in Fig. 1) connected by six inde-pendent circuits. The P2 coil can be used to achieve the desired DND

by Elsevier B.V. All rights reserved.

1092 G. Artaserse et al. / Fusion Engineering a

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Fig. 1. MAST upper part of poloidal field coils system.

onfiguration and compensate the stray field from the solenoid.he flux from the startup coil P3 is used to obtain the poloidal fieldull and then the breakdown. A vertical field is applied from the P4nd P5 coils, for the radial position control. Shape and elongationepend both on the plasma internal profile and how the totalertical field current is balanced between P4 and P5. The P6 coilsre connected in up-down anti-series and used exclusively forertical position feedback control. Metallic structures sources of

assive currents in MAST (see Fig. 2) are the vessel, the mechanicalupports and the PF coil cases, which are continuous.

The modelling activity carried out for this study uses a lin-arized dynamic model of MAST provided by 2D axisymmetric

Fig. 2. MAST upper part of the conducting structures.

nd Design 88 (2013) 1091– 1096

finite element method (FEM) code CREATE L [4]. The electro-magnetic model used to obtain the linearized model includes anequivalent 2D axisymmetric modelling of PF circuits, vacuum ves-sel, and other conducting structures. Both active and passive coilsare schematized with a dedicated set of circuit equations coupledto electromagnetic and magneto hydrodynamic (MHD) equations,in order to take into account the plasma presence.

As reported in [4], starting from a nonlinear form of the problem,the dynamics of active and passive conductors is determined bycircuit equations (where � is the poloidal flux per radian linkedto each circuit and R is the resistance matrix associated to eachcircuit):{

d /dt + R i = u

[ , y]T = �(i, w)(1)

linearizing Eq. (1) and assuming that the perturbed quantities areiı = i0 + i, uı = u0 + u, wı = w0 + w, yı = y0 + y (where i0, u0, w0 and y0are the reference values) we obtain{

L∗ di/dt + R i = u − L∗E dw/dt

y = C i + D w(2)

where L∗ = ∂ /∂i, L∗E = ∂ /∂w, C = ∂y/∂i, D = ∂y/∂w.

The linearized model (2) describes the electromagneticbehaviour of plasma surrounded by conducting structures and isvalid in the neighbourhood of an equilibrium point. The state vari-ables i are the coils (active and passive currents) and plasma currentIp; the inputs u are the applied voltages (or currents), whereaspoloidal beta ˇP and internal inductance �i play the role of distur-bances (non-controllable inputs w). The outputs y are field and fluxvalues and some basic plasma parameters of interest (plasma cur-rent moments, X point position, gaps, strike points, triangularity,elongation, etc.). Assuming:

x = i, A = −(L∗)−1R, B = (L∗)−1, E = −(L∗)−1L∗E

we obtain the state space form of (2) [4]:{dx/dt = A x + B u + E dw/dt

y = C x + D w(3)

L* is an inductance matrix modified by the presence of the plasmalinearization carried out using any MHD equilibrium code usingincremental ratios (e.g., ��/�i) or Jacobian matrix (available withNewton’s method).

3. Porting of XSCTools on MAST

CREATE L code is part of a suite of procedures, the XSCTools(eXtreme Shape Controller Tools) [5] written in MatLab with aGraphical User Interface (GUI), to design and validate plasma shapecontrollers. They have been designed to be machine independent(to be used and ‘easily’ ported on any tokamaks) by using ASCII filescontaining a standard description of the tokamak. Custom versionsof the XSCTools for MAST both in Windows and Linux environmentsto be run also remotely have been developed and installed.

To extend the XSCTools on MAST we consider: (i) a first orderFEM mesh with 51,016 triangles and 25,585 nodes (built using thepdetool of MatLab). Note that we designed a less detailed first wallespecially in the proximity of the central rod to avoid unnecessarycomputational efforts; (ii) circuit schematization of poloidal field

coil connections and passive structures; and (iii) a subset of reliableexperimental magnetic signals (providing magnetic field and flux)fit in the least square sense to obtain the plasma current densityprofile parameters for a given experimental configuration.

G. Artaserse et al. / Fusion Engineering and Design 88 (2013) 1091– 1096 1093

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ig. 3. Comparison between the reconstructed and the experimental measure-ents: (a) pick up coils in the low field side region and (b) flux loops. The arrows

how mismatches probably due to broken sensors.

. Benchmark cases

To provide reliable linearized models for a new magnetic con-rol in MAST we firstly tried to asses if the XSCTools were properlymplemented. As validating procedure a plasmaless and a DND con-guration have been chosen for the comparison with experimentalata and EFIT reconstructions. Once established the reliability ofhe reconstructed equilibrium point we linearized and carried outhe dynamic simulations of experimental data including modellingf the effects of the passive structures.

.1. Magnetic reconstruction

.1.1. Plasmaless case #24007@0.3 sFig. 3 shows the comparison between the reconstructed and the

xperimental measurements for the whole set of signals providedy pick up coils and flux loops, not only those of the subset chosen

or the least square fit. Good agreement has been found with thexperimental signals coming from magnetic probes with only fewismatches probably due to broken sensors. The reconstruction

rror for many of them is less than 10% for the pick-up coils, both

Fig. 4. Equilibrium configuration calculated by the XSCTools for MAST pulse #24542@0.27 s.

close to the central column and in the low field side region. As forthe flux measurements, the reconstruction error is less than 1%.

4.1.2. Plasma equilibrium case #24542@0.27 sThe benchmark pulse is a DND configuration, with upper domi-

nant X point. Fig. 4 shows the equilibrium provided by the XSCTools,and in particular the reconstructed boundary (outermost closedmagnetic surface) at the time instant of interest. A good agreementhas been found with the EFIT flux map (see Fig. 5) interpolatedinto the XSCTools mesh. Still a good agreement with the field andfluxes signals with the same few mismatches of plasmaless case.The reconstruction error for a large amount of pick up coils is <8%and for the fluxes measurements still the error less than 1%.

4.2. Dynamic simulations

Once obtained a reliable equilibrium reconstruction we couldproceed to linearize the model in the neighbourhood of the equilib-rium point. The open loop dynamic simulations have been carriedout using two different models: one with eddy and the other with-out eddy currents to assess the benefits of inserting the eddycurrents into the model.

To simulate the experimental data using the model withouteddy currents we simply used the output matrix (C) of the lin-earized model in (3), while for the simulation using the model witheddy currents we used a current driven model [6] to obtain a statespace model having the PF coils currents as inputs in addition to thedisturbance terms. The need to use a current driven model comesfrom that the voltage measurements in MAST are too noisy to beused in the dynamic simulations.

In terms of formulation rewriting the circuit equation (2) in a

simple way, we obtain

L x + R x = S u − LE w (4)

1094 G. Artaserse et al. / Fusion Engineering a

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ig. 5. Comparison of the flux maps provided by XSCTools and EFIT for MAST pulse24542 @0.27 s.

here following, we divide the contribution of the states x in pas-ive currents xe and active currents xa, x = [xe xa]T. In this way weet:

Le Lea

Lae La

][xe

xa

]+

[Re 0

0 Ra

][xe

xa

]=

[0

Sa

]u −

[LEe

LEa

]w (5)

hen we define a new state vector pe associated to the passiveurrents, pe = Lexe + Leaxa + LEew which yields the following newystem

pe = Lexe + Leaxa + LEew

xe = L−1e pe − L−1

e Leaxa − L−1e LEew

(6)

ig. 6. MAST open loop simulation of plasmaless case #24936 with (grey line, red in theersion) eddy currents: comparison with experimental (dark line, blue in the web version

nd Design 88 (2013) 1091– 1096

obtaining a new state space model [6], where pe is the new statevariable:

pe = Ape + B�

y = Cpe + D�(7)

assuming A = −ReL−1e , B = [ReL−1

e Lea ReL−1e LEe], C = CeL−1

e , D =[Ca − CeL−1

e Lea D − CeL−1e LEe], � = [xa w]T.

Note that � contain the currents in the poloidal field circuits xaand the disturbances w as the new inputs of the system. The currentdriven model (7) has a lower order than the original one (pe hasthe same dimension of xe) because it totally ignores the electricdynamics on the poloidal coils and assumes that the value of thecurrents can be arbitrarily imposed. Moreover the growth rate �associated to the unstable mode of the system (7) of the matrixA = −ReL−1

e is bigger than that one of system (4) of the matrix A =−(L∗)−1R, due the reduced order of the new system �A > �A.

4.2.1. Plasmaless case #1To understand the contribution of using the eddy currents in the

CREATE L linearized model, we have chosen a calibration pulse. Inshot #24936 the P2U, P3U, P4U, P5U currents are individually cali-brated. Dynamic simulations have been carried out using y = C x forthe case without eddy currents. To insert the eddy currents effectson the dynamic predictions we use a simplified formulation of (7),since in this case the absence of plasma the disturbances term wdisappear:

{pe = A0pe + B0xa

y = C0pe + D0xa

(8)

where A0 = −ReL−1e , B0 = [ReL−1

e Lea], C0 = CeL−1e , D0 = [Ca −

CeL−1e Lea].Fig. 6 shows the linearized model predictions of some of the

magnetic signals versus the experimental one, in both cases withand without taking into the modelling the effects of parasiticcurrents in the metallic structures facing the plasma. We choose asimulation time windows of 40 ms when only P2U was acting. Wediscovered a fair agreement using the model with eddy currents, so

the decision for the further open loop analysis to take into accountthem into the model. Even the transition (see Fig. 6 on the left)from ramp up to flat top of P2U currents is well reproduced by thelinearized model.

web version) and without (upward pointing triangles grey line, green in the web) signals coming from a pick-up coil (left) and a flux loop (right).

G. Artaserse et al. / Fusion Engineering and Design 88 (2013) 1091– 1096 1095

Fig. 7. MAST open loop simulation dry run #24007 with (grey line, red in the web version) eddy currents: comparison with experimental (dark line, blue in the web version)signals coming from a pick-up coil (left) and a flux loop (right).

Fig. 8. MAST open loop simulation of plasma run case #12758 with (grey line, red in the web version) eddy currents: comparison with various experimental (dark line, bluein the web version) signals: (a) pick-up coils, (b) PF coil cases, (c) plasma current, and (d) plasma radial position.

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.2.2. Plasmaless case #2We also analyzed the standard MAST dry run #24007 already

sed for magneto-static calibrations in Section 4.1. This time wearried out dynamic simulations using system (8). We also predicthe currents flowing in the PF circuits, which are measured (P2,3, P4 and P5) and here considered as passive conductors. Fig. 7hows a good agreement between linearized model predictions andxperimental data. Some discrepancies, especially for the verticalagnetic signals (see Fig. 7 on the right) in the low field side region,

ue to some passive structures model inaccuracies (e.g. equivalenteometry, material properties, 3D effects), are under investigation.

.2.3. Plasma run case, DND #12758The chosen equilibrium reconstruction is 0.15 s, when fast

henomena do not occur and before the observed plasma cur-ent oscillation due to deliberately driven radial position oscillationithout compensation so as to measure the coupling with Ip.e carried out dynamic simulations using system (7) taking into

ccounts the eddy currents effects and disturbances. We simulatehe magnetic signals, plasma current, eddy currents flowing in theF coils cases and plasma column radial position. Fig. 8 shows aair agreement between the simulations and the experimental data,eproducing accurately the interaction between plasma currentnd radial position (see Fig. 8c and d) control loops.

. Summary and conclusions

Linearized models for a new magnetic control on MAST haveeen obtained using a 2D axisymmetric modelling of PF circuits,acuum vessel, and other conducting structures.

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nd Design 88 (2013) 1091– 1096

The suite of procedures XSCTools, conceived to be machine inde-pendent, have been applied to MAST analysis and installed on Linuxenvironment so as to be run both on-site and remotely. These setof procedures can be easily ported on MAST Upgrade. The bench-mark cases show good agreement of the model-based simulationswith the EFIT flux maps and the experimental magnetic signals.Only few mismatches have been noticed: some are probably dueto broken, misaligned or not calibrated measurement; others, cur-rently under investigations are likely due to inaccurate modellingof the geometry or the material properties of some conductingstructures.

The authors applied a current driven model to obtain a statespace model for the dynamic simulations of the experimental data.The linearized models including the effects of the passive structuresshow fair agreement with the experimental data. The modellingactivity has been useful also to reproduce accurately the interactionbetween plasma current and radial position control loops. Betterresults could be achieved providing a more detailed schematizationof the passive structures.

References

1] R. Albanese, M. Mattei, F. Villone, Nuclear Fusion 44 (2004).2] A. Portone, R. Albanese, R. Fresa, M. Mattei, G. Rubinacci, F. Villone, Fusion Engi-

neering and Design 74 (2005).3] J.R. Ferron, M.L. Walker, L.L. Lao, H.E. St. John, D.A. Humphreys, J.A. Leuer, Nuclear

Fusion 38 (1998).

4] R. Albanese, F. Villone, Nuclear Fusion 38 (1998).5] G. De Tommasi, R. Albanese, G. Ambrosino, M. Ariola, M. Mattei, A. Pironti, et al.,

IEEE Transactions on Plasma Science 35 (3) (2007).6] M. Ariola, A. Pironti, Advanced in Fusion Control, 1st ed., Springer, 2008, pp.

73–75.