**Êtes-vous un étudiant de l'EPFL à la recherche d'un projet de semestre?**

Travaillez avec nous sur des projets en science des données et en visualisation, et déployez votre projet sous forme d'application sur GraphSearch.

Publication# Enhancing the control of tokamaks via a continuous nonlinear control law

Résumé

The control of the current, position and shape of an elongated cross-section tokamak plasma is complicated by the instability of the plasma vertical position. In this case the control becomes a significant problem when saturation of the power supplies is considered. Current saturation is relatively benign due to the integrating nature of the tokamak, resulting in a reasonable time horizon for strategically handling this problem. On the other hand, voltage saturation is produced by the feedback controller itself, with no intrinsic delay. In practice, during large plasma disturbances, such as sawteeth, ELMs and minor disruptions, voltage saturation of the power supply can occur and as a consequence the vertical position control can be lost. If such a loss of control happens the plasma displaces vertically and hits the wall of the vessel, which can cause damage to the tokamak. The consideration and study of voltage saturation is especially important for ITER. Due to the size and therefore the cost of ITER, there will naturally be smaller margins in the Poloidal Field coil power supplies implying that the feedback will experience actuator saturation during large transients due to a variety of plasma disturbances. The next generation of tokamaks under construction will require vertical position and active shape control and will be fully superconducting. When the magnetic transverse field in superconducting magnets changes, the magnet generates two types of heat loss, the so-called coupling loss and the so-called hysteresis loss, grouped together as AC losses. Superconducting coils possess superconducting properties only below a critical temperature around a few K. AC losses are detrimental since they heat up the superconducting material. Thus, if AC losses are too large, the cryogenic plant can no longer hold the required temperature to maintain the superconductivity properties. Once the superconductivity is lost, the electric currents in the coils produce an enormous heat loss due to the ohmic resistivity, which can lead to a possible damage to the coils. In general, the coils are designed with enough margin to absorb all likely losses. A possible loss reduction could allow us to downsize the superconducting cross section in the cables, reducing the overall cost, or simply increase the operational cooling margin for given coils. In this thesis we have tried to take into consideration these two major problems. The thesis is therefore focused on the following main objectives: i) the stability analysis of the tokamak considering voltage saturation of the power supplies and ii) the proposition of a new controller which enhances the stability properties of the tokamak under voltage saturation and iii) the proposition of a controller which takes into consideration the problem of reducing the AC losses. The subject of the thesis is therefore situated in an interdisciplinary framework and as a result the thesis is subdivided into two principal parts. The first part is devoted to tokamak physics and engineering, while the second part focuses on control theory. In the tokamak physics and engineering part we present the linear tokamak models and the nonlinear tokamak code used for the controller design and the validation of the new proposed controller. The discussion is especially focused on the presence of a single unstable pole when the vertical plasma position is unstable since this characteristic is essential for the work presented in the control theory part. In order to determine the enhancement of the stability properties we have to bring the new proposed controller to its stability limits by means of large disturbances. Validation by means of simulations with either linear or nonlinear tokamak models are imperatively required before considering the implementation of the new controller on a tokamak in operation. A linear tokamak model will probably be inadequate since large disturbances can move its state outside its validity regions. A full nonlinear tokamak evolution code like DINA is indispensable for this purpose. We give a detailed description of the principal plasma physics implemented in the DINA code. Additionally, validation of DINA is provided by comparing TCV experimental VDE responses with DINA code simulations. To allow a study of the AC losses reduction, the nature of the AC losses has to be reduced to a simplified form. We analyse to what extent the accumulated AC losses in ITER could be reduced by taking into account the losses themselves when designing the feedback control loops. In order to be able to carry out this investigation a simple and fast AC loss model, referred to as "AC-CRPP" model, is proposed. In the control theory part we study the stability region in state space, referred to as the region of attraction, for linear tokamak-like systems with input saturation (voltage saturation) and a linear state feedback. Only linear systems with a single unstable pole (mode) and a single saturated input are considered. We demonstrate that the characterisation of the region of attraction is possible for a second order linear system with one unstable and one stable pole. For such systems the region of attraction possesses a topological bifurcation and we provide an analytical condition under which this bifurcation occurs. Since the analysis relies on methodologies like Poincaré and Bendixson's theorems which are unfortunately only valid for second order systems it is evident that there is no way to apply the results for second order systems to higher order systems. It turned out that the search for characterising the region of attraction for higher order systems was illusory and thus this research direction had to be abandoned. We therefore focused on controllers for which the region of attraction is the maximal region of attraction that can be achieved under input saturation. This region is referred to as the null controllable region and its characterisation is simple for any arbitrary high order system possessing a single unstable pole. We present a new globally stabilising controller for which its region of attraction is equal to the null controllable region. This result is obtained by incorporating a simple continuous nonlinear function into a linear state feedback controller. There are several advantages linked to this new controller: i) the stability properties are enhanced, ii) the performance, AC loss reduction and fast disturbance rejection, can be taken into account, iii) the controller can be applied to any arbitrary high order system and iv) the controller possesses a simple structure which simplifies the design procedure. We close the control theory part by focusing on the application of the proposed new controller to tokamaks. Since this controller is a state feedback controller one of the major problems is linked to the state reconstruction. Other pertinent topics are: i) the study of the effect of the disturbances on the closed-loop system stability, ii) the problem inherent to the nature of a state feedback controller when we want an output of the system to track a reference signal and iii) the discussion of the detrimental effects on stability if a pure time delay or a limited bandwidth are added to the closed-loop system, as is the case in reality. The validation of the proposed controller is carried out by means of simulations. We present results for ITER-FEAT and JET using the linear tokamak model CREATE-L. Finally, we present a validation for the case of TCV using the nonlinear DINA-CH code.

Official source

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Concepts associés

Chargement

Publications associées

Chargement

Concepts associés (51)

Tokamak

thumb|Vue intérieure du tore du Tokamak à configuration variable (TCV), dont les parois sont recouvertes de tuiles de graphite.
Un tokamak est un dispositif de confinement magnétique expérimental ex

État plasma

thumb|upright|Le soleil est une boule de plasma.
thumb|Lampe à plasma.|168x168px
thumb|upright|Les flammes de haute température sont des plasmas.
L'état plasma est un état de la matière, tout comme l

Rétroaction

vignette|Représentation d'une boucle de rétroaction.
La rétroaction (en anglais feedback) est un processus dans lequel un effet intervient aussi comme agent causal sur sa propre origine, la séquence

Publications associées (102)

Chargement

Chargement

Chargement

Jean-Yves Favez, Jonathan Bryan Lister, Philippe Müllhaupt

The control of the current, position and shape of an elongated cross-section tokamak plasma is complicated by the so-called instability of the current vertical position. Linearized models all share the feature of a single unstable eigenmode, attributable to this vertical instability of the plasma equilibrium movement, and a large number of stable or marginally stable eigenmodes, attributable to zero or positive resistance in all other model circuit equations. Due to the size and therefore cost of the ITER tokamak, there will naturally be smaller margins in the poloidal field coil power supplies, implying that the feedback control will experience actuator saturation during large transients due to a variety of plasma disturbances. Current saturation is relatively benign, due to the integrating nature of the tokamak, resulting in a reasonable time horizon for strategically handling the approach to saturation which leads to the loss of one degree of freedom in the feedback control for each saturated coil. On the other hand, voltage saturation is produced. by the feedback controller itself, with no intrinsic delay. This paper presents a feedback controller design approach which explicitly takes saturation of the power supply voltage into account when producing the power supply demand signals. We consider the vertically stabilizing part of the ITER controller (fast controller) with one power supply and therefore a single saturated input. We. consider an existing ITER controller and enlarge its region of attraction to the full null controllable region by adding a continuous nonlinearity into the control. In a system with a single unstable eigenmode and a single stable eigenmode we have already provided a proof of the asymptotical stability of the closed loop system, and we have examined the performance of this new continuous nonlinear controller. We have subsequently extended this analysis to a system with a single eigenmode and multiple stable eigenmodes. The method requires state feedback control, and therefore a reconstruction of the states is indispensable. We discuss the feasibility of extracting these states from the available diagnostic information as well as other implementation details. As a complement to our ITER simulations we confirm the enlargement of the region of attraction by the new controller by a JET simulation.

The goal of thermonuclear fusion research is to provide power plants, that will be able to produce one gigawatt of electricity. Among the different ways to achieve fusion, the tokamak, based on magnetic confinement, is the most promising one. A gas is heated up to hundreds of millions of degrees and becomes a plasma, which is maintained – or confined – in a toroidal vessel by helical magnetic field lines. Then, deuterium and tritium are injected and fuse to create an α particle and an energetic neutron. In order to have a favorable power balance, the power produced by fusion reactions must exceed the power needed to heat the plasma and the power losses. This can be cast in a very simple expression which stipulates that the product of the density, the temperature and the energy confinement time must exceed some given value. Unfortunately, present-days tokamaks are not able to reach this condition, mostly due to plasma turbulence. The latter phenomenon enhances the heat losses and degrades the energy confinement time, which cannot be predicted by analytical theories such as the so-called neoclassical theory in which the heat losses are caused by Coulomb collisions. Therefore, numerical simulations are being developed to model plasma turbulence, mainly caused by the Ion and Electron Temperature-Gradient and the Trapped-Electron-Mode instabilities. The plasma is described by a distribution function which evolves according to the Vlasov equation. The electromagnetic fields created by the particles are self-consistently obtained through Maxwell's equations. The resulting Vlasov-Maxwell system is greatly simplified by using the gyrokinetic theory, which consists, through an appropriate ordering, of eliminating the fast gyromotion (compared to the typical frequency of instabilities). Nevertheless, it is still extremely difficult to solve this system numerically due to the large range of time and spatial scales to be resolved. In this thesis, the Vlasov-Maxwell system is solved in the electrostatic and collisionless limit with the Particle-In-Cell (PIC) ORB5 code in global tokamak geometry. This Monte-Carlo approach suffers from statistical noise which unavoidably degrades the quality of the simulation. Consequently, the first part of this work has been devoted to the optimization of the code with a view to reduce the numerical noise. The code has been rewritten in a new coordinate system which takes advantage of the anisotropy of turbulence, which is mostly aligned with the magnetic field lines. The overall result of the optimization is that for a given accuracy, the CPU time has been decreased by a factor two thousand, the total memory has been decreased by a factor ten and the numerical noise has been reduced by a factor two hundred. In addition, the scaling of the code with respect to plasma size is presently optimal, suggesting that ORB5 could compute heat transport for future fusion devices such as ITER. The second part of this thesis presents the validation of the code with numerical convergence tests, linear (including dispersion relations) and nonlinear benchmarks. Furthermore, the code has been applied to important issues in gyrokinetic theory. It is shown for the first time that a 5D global delta-f PIC code can achieve a thermodynamic steady state on the condition that some dissipation is present. This is a fundamental result as the main criticism against delta-f PIC codes is their inability to deal with long time simulations. Next, the role of the parallel nonlinearity is studied and it is demonstrated in this work that this term has no real influence on turbulence, provided the numerical noise is sufficiently low. This result should put an end to the controversy that recently occurred, in which gyrokinetic simulations using different numerical approaches yielded contradictory results. Finally, thanks to the optimization of the code, the gyrokinetic model has been extended to include the kinetic response of trapped-electrons, in place to the usual adiabatic (Boltzmann) approximation. For the first time, global TEM nonlinear simulations are presented, and the role of the zonal flow on heat transport is analyzed. This study will help in acquiring some knowledge on the less-known TEM turbulence (as compared to ITG). In conclusion, this thesis is one of the main steps of the development of ORB5, which is now a state-of-the-art gyrokinetic code for collisionless ITG and TEM turbulence, and has brought several contributions to the understanding of these phenomena.

Joel Albrektsson, Daniel Favrat, Leonidas Tsikonis, Jan Van Herle

An efficient control system is paramount for the operability of Fuel Cell systems since, in ideal cases, it allows the regulation of power output, temperatures and economic performance under a dynamic working environment where they need to operate. Although several control strategies, scenarios and methodologies have been broadly investigated, it is usually taken for granted that the measurements from the system, necessary for the control feedback, are correct. Nonetheless, when simple thermocouples are used to measure gas temperatures there is a significant danger of systematic errors due to radiation effects between the surroundings and the thermocouple. The discrepancy between a real gas temperature and the one measured depends mainly on the temperature difference between the gas and the solids around as well as the gas velocity, radiation factors etc. The phenomenon has been described in our past publications. In this work we simulate an SOFC system and apply control scenarios in order to investigate potential problems arising from such systematic errors. The results show that important dysfunctions may occur and caution should be applied in design of both control and of the systems themselves.

2011