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Model based approach to resistive wall magnetohydrodynamic instability control: Experimental modeling and optimal control for the reversed-field pinch
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The primary objective of fusion research is to realize a thermonuclear fusion power plant. The main method to confine the hot plasma is by using a magnetic field. The reversed-field pinch is a type of magnetic confinement device which suffers from variety of magnetohy- drodynamic (MHD) instabilities. A particular unstable mode that is treated in this work is the resistive wall mode (RWM), which occurs due to the current gradient in the RFP and has growth rates of the order of the magnetic diffusion time of the wall. Application of control engineering tools appears to allow a robust and stable RFP operation.A model-based approach to stabilize the RWMs is pursued in this thesis. The approach consists of empirical modeling of RWMs using a class of subspace identification methodology. The obtained model is then used as a basis for a model based controller. In particular the first experimental results of using a predictive control for RWM stabilization are obtained. It is shown that the formulation of the model based controller allows the user to incorporate several physics relevant phenomena along with the stabilization of RWM. Another use of the model is shown to estimate and compensate the inherent error field. The results are encouraging, and the methods appear to be generically useful as research tools in controlled magnetic confinement fusion.

Abstract [sv]

Fusionsforskningens primära mål är att förverkliga en ny typ av kraftverk baserade på termonukleär fusion. Den viktigaste metoden för att innesluta det heta plasmat är användandet av  magnetfält. ”Reverserat-fält pinch” (RFP) är en typ av anläggning för magnetisk inneslutning av fusionsplasma som uppvisar ett flertal magneto-hydrodynamiska instabiliteter. En specifik instabil mod som behandlas i detta arbete är”resistiv-vägg” moden (RWM). Den orsakas av strömgradienten i RFPn och tillväxer med en tidskonstant som är av samma storleksordning som magnetfältets diffusionstid i det omgivande metallskalet.  Tillämpning av verktyg från reglerteknikområdet förefaller tillåta en robust och stabil RFP drift. I detta arbete används ett modell-baserat tillvägagångssätt för kompensering av RWM. Det innefattar empirisk modellering av RWM med användning av ”subspace” system-identifieringsmetoder. Den erhållna modellen används sedan som grund för en modell-baserad regulator. De första experimentella resultaten från modell-prediktiv kompensering av RWM har erhållits.  I detta arbete har också visats att formuleringen av den modellbaserade regulatorn tillåter användaren att integrera flera relevanta fysikaliska aspekter förutom RWM. Ytterligare en användning av modellen är för att göra uppskattning och kompensering av avvikelser i anläggningens magnetfält, så kallade fält-fel. Resultaten är uppmuntrande, och det förefaller som om de undersökta metoderna är allmänt användbara som verktyg för forskning om magnetisk inneslutning av fusionsplasma.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. , p. 59
Series
TRITA-EE, ISSN 1653-5146 ; 2016:192
Keywords [en]
magnetohydrodynamic, model based control, reversed-field pinch
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-200817ISBN: 978-91-7729-228-9 (print)OAI: oai:DiVA.org:kth-200817DiVA, id: diva2:1070904
Public defence
2017-02-09, F3, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Supervisors
Note

QC 20170202

Available from: 2017-02-02 Created: 2017-02-02 Last updated: 2017-02-02Bibliographically approved
List of papers
1. Graybox Modelling of EXTRAP T2R with Vacuum-Plasma Separation and Optimal Control Design of Resistive Wall Modes
Open this publication in new window or tab >>Graybox Modelling of EXTRAP T2R with Vacuum-Plasma Separation and Optimal Control Design of Resistive Wall Modes
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(English)Article in journal (Refereed) Submitted
Abstract [en]

This paper presents a graybox methodology to model the Resistive Wall Mode instability by combining first principle approach and system identification technique. In particular we propose a separate vacuum and plasma modeling with cascade interconnection. The shell is modeled using CARIDDI code which solves the 3D integral formulation of eddy current problem, whereas the plasma response is obtained empirically by system identification. Furthermore the resulting model is used to design an optimal feedback control. The model and feedback control is validated experimentally in EXTRAP T2R reversed-field pinch, where RWMs stabilization and non-axisymmetric mode sustainment is considered.

Keywords
resistive wall mode, reversed-field pinch, electrodynamic model, system identification, optimal feedback control
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-200828 (URN)
Note

QC 20170203

Available from: 2017-02-02 Created: 2017-02-02 Last updated: 2017-02-03Bibliographically approved
2. Reduced Order Modelling of Resistive Wall Modes in EXTRAP T2R Reversed-Field Pinch
Open this publication in new window or tab >>Reduced Order Modelling of Resistive Wall Modes in EXTRAP T2R Reversed-Field Pinch
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2016 (English)In: 43rd European Physical Society Conference on Plasma Physics, EPS 2016, European Physical Society , 2016Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, we study the Resistive Wall Mode (RWM) instability in the EXTRAP T2R Reversed-Field Pinch. The RWM is a kink-like instability that grows in the time scale of magnetic field diffusion time through the conducting structures. The RWMs are highly affected by the complex three-dimensional conducting structures surrounding the plasma. The first part of the paper will describe the RWM modelling process in EXTRAP T2R using the CarMa computational tool. The code can rigorously take into account the complex geometry of the conducting structures in the solution of the plasma stability problem. The resulting model can be cast into a state space form, with the number of state variables up to several thousands. In the time scale of magnetic field diffusion time, it is possible to stabilize the RWMs by using feedback-controlled external magnetic perturbation to counteract the growing magnetic field caused by the RWMs. Hence, the final suppression level of the RWM is highly dependent on the features of the feedback controller; thus its careful design is needed. Advanced feedback control design method requires an accurate model and the CarMa computational tool can be used in this respect. However, handling such a complex model may pose severe problems both in the design phase and when implemented in real-time due to the computational load. Several model reduction techniques will be employed to address this issue, with the aim of getting to a simpler approximation of RWM response without neglecting the crucial physics information

Place, publisher, year, edition, pages
European Physical Society, 2016
Keywords
Reduced order model, reversed-field pinch, magnetohydrodynamic
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-200826 (URN)2-s2.0-85013927660 (Scopus ID)
Conference
43rd European Physical Society Conference on Plasma Physics, EPS 2016, KU Leuven, Leuven, Belgium, 4 July 2016 through 8 July 2016
Note

QC 20170203

Available from: 2017-02-02 Created: 2017-02-02 Last updated: 2018-03-06Bibliographically approved
3. Improved model predictive control of resistive wall modes by error field estimator in EXTRAP T2R
Open this publication in new window or tab >>Improved model predictive control of resistive wall modes by error field estimator in EXTRAP T2R
2016 (English)In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 58, no 12, article id 124002Article in journal (Refereed) Published
Abstract [en]

Many implementations of a model-based approach for toroidal plasma have shown better control performance compared to the conventional type of feedback controller. One prerequisite of model-based control is the availability of a control oriented model. This model can be obtained empirically through a systematic procedure called system identification. Such a model is used in this work to design a model predictive controller to stabilize multiple resistive wall modes in EXTRAP T2R reversed-field pinch. Model predictive control is an advanced control method that can optimize the future behaviour of a system. Furthermore, this paper will discuss an additional use of the empirical model which is to estimate the error field in EXTRAP T2R. Two potential methods are discussed that can estimate the error field. The error field estimator is then combined with the model predictive control and yields better radial magnetic field suppression.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2016
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-200824 (URN)10.1088/0741-3335/58/12/124002 (DOI)000399802800002 ()2-s2.0-84997606102 (Scopus ID)
Note

QC 20170203

Available from: 2017-02-02 Created: 2017-02-02 Last updated: 2017-05-08Bibliographically approved
4. Design and operation of fast model predictive controller for stabilization of magnetohydrodynamic modes in a fusion device
Open this publication in new window or tab >>Design and operation of fast model predictive controller for stabilization of magnetohydrodynamic modes in a fusion device
2016 (English)In: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2016, p. 7347-7352Conference paper, Published paper (Refereed)
Abstract [en]

Magnetic confinement fusion (MCF) devices suffer from magnetohydrodynamic (MHD) instabilities. A particular unstable mode, known as the resistive wall mode (RWM), is treated in this work. The RWM perturbs the plasma globally and can degrade the confinement or even terminate the plasma if not stabilized. This paper presents a control design approach to stabilize the RWM in the reversed-field pinch (RFP). The approach consists of: closed-loop system identification of the RFP, design of a fast model predictive controller and experimental validation of the controller. Experimental results shows that the proposed controller manages to stabilize the RWM in plasma.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2016
Keywords
Coils, Control design, Magnetohydrodynamic power generation, Magnetohydrodynamics, Plasmas, Predictive models, Yttrium
National Category
Fusion, Plasma and Space Physics Control Engineering
Identifiers
urn:nbn:se:kth:diva-188273 (URN)10.1109/CDC.2015.7403379 (DOI)000381554507089 ()2-s2.0-84962016878 (Scopus ID)9781479978861 (ISBN)
Conference
54th IEEE Conference on Decision and Control, CDC 2015, 15 December 2015 through 18 December 2015
Note

QC 20160615

Available from: 2016-06-15 Created: 2016-06-09 Last updated: 2017-02-02Bibliographically approved
5. Implementation of model predictive control for resistive wall mode stabilization on EXTRAP T2R
Open this publication in new window or tab >>Implementation of model predictive control for resistive wall mode stabilization on EXTRAP T2R
2015 (English)In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 57, no 10, article id 104005Article in journal (Refereed) Published
Abstract [en]

A model predictive control (MPC) method for stabilization of the resistive wall mode (RWM) in the EXTRAP T2R reversed-field pinch is presented. The system identification technique is used to obtain a linearized empirical model of EXTRAP T2R. MPC employs the model for prediction and computes optimal control inputs that satisfy performance criterion. The use of a linearized form of the model allows for compact formulation of MPC, implemented on a millisecond timescale, that can be used for real-time control. The design allows the user to arbitrarily suppress any selected Fourier mode. The experimental results from EXTRAP T2R show that the designed and implemented MPC successfully stabilizes the RWM.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2015
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-168631 (URN)10.1088/0741-3335/57/10/104005 (DOI)000366679100006 ()2-s2.0-84940854105 (Scopus ID)
Note

Updated from manuscript to article.

QC 20151127

Available from: 2015-06-05 Created: 2015-06-05 Last updated: 2017-12-04Bibliographically approved
6. A method for the estimate of the wall diffusion for non-axisymmetric fields using rotating external fields
Open this publication in new window or tab >>A method for the estimate of the wall diffusion for non-axisymmetric fields using rotating external fields
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2013 (English)In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 55, no 8, p. 084001-Article in journal (Refereed) Published
Abstract [en]

A new method for the estimate of the wall diffusion time of non-axisymmetric fields is developed. The method based on rotating external fields and on the measurement of the wall frequency response is developed and tested in EXTRAP T2R. The method allows the experimental estimate of the wall diffusion time for each Fourier harmonic and the estimate of the wall diffusion toroidal asymmetries. The method intrinsically considers the effects of three-dimensional structures and of the shell gaps. Far from the gaps, experimental results are in good agreement with the diffusion time estimated with a simple cylindrical model that assumes a homogeneous wall. The method is also applied with non-standard configurations of the coil array, in order to mimic tokamak-relevant settings with a partial wall coverage and active coils of large toroidal extent. The comparison with the full coverage results shows good agreement if the effects of the relevant sidebands are considered.

Keywords
Resistive-Wall, Feedback Stabilization, Active Control, DIII-D, Modes, Pinch, Device
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-127495 (URN)10.1088/0741-3335/55/8/084001 (DOI)000322702700002 ()2-s2.0-84881511440 (Scopus ID)
Conference
17th Annual Workshop on Magnetohydrodynamic (MHD) Stability Control - Addressing the Disruption Challenge for ITER, NOV 05-07, 2012, New York, NY
Note

QC 20130902

Available from: 2013-09-02 Created: 2013-08-30 Last updated: 2017-12-06Bibliographically approved
7. Resistive Wall Mode Studies utilizing External Magnetic Perturbations
Open this publication in new window or tab >>Resistive Wall Mode Studies utilizing External Magnetic Perturbations
Show others...
2014 (English)In: Proceeding of the 25th IAEA Fusion Energy Conference, 2014, article id Paper EX/P4-20Conference paper, Published paper (Other academic)
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-200835 (URN)
Conference
25th IAEA Fusion Energy Conference, St. Petersburg, Russian Federation, 2014
Note

QC 20170202

Available from: 2017-02-02 Created: 2017-02-02 Last updated: 2017-02-02Bibliographically approved
8. A Technique for the Estimation of the Wall Diffusion Time
Open this publication in new window or tab >>A Technique for the Estimation of the Wall Diffusion Time
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2012 (English)In: 54th Meeting of the APS Division of Plasma Physics, November 2012,  Providence, USA, 2012Conference paper, Poster (with or without abstract) (Refereed)
Abstract [en]

Feedback systems are important tools for an advanced control of the MHD instabilities in fusion plasmas, both for the suppression of undesired modes, such as RWMs, and for the generation of external perturbations for ELM suppression. A good knowledge of the diffusion time through the machine wall of each external harmonics is necessary for reaching optimal performances of the feedback algorithms.A correct theoretical estimation is not easy due the presence of three-dimensional mechanical structures in the devices, such as shell cuts and external conductive structures that need to be considered. Identification of differences in the vertical and horizontal diffusion time are not simple from a theoretical point of view.This work will present a relatively simple technique to experimentally estimate the diffusion time for each harmonic. The technique is based on the generation of rotating external magnetic perturbations in vacuum and on the quantification of the wall screening from the measured field inside the wall. The technique will be able to quantify possible differences among the horizontal and vertical diffusion time. In the final part of the work, the comparison with the results obtained with a closed-loop identification algorithm of the machine plant will be discussed.

National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-109413 (URN)
Conference
54th Meeting of the APS Division of Plasma Physics, November 2012, Providence, USA
Note

QC 20130530

Available from: 2013-01-03 Created: 2013-01-03 Last updated: 2017-02-02Bibliographically approved

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