phd thesis in control engineering - ce.uniroma2.it

Universita degli Studi di Roma“Tor Vergata”

Facolta di Ingegneria

Dottorato di Ricerca inInformatica ed Ingegneria dell’Automazione

XXIV Ciclo del Corso di Dottorato

Real-time control solutions

for plasma control problemsin Tokamak experiments

Riccardo Vitelli

A.A. 2010/2011

Relatore: Prof. Luca Zaccarian

Alla mia famigliaAgli amici

Acknowledgements

This work couldn’t have been carried out without the support of many

people who helped me with their knowledge, their time and, most impor-

tant, their friendship. Starting from my tutor, Prof. Luca Zaccarian, who

introduced me to the world of Tokamaks and Nuclear Fusion during my de-

gree thesis, and supported me since then up to the “Laurea Specialistica”

(master degree) and now the doctorate. Then I’d like to thank the whole

PPCC Team at the JET, which guided me during my master degree thesis

and with which I still have the pleasure to work. Dr. Filippo Sartori, Dr.

Andre Neto, Dr. Luca Zabeo, Dr. Fabio Piccolo, Dr. Katiuscia Zedda,

thank you very much for all that you have done for me. Together with the

JET staff, I’d like to thank the CREATE people, in particular Dr. Gian-

maria De Tommasi, Prof. Vincenzo Coccorese, Prof. Giuseppe Ambrosino,

Prof. Alfredo Pironti and Prof. Raffaele Albanese, who made the whole

JET experience possible. A special thank you goes to Dr. Teresa Bellizio,

with whom I had the pleasure to work, and to the other italians that were

working at the JET: Dr. Carmelenzo Labate, Dr. Antonio Barbalace and

Dr. Massimo Camplani.

Last but not least I want to thank my family, which has always been so

supportive, expecially during the long periods I was far from home.

I

Contents

1 Introduction 1

2 Tokamaks and Nuclear Fusion 3

2.1 Nuclear fusion . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Plasma and confinement . . . . . . . . . . . . . . . . 4

2.2 Tokamaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 The state of the art: the JET . . . . . . . . . . . . . . . . . 8

2.4 The Road Ahead: ITER and DEMO . . . . . . . . . . . . . 9

3 Plasma control problems and solutions 11

3.1 The Vertical Stabilisation . . . . . . . . . . . . . . . . . . . 11

3.1.1 The Vertical Instability problem . . . . . . . . . . . 11

3.1.2 The JET Vertical Stabilization system . . . . . . . . 14

3.1.2.1 Estimation of the vertical plasma velocity . 16

3.1.2.2 JET’s Vertical Stabilisation and ELM pacing 23

3.2 Plasma shape and position control . . . . . . . . . . . . . . 25

3.2.1 JET Shape Control . . . . . . . . . . . . . . . . . . . 25

3.2.1.1 XSC: eXtreme Shape Controller . . . . . . 28

3.2.1.2 CLA: Current Limit Avoidance . . . . . . . 30

3.3 Power supplies related problems . . . . . . . . . . . . . . . . 37

3.3.1 Induced plasma oscillations: the AL-F amplifier . . . 37

3.3.1.1 Model of the AL-F feedback . . . . . . . . 41

CONTENTS II

CONTENTS

3.3.1.2 Anti-windup solution . . . . . . . . . . . . 51

3.3.2 The JET EFCC Coils control system . . . . . . . . . 58

4 Technical solutions and implementation 61

4.1 The MARTe Framework . . . . . . . . . . . . . . . . . . . . 61

4.1.1 The BaseLib2 . . . . . . . . . . . . . . . . . . . . . . 62

4.1.2 Multithreaded Application Realtime executor (MARTe) 67

4.1.2.1 Generic Application Module . . . . . . . . 67

4.1.3 Code generation via SysML . . . . . . . . . . . . . . 75

4.1.3.1 Sample application to the FTU Tokamak . 82

4.2 The JET systems . . . . . . . . . . . . . . . . . . . . . . . . 87

4.2.1 The Vertical Stabilisation system . . . . . . . . . . . 87

4.2.1.1 The Vertical Stabilization hardware . . . . 88

4.2.1.2 Interfacing with JET . . . . . . . . . . . . 90

4.2.1.3 Vertical Stabilization GAMs . . . . . . . . 91

4.2.1.4 User Interface . . . . . . . . . . . . . . . . 100

4.2.1.5 First Results . . . . . . . . . . . . . . . . . 102

4.3 The new FTU Feedback System . . . . . . . . . . . . . . . . 106

4.3.1 Experimental results . . . . . . . . . . . . . . . . . . 107

5 Conclusions and future work 113

Bibliography 115

List of Figures 126

List of Acronyms 131

CONTENTS III

Chapter 1

Introduction

The energy problem is one of the greatest challenges mankind will have to

face in the following years. The progressive depleting of fossil fuels, the

necessity of cleaner ways to produce energy and the growing demand for

electrical power from developing countries, will force humanity to invest

more and more in the research for alternative power sources.

While renewable power sources, such as photovoltaic and wind, don’t

provide the required reliability, nuclear fission can’t be seen as a long-term

solution to the power generation problem due to the production of long

lived radioactive waste.

In this framework, nuclear fusion is becoming more and more considered

as the most probable solution to the energy problem due to the short life of

the nuclear waste produced, as well as the huge availability of fuel, namely

deuterium (present in big quantities in salt water) and tritium (that can

easily be bred from lithium, which makes up the vast majority of Earth’s

crust, directly in the blanket of a Tokamak [1]).

The trait d’union of this Thesis is fusion technology, particularly related

to control systems for Tokamaks device. After a brief introduction on the

experimental devices and on fusion in general, some of the main problems

1

1 Introduction

related to the magnetic control of nuclear fusion experiments (particularly

the vertical stabilization problem [2] and the plasma shape control [3]),

together with their control solutions are reported. Finally the implementa-

tion of the aforementioned solutions is illustrated, in particular concerning

the development carried on the MARTe Framework [4].

2

Chapter 2

Tokamaks and Nuclear

Fusion

2.1 Nuclear fusion

Nuclear fusion is the basic form of energy production in the stars. It is a

process in which atomic nuclei join to form an heavier atom whose mass

is less than the sum of the masses of the reactants [5, 6]. This reduction

of mass leads to the production of large amounts of energy following the

famous Einstein equation E = mc2. Of the various known fusion reactions,

the most promising one uses two hydrogen isotopes, deuterium and tritium,

which result in the reaction:

21D + 3

1T → 42He(3.5MeV ) + n(14.1MeV )

The D-T reaction has been chosen as the most promising one as it is

a good compromise between energy produced, large cross section (from

which depends the likelihood of interactions) and, above everything, the

availability of both isotopes on Earth.

An important law for nuclear reactions is the Lawson Criterion [7]

3

2 Tokamaks and Nuclear Fusion 2.1 Nuclear fusion

(also known as “triple product”), which defines the conditions needed to

reach ignition, that is when the heating generated by the nuclear reaction

is capable of maintaining the temperature of the plasma against all losses

or, in other words, of keeping the nuclear reaction going on theoretically

forever while confined. In the case of the D-T reaction the Lawson Criterion

states that:

nTτE ≥ 1021keV · s−1 ·m−3 (2.1)

where n is the plasma density, T the plasma temperature and τE the con-

finement time. The Lawson Criterion basically states that ignition condi-

tions can be achieved either by dense plasmas with low τE or by less dense

plasmas with an higher τE .

Directly derived from the Lawson Criterion, the Fusion Energy Gain

Factor Q is defined as the ratio between generated fusion power and power

used for plasma heating. Ignition is when Q =∞, however a value of Q in

the order of 20 is considered enough for a practical reactor. The particular

condition of Q = 1 is called breakeven and reaching it is considered as a

sort of milestone in the fusion power research field. Currently the largest

Q factor obtained on Earth is 0.61 registered at the JET Tokamak in 1997.

2.1.1 Plasma and confinement

At the high temperatures needed for fusion reactions to happen, matter

is subject to another change of state becoming plasma. In a plasma the

electrostatic forces which bind electrons and nuclei are overcome as they

become two distinct populations of negatively charged electrons and posi-

tively charged ions. This gives to plasma the important property of being

capable of conducting currents and reacting to magnetic fields, which is of

paramount importance in the development of magnetic confinement fusion

device as it will be shown later.

4

2 Tokamaks and Nuclear Fusion 2.1 Nuclear fusion

Burning plasmas in fusion research are usually macroscopically studied

by means of the MagnetoHydroDynamics (MHD) equations [5]. This dis-

cipline, initiated by Alfven in 1942 [8], studies the dynamics of conducting

fluids under the action of magnetic fields. Plasmas, due to their aforemen-

tioned properties, fit perfectly in this category.

MHD equations consists fundamentally of a combination of the Navier-

Stokes equations of fluid dynamics, together with Maxwell’s equations of

electromagnetism: the basic idea is to model in this way the dynamics of

the magnetic fields due to the action-reaction of conductiong fluids.

A simplified explanation of the ideal MHD equations for plama model-

ing can be found in [9].

The Lawson Criterion (2.1) basically states that in order to achieve

steady-state operations, a fusion machine should achieve high plasma den-

sities (n) and temperatures (T ) for enough time (τE). In stars due to their

immense mass, the gravitational force is capable of confining the plasma

long enough to achieve fusion reactions. This kind of gravitational confine-

ment, however, is unthinkable to be obtained on Earth.

Two main approaches have so arisen to confine plasma: inertial con-

finement and magnetic confinement. In the former approach a small pellet

of D-T fuel is bombarded by high-power laser causing it to explode, so cre-

ating very high density plasmas for few nanoseconds1. The latter approach

is more widespread and uses lower density gaseous fuel but with longer τE

by constraining the plasma via magnetic fields. Tokamak devices are the

most common form of magnetic confinement devices.

1In the USA this approach to nuclear fusion is being carried out in the NationalIgnition Facility (NIF) at the Lawrence Livermore National Laboratory in Livermore,California.

5

2 Tokamaks and Nuclear Fusion 2.2 Tokamaks

2.2 Tokamaks

A Tokamak (Russian acronym for toroidalnaya kamera i magnitnaya katiushka,

“toroidal chamber and magnetic coil”) is a fusion device that uses strong

magnetic fields to confine the plasma within a vacuum vessel with a toroidal

shape. The first Tokamaks were first developed in the former Soviet Union

in the 60s [5].

Inner Poloidal Field Coils(Primary winding)

VacuumVessel

Outer PoloidalField Coils

ToroidalField Coils

MechanicalStructure

TransformerLimbs

JG98.356/24c

Figure 2.1: Structure and scale of a Tokamak: the JET (Joint EuropeanTorus).

In Tokamaks the plasma is confined in a vacuum vessel (or chamber)

by means of a set of toroidal field (TF) coils, while poloidal field (PF) coils

permit a precise shaping and positioning of the plasma, as well as the in-

duction of a current in the plasma via transformer effect (central solenoid),

and the stabilization of vertical instabilities in case of elongated plasmas.

In Figure 2.1 the standard structure of a Tokamak device is reported.

6

2 Tokamaks and Nuclear Fusion 2.2 Tokamaks

Being gaseous, it is not possible to define a precise position and shape

for the plasma. However the plasma “border” is usually considered coin-

cident with the LCMS (Last Closed Magnetic Surface), i.e. the last mag-

netic surface which doesn’t intersect any physical object (in case of limiter

configuration), or on which lies the X-point2 for a divertor configuration

(separatrix ). In Figure 2.2 the differences between a limiter and a divertor

plasma is shown.

Figure 2.2: Differences between a limiter and a divertor plasma (JET pre-divertor and JET as of today).

One of the major advantages of the divertor configuration plasmas is

the mitigation of the sputtering or melting of material from the limiters to

inside the plasma, as impurities in the plasma tend to dilute the fuel and

generate radiation losses [5]. Moreover it has been shown that the presence

of an X-point greatly helps in reaching high confinement modes (H-mode),

thus improving fusion performances [10].

2The X-point is a point at which the poloidal magnetic field is zero.

7

2 Tokamaks and Nuclear Fusion 2.3 The state of the art: the JET

In a Tokamak device plasma is heated partially via the Joule effect due

to the plasma current (ohmic heating). However as the resistivity of the

plasma falls sharply with the increase of temperature, additional exter-

nal heating system are needed, such as Neutral Beam Injection (NBI),

which uses beams of accelerated ions to move energy to the plasma; Ion

Cyclotron Resonant Heating (ICRH), which heats the plasma through

radio waves resonating with the plasma ion rotation; Lower Hybrid Cur-

rent Drive (LHCD) which uses microwaves with several MW of power at

frequencies in the range of 1-5 GHz accelerate the plasma electrons.

2.3 The state of the art: the JET

The Joint European Torus (JET) is the world’s largest Tokamak [11]. It has

a major radius R0 = 2.96m, minor radius a = 0.96m, elongation k ≤ 1.6,

plasma current Ip < 6MA and a toroidal field Bt < 4T and is equipped

with several additional heating systems, which enable the injection of large

amounts of external power into the plasma. The ICRH has 32MW of

installed power, while the LHCD system is able to provide 12MW , for

20s, at the generator source. After the 2010 upgrades, the neutral beam

injector (NBI) is able to provide up 34MW of power for a maximum of 20s.

Moreover, the ICRH and NBI can also be used to produce non-inductive

current drive. The NBI system has also the ability of generating toroidal

angular momentum, a very important feature for the overall MHD stability

of the plasma. An overview of JET, together with its scale, is shown in

Figure 2.1.

Although JET was not initially designed to operate with a divertor, new

scientific results, in particular the discovery of the high confinement mode

in ASDEX-Upgrade, lead to a major upgrade of JET and the consequent

installation of a divertor system. The latest version of the JET divertor is

known as mark-II and is depicted in Figure 2.3.

For an overview of the JET results see [12].

8

2 Tokamaks and Nuclear Fusion 2.4 The Road Ahead: ITER and DEMO

JG00.47/32c

Divertor

tiles

Coils

Cryopump

Figure 2.3: Structure of the JET Tokamak divertor region.

2.4 The Road Ahead: ITER and DEMO

ITER (International Thermonuclear Experimental Reactor) is the next step

in the race towards power production from nuclear fusion [13, 14, 15]. ITER

will become the world’s largest Tokamak device, built by seven cooperating

members (the European Union, India, Japan, People’s Republic of China,

Russia, South Korea and USA), and will be hosted in Cadarache, France.

Figure 2.4: 3D model of the ITER Tokamak.

It has been designed to reach a Q factor of up to 10 (500MW output

with 50MW of input power), and is intended to study plasmas after the

9

2 Tokamaks and Nuclear Fusion 2.4 The Road Ahead: ITER and DEMO

breakeven threshold. A plasma pulse in ITER should last up to 480 sec-

onds (roughly an order of magnitude more than in JET). Construction of

the site begun in 2007, and the first plasma is planned in 2019. ITER is

planned to be built by outsourcing the design and construction phase as

much as possible, in order to develop industrial interest in nuclear fusion

energy production.

DEMO (DEMOnstration Plant) [16, 17] is intended to build on the

success of ITER the first real fusion power plant. The envisaged goal of

DEMO is to produce at least 2000MW of electrical power on a continual

basis. To achieve this goal DEMO should be at least a 15% bigger than

ITER and with an higher plasma density. However a success of ITER is

considered more than enough to proceed with the development of DEMO,

which, if everything proceeds on schedule, should be ready by 2033.

10

Chapter 3

Plasma control problems

and solutions

3.1 The Vertical Stabilisation

3.1.1 The Vertical Instability problem

Non-circular, elongated plasmas have naturally considerable advantages re-

garding confinement, achievable pressure and space utilisation1. However

elongated plasmas suffer from a natural fast vertical instability which re-

quires closed-loop feedback control, without which no experiment could be

carried out.

This instability can be explained in a simplified way by considering Fig-

ure 3.1, which depicts the vertical instability problem in the JET Tokamak.

In JET the plasma is elongated via two iron bar in which reflected currents

due to the plasma current flow (iron polar expansions in the Figure). The

vertical force generated on the plasma is inversely proportional to the dis-

tance. Assuming the current flowing in the two polar expansions identical,

1Vacuum chambers, in fact, need to have a vertically elongated shape in order tohave a big enough support structure to whitstand the enormous vertical forces due todisruptions.

11

3 Plasma control problems and solutions 3.1 The Vertical Stabilisation

the upwards and downwards forces are in equilibrium. However it is evi-

dent that the centre of the chamber is an unstable equilibrium point, and

so even a small perturbation δ from it will lead the plasma to hit the upper

or lower part of the chamber. The inverse of the time in which the plasma

hits the superior or inferior wall when not stabilized is called growth rate

γ.

Figure 3.1: The mechanism of plasma elongation and resulting verticalinstability. The iron polar expansions (shoes), colored in purple, are themain reason for the natural elongation of JET plasmas. Different plasmaelongation can be obtained by adjusting the currents in the shaping cir-cuit (blue) and PFX circuit (yellow). The vessel (green) provides somepassive stabilization, and the RFA circuit (red) is the actuator for activestabilization.

It is possible to estimate the growth rate by using a simplified model of

12


the vertical instability called rigid displacement model. In this model the

plasma is represented by one or more rigid filaments in which a constant

current flows. Those filaments are considered as having a single degree of

freedom, i.e. the vertical position of their current centroid. Combining

the equations of the poloidal circuits and passive structures with the force

balance equation, it is possible to obtain [2]:

~ψ(~I(t), zp(t)

)+R~I(t) = ~u(t)

mpzp(t) = −2πrpBr

(~I(t), zp(t)

)Ip

(3.1)

where ~ψ is the flux through circuits, passive structures and plasma fil-

aments; R is the resistance matrix; ~I is the vector of the poloidal field

currents and ~u are the tensions applied to the various circuits (zero for

the passive structures); mp, zp and rp represent mass, vertical and radial

position of the plasma; Ip is the plasma current and Br the magnetic field

on the plasma.

The model can be then linearized:

∂ ~ψ

∂~Iδ~I +

∂ ~ψ

∂zpδzp +Rδ~I = δ~u(t)

mpδzp = −2πrp

(∂ ~Br

∂~Iδ~I +

∂ ~Br∂zp

δzp

)Ip

(3.2)

Substituting then for simplicity sake the following:

∂ ~ψ

∂~I= L

∂ ~ψ

∂zp= Ip

∂M

∂zp

.= g

−2πrp

(∂ ~Br

∂~I

)= Ip

(∂M

∂zp

)T.= gT −2πrp

(∂ ~Br∂zp

)= F

13


where L and M are the matrices of the mutual inductance between the

circuits and between the circuits and the plasma, and F the force, the

model becomes: Lδ~I + gδzp +Rδ~I = δ~u(t)

mpδzp = gT δ~I + Fδzp

(3.3)

Neglecting the plasma mass (mp = 0), (3.3) becomes:(L− g · gT

F

)δ~I +Rδ~I = δ~u (3.4)

from which it is possible to evaluate the growth rate [2] by analyzing the

eigenvalues with real part greater than zero of:

−(L− g · gT

F

)−1

R

In JET the growth rate can be estimated to be in the order of magnitude

of 102 − 103s−1.

3.1.2 The JET Vertical Stabilization system

In JET the vertical stabilization system is made by two different control

loops (Figure 3.2): a velocity loop which tries to regulate to zero the vertical

velocity of the plasma (thus halting its vertical movement) and a slower

current loop which regulates the current in the vertical amplifier ERFA to

a set point value (usually zero). While the two control loops may seem

at a first sight in opposition, actually, when considering the presence of

a shape controller system which will slowly “reshape” the plasma in the

desired position, their objective is easier to understand: the velocity loop

reacts rapidly to unwanted vertical movements by unbalancing the radial

field, while the slower current loops tries to recover the normal operating

14


mode.

vest

Adaptive controller

Figure 3.2: The JET Vertical Stabilisation controller.

The velocity loop is a simple proportional controller:

Vref (t) = GV (t) · vest(t) (3.5)

where Vref (t) is the control voltage component for the ERFA amplifier

due to the velocity loop, GV (t) is the proportional gain and vest(t) the

estimation of the plasma centroid vertical velocity. The current loop is

instead a PI controller:

Iref (t) = GI(t) · (eIERFA(t) +KI

∫ t

0eIERFA

(t)dt) (3.6)

where Iref (t) is the control voltage component for the ERFA amplifier due

to the current loop, GI(t) is the current loop gain, KI is the integral gain

and eIERFA(t) is the current error measured.

Notice that the gains GV (t) and GI(t) of the two controllers are time

varying. They are computed by an adaptive controller whose aim is to

change the gains (within certain thresholds) depending on the ERFA am-

15


plifier switching frequency, whose temperature is directly correlated to. In

fact, should the temperature raise above a certain threshold, the amplifier

could switch off causing a loss of control.

The gain of the velocity loop Gv(t) is computed as:

Gv(t) = Gv,FF (t) +GA

∫ t

0(fref − fsw(t))dt (3.7)

where Gv,FF (t) is a feedforward component (baseline gain for the velocity

loop), GA is an adaptation gain, fref is a reference switching frequency

(manually tuned to “safe” values) and fsw(t) is the ERFA switching fre-

quency, measured as the number of times the amplifier voltage crosses zero.

The gain of the current loop is proportional to the velocity one:

GI(t) = GI,FF (t) +KGv(t) (3.8)

where GI,FF (t) is a feedforward component and K is a gain.

3.1.2.1 Estimation of the vertical plasma velocity

One of the most critical parts of JET Vertical Stabilisation system is the

evaluation of the plasma vertical velocity. Due to the small required cycle

time it is not possible to run full shape reconstruction algorithms in real

time, so it is necessary to obtain an estimation of the required measure by

using the various magnetic signals coming from the Tokamak.

In particular at JET these measures are provided by different type of

probes situated in different poloidal, radial and toroidal locations. The

Internal Discrete Coils (IDC, also known as “Mirnov coils”, Figure 3.3) have

a 3dB cut-off frequency of 10kHz. IDC provide a direct flux measurement

of the tangential component of the poloidal magnetic field. Each of the JET

octants2 contains 18 IDC coils, so that eight different measurements, in the

2The JET machine is commonly subdivided in eight sectors, called octants, in thetoroidal direction.

16


same poloidal position, are available at eight different toroidal positions.

In Figure 3.4 the position of the IDC in the JET Tokamak is reported.

Figure 3.3: Photo of an internal discrete coil.

The normal component of the poloidal magnetic field is measured in-

stead by the saddle coils, 3.2mm diameter cables shaped to form a rect-

angular loop and mounted outside the vessel. Each octant has 14 saddle

coils installed. Figure 3.5 shows the positions of IDCs and saddle coils in a

single octant.

The estimation of the vertical velocity is carried out by using a tech-

nique elaborated by Zakharov [18], which relates the vertical position of the

plasma centroid zc (scaled by the concatenated toroidal current IΦ) with

the measures of the tangential (Bt) and normal (Bn) components of the

magnetic field around a closed curve l. Zakharov equation is reported in

(3.9), where r and z represent the radial and vertical coordinates.

IΦzc =1

µ

∮l

[Bt(r, z)z − r log

(r

R0

)Bn(r, z)

]dl (3.9)

By deriving (3.9), making l coincide with the JET’s vacuum vessel and

taking into account the fact that the magnetic field can be measured only in

certain discrete position along the chamber (where the sensors are placed),

it is possible to rewrite the Zakharov equation as:

17


Figure 3.4: Position of the magnetic sensors in the JET Tokamak.

Ipzp =18∑i=1

aiBt(i) +14∑i=1

biBn(i)− Ipzp − Ipasszpass (3.10)

where Ipasszpass is relative to the passive structures, and ai and bi are

weights obtained by solving (3.9) in the locations where the sensors are

placed. For the JET the 18 weights of the Mirnov coils and the 14 ones for

the saddle loops are reported in Figure 3.6 [2].

In Figure 3.7 a sample of the signals of the JET Vertical Stabilization

system is reported (pulse #796323). The top plot shows the control ac-

tion of the feedback (voltage applied to the coil), while the bottom one,

VSEL, shows the estimation (weighted by the plasma current) of the verti-

3All signals acquired during each JET experiment are archived sequentially in adatabase since the beginning of operations.

18


Figure 3.5: Position of the saddle coils in the JET Tokamak.

cal velocity of the plasma. The middle plot reports IFRFA, i.e. the current

flowing in the vertical stabilization coils. This burst behavior is common

in the operation of the vertical stabilization system and is due to the fast

dynamics of the system which has to keep the plasma centroid near to the

unstable equilibrium in the center of the vacuum vessel.

Figure 3.8 shows pulse #79698, where a record current of 4.5MA was

reached, just before the long JET shutdown for the substitution of the

first wall. Notice the bursts of vertical velocity due to the inevitable Edge

Localized Modes (ELMs) with such energetic plasmas.

19


0 5 10 15 20 25 30 35−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Coil Number

Weig

ht

Modified Set

Mirnov Coils

Saddle Loops

Figure 3.6: JET weights for Mirnov coils and saddle loops. Notice how theintroduction of the divertor pratically made unusable the coils in the lowerpart of the vacuum vessel due to the shielding effect of the divertor itself,leading to the necessity of setting to zero the relative weights (coils 10-18).

20


59.455 59.46 59.465 59.47 59.475 59.48 59.485−5000

0

5000

Time [s]

Vo

lta

ge

[V

]

Tension on ERFA coils (V5−VFRFA<S)

59.455 59.46 59.465 59.47 59.475 59.48 59.4850

50

100

150

200

250

300

350

Time [s]

Cu

rre

nt

[A]

Current on ERFA coils (V5−IFRFA<S)

59.455 59.46 59.465 59.47 59.475 59.48 59.485

−2

−1

0

1

2

x 106

Time [s]

Zp

dIp

ZpdIp signal (Ip weighted vertical velocity) (V5−VSEL<S)

Figure 3.7: JET Vertical Stabilization system, pulse #79632.

21


52 52.1 52.2 52.3 52.4 52.5 52.6 52.7 52.8 52.9 53

−1

−0.5

0

0.5

1

x 104

Time [s]

Vo

lta

ge

[V

]

Tension on ERFA coils (V5−VFRFA<S)

52 52.1 52.2 52.3 52.4 52.5 52.6 52.7 52.8 52.9 53−1000

−500

0

500

1000

Time [s]

Cu

rre

nt

[A]

Current on ERFA coils (V5−IFRFA<S)

52 52.1 52.2 52.3 52.4 52.5 52.6 52.7 52.8 52.9 53

−5

0

5

10

15

x 107

Time [s]

Zp

dIp

ZpdIp signal (Ip weighted vertical velocity) (V5−VSEL<S)

Figure 3.8: JET Vertical Stabilization system, pulse #79698.

22


3.1.2.2 JET’s Vertical Stabilisation and ELM pacing

A particular use of the Vertical Stabilisation of the JET is to stimulate

Edge Localised Modes (ELMs).

ELMs are a class of MHD instabilities identifiable by the release of

large amounts of plasma internal energy and particles [5, 19]. The edge of

high confinement plasmas (H-mode plasmas), such as those of the JET, is in

fact characterized by very strong plasma density and temperature gradients

due to the formation of what is called an Edge Transport Barrier (ETB), as

shown in Figure 3.9. After an ELM the plasma pressure decreases abruptly

to slowly rise again. The phenomena is then repeated with an irregular

frequency.

Pla

sm

a p

ressure

0 1r/a

L-Mode

H-Mode

Pedestal

Collapse of pedestal

due to ELM

Formation of edge

transport barrier

Figure 3.9: Collapse of pedestal causes ELMs.

The main problem due to ELMs is the high energy load they unload

on the vacuum vessel walls. However, as the energy of an ELM is directly

proportional to the amount of time between two consecutive ELMs [20], it

is possible to partially mitigate this phenomena by instigating ELMs with

an high enough frequency. ELM pacing is still an open field of research,

however various techniques have been studied to force trigger ELMs, such

as impurity gas puffing and magnetic triggering (see [21, 22] for studies of

magnetic ELM triggering in the TCV and ASDEX Tokamak). Magnetic

23


triggering, in particular, is the standard technique used for ELM pacing in

JET. ELMs are triggered via impulses on the vertical amplifier [23], called,

in the JET gergon, “vertical kicks”.

−10

0

10

(kV

)

ELM pacing for Pulse #78442

a)

ERFA voltage

0

0.5

1

(a.u

.)

b)

D−alpha

−2

0

2

(kA

)

c)

Amplifier Current

9

9.5

10

(MJ)

d)

Diamagnetic energy

24.82 24.84 24.86 24.88 24.9 24.92 24.94 24.96 24.98 25−100

0

100

200

Time (s)

(MA

.m.s

−1)

e)

Vertical velocity

Figure 3.10: Example of ELM pacing via vertical kicks in pulse #78422.

In Figure 3.10 an example of ELM pacing via vertical kicks is shown

(pulse #78422). In the first and third plot, respectively, the voltage applied

and the current on the vertical stabilization coils are reported. The second

plot shows the Dα emission, which indicates the triggering of an ELM.

Notice in the last plot the vertical velocity estimation, which indicates how

the plasma reacts to each “kick”.

24

3 Plasma control problems and solutions 3.2 Plasma shape and position control

3.2 Plasma shape and position control

Precise positioning of the plasma column inside the vacuum vessel is one

of the most important aspects in Tokamak devices. Via shape control it is

possible to maximize the area occupied by the plasma inside the vacuum

vessel, to avoid excessive heat loads on components of the vacuum vessel

such as the divertor tiles [24], and generally to optimize plasma parameters.

3.2.1 JET Shape Control

The Shape Controller (SC) [25, 3] is the system responsible for shaping the

plasma column in the JET Tokamak by controlling the voltages applied on

the Poloidal Field (PF) coils whose name and positions are shown in Figure

3.11.

Circuit name

Toroidal Field

Magnetising

Vertical Field

Fast Radial Field

Radial Field

X-Point

Shaping

Divertors

(TF)

(P1)

(P4T)

(RFA)

(IMB)

(PFX)

(SHA)

(D1-4)

Coils series

24 toroidal coils

P3MU/L+P1EU/L+P1C

P4U+P4L

P2/3RU-P2/3RL

P4U-P4L

P1C

P2SU/L+P3SU/L

D1, D2, D3, D4

U

Figure 3.11: JET circuits generating the poloidal field.

While the P1 circuit is responsible for the generation of the plasma

current, all the other circuits take an active role in shaping the plasma

25


column. In particular the PFX circuit is mostly used to control the position

of the X-point and to reduce the stray fields from the P1 circuit, increasing

the inboard vertical field and allowing for a more D shaped plasma; the P4T

and IMB circuits share the same windings and produce the vertical field

of equilibrium and the radial field for the vertical position of the plasma

centroid; the Shaping circuit is responsible for changing and elongating the

plasma shape; finally the four divertor coils allow the formation of an X-

point and the control of its position, as well as the last close field surface

strike positions.

Each circuit can be controlled either in absolute current, proportional

(to the plasma current) current or against a geometrical parameter, defined

as a vector named Gap (see Figure 3.12). Examples of Gaps are the Radial

Outer Gap (ROG), which defines the distance between the outer limiter

and the plasma, and the Radial Inner Gap (RIG), the inner limiter ROG

analogue. The amplifiers can also be set in blocked state, where minimum

negative voltage is applied, and no induced current is allowed to flow in the

circuit (due to the presence of a diode); or in the free-wheeling state where

0 V are applied across the circuit.

Although the PF circuits are independently controlled, they are strongly

coupled due to their mutual inductances. In the absence of plasma the full

circuit equations can be written as:

VC = RCIC +MIC (3.11)

where VC is a column vector with the circuits voltages, RC is a diagonal

square matrix with the circuits resistances, IC is the circuits measured

currents, and M is a square matrix containing all the self and mutual

inductance terms.

The controller structure was designed to be independent of the control

26


Figure 3.12: Main Gaps in the JET Tokamak. Gaps are geometrical dis-tances of the plasma to a given point, that can be controlled by shapecontroller to a prescribed value. One of the most used is the Radial OuterGap (ROG), controlled by changing the vertical field produced by the P4Tcircuit.

mode selection and it can be summarised [3] as:

Vref = RCIC +K(Yref − Y ) (3.12)

where Y and Yref are respectively the vectors of measures and references

of the controlled variables, and K is a gain matrix defined as:

K = H · (MT−1C−1) (3.13)

where H is named cancellation matrix and cancels the coupling effects of

the faster circuits, and C contains the delays due to the dynamics of each

circuit. T has the role of translating the current measurements in mean-

ingful control variables.

27


In order to control Gaps, Shape Controller needs to receive as input

measurements of the plasma surface along the Gaps. In order to do so a

software named Felix [26] implements the XLOC equilibrium reconstruction

code [27, 28].

3.2.1.1 XSC: eXtreme Shape Controller

The eXtreme Shape Controller (XSC) is a recent addition to the historical

Shape Controller of JET. It is structured as an add-on module and was

designed to allow full boundary control of the plasma shape [29, 30], as

opposed to SC simpler Gap control. XSC has been succesfully validated in

the JET Tokamak in 2003 [31], and is now regularly used, in particular to

control ITER-like plasmas [32, 33].

The main idea behind the XSC algorithm is to control the full plasma

boundary, while minimising the error over a large set of geometrical shape

descriptors (32 Gaps, strike points and X-point position), so that the system

is no longer limited to the accurate control of only a few Gaps.

The XSC operational scenarios are implemented [34] around a given

plasma shape and equilibrium (in terms of plasma current, internal induc-

tance li and the ratio of the poloidal kinetic to magnetic pressure βp). The

system made by the plasma, JET’s passive structures and PF coils is a

distributed parameter system described by a set of nonlinear PDEs [35].

However by using the axisymmetry of the Tokamak device and some ap-

proximations it is possible to obtain a nonlinear lumped parameters approx-

imation of the PDEs. As the plasma basically moves between equilibrium

states, the obtained lumped parameter rapresentation can be further sim-

plified by linearizing it around a desired equilibrium, obtaining a linearized

plasma model [36, 37] in the form:

28


x(t) = Ax(t) +Bu(t) + Ew(t) (3.14)

Ip,eq · g(t) = CIPF (t) + Fw(t) (3.15)

where A, B, E, C, F are the model matrices obtained via linearization;

x(t) is the state vector and is made by the variations of the currents in the

PF circuits and of the plasma current; u(t) is the input voltage variations

on the PF circuits (zero for the plasma current “virtual” circuit); w(t)

are the disturbances (βp and li variations); g(t) is the variation of the

shape descriptors and, finally, Ip,eq is the value of the plasma current at the

equilibrium.

As the decoupling of the PF coils is already carried out by the SC system

(which XSC leverages), and the power supplies can be modeled as simple

first order SISO systems:

IPFi(s) =Iref,PFi

(s)

1 + sτPF(3.16)

where τPF is conservatively chosen as the slowest time constant between

all power supplies, the XSC controller can be modeled by simply using the

second equation of system (3.15).

XSC minimizes a steady-state performance index:

J = limt→∞

[gref − g(t)]T [gref − g(t)] (3.17)

which penalizes the error on the whole plasma shape with respect to a ref-

erence shape gref .

In Figure 3.13 the block diagram of the extended JET Shape Control

system is reported (as implemented on the actual plant), with the XSC

highlighted and made up of the Gap Controller part (minimizing the shape

error cost function), and of the set of low pass filters “adapting” the re-

29


sponse of the XSC to the slowest power supply.

Figure 3.13: Block diagram of the Shape Controller system augmented withthe XSC.

The generation of a XSC scenario is completely automated by a set of

XSC Tools [34]. With these tools it is possible to define an XSC Configura-

tion Files which basically is a set of XSC parameters and the linear plasma

model on which that particular configuration is based. An XSC Simulator

is also present in the suite of tools to help with carrying out closed loop

simulations of the XSC together with the linear model of the plant.

3.2.1.2 CLA: Current Limit Avoidance

The main issue with the XSC system was the fact that it didn’t take into

account the current limits on the PF coils which, if reached, cause the

controlled termination of the experiment or, in extreme cases, even a dis-

ruption.

As stated in the previous section, XSC scenarios had to be accurately

tuned by hand in order to ensure that all PF currents where safely far from

the current saturations. This led to difficulties in the development of said

scenarios, and deepened the dependence of XSC on a correct model of the

30


whole plasma shaping system.

The Current Limit Avoidance (CLA) system was developed as an add-

on module for XSC in order to keep a balance between plasma shape con-

straints and distance of the currents from the saturation limits in real-time

[38, 39, 40, 41].

The CLA system is based on the dynamic input allocation theory de-

veloped in [42]. The same theoretical framework was already successfully

applied in FTU plasma elongation control system [43, 44]. The idea behind

this theory is that in a MIMO system, when the number of actuators ex-

ceeds the number of controlled outputs, different choices of the inputs can

raise the same output response (at least at steady state). A dynamic input

allocator leverages this property by modifying the input to a plant in order

to obtain a better allocation of it (for instance by keeping actuators away

from saturations) without compromising the outputs.

In particular, given a system in the state space standard form:x = Ax+Bu+Bdd

y = Cx+Du+Ddd(3.18)

P (s) = C(sI −A)−1B +D, P ∗ := P (0) (3.19)

and a controller defined as:xc = Acxc +Bcuc +Brr

yc = Ccxc +Dcuc +Drr(3.20)

the dynamic input allocation theory developed in [42] is applicable only

either to strongly input redundant system, i.e. systems where ker(B) ∩ker(D) 6= ∅, or to weakly input redundant systems, i.e. system where

ker(P ?) 6= ∅. In the former case input allocation allows to keep the value

of the plant inputs inside a desirable region without affecting the output

response of the system, while in the latter the same can only be guaranteed

at steady state (so the input allocation should be sufficiently slow to avoid

31


instability).

In the case of the XSC system, however, the system is not even weakly

input redundant as is the general case when the number of outputs is greater

than the number of inputs of a plant. However, as small deviations from

the desired shape are acceptable as long as they guarantee the current

limit avoidance, there was margin to operate. In particular the theory in

[42] needed to be extended. In [41] the problem has been throughly ana-

lyzed and solved by introducing a continously differentiable cost function

J(u∗, δy∗) measuring the trade-off between the modified steady-state input

of the plant u∗, and the associated output modification δy∗.

r e yc u y

ya δyAlloc. P*

XSC Plant

JG10.245-6c

+ ++

+−

−

Figure 3.14: Block diagram of the control system with the insertion of theallocator block.

Defining the following allocator system: w = −ρK(∇J)′

= −ρK

(∇J

[I

P ?

]B0

)′ya = B0w

(3.21)

where ρ is a scalar parameter tuning the allocation speed, K is a sym-

metric positive definite gain matrix and B0 is a full column rank matrix

specifying the allocation directions in the input space4 [40]; and intercon-

4B0 leads to the possibility of “denying” certain directions, thus blocking the allocatorfrom applying any control action to them. This has been used extensively to forcibly blockcertain points in the plasma shape, such as the X-Point position.

32


necting the allocator to the systems (3.18) and (3.20) as shown in Figure

3.14: uc = y − P ?yau = yc + ya

(3.22)

and assuming that the feedback system made by (3.18) and (3.20) is well

posed and exponentially stable, it is possible to show that the input al-

located closed loop system converges, for sufficiently small values of the

allocation speed, to a steady state which minimizes J(u∗, δy∗) [41].

The CLA system has been recently commissioned at JET. In particular

pulses #81710 and #81715 have been carried out keeping all the parame-

ters constant with the exception of the enabling of the CLA in the latter

pulse (at 61s) with the following “artificial” limits on the divertor currents

in order to force the intervention of the allocator system:

ID1 ∈ [−16.5 − 4] kA ID2 ∈ [−31.45 − 10] kA

ID3 ∈ [−11 − 2] kA ID4 ∈ [6 13.5] kA

Figure 3.16 shows that the limits on the currents in the various divertors

are quickly enforced upon enabling the CLA. Notice the oscillation in the

ID2 current do to the reallocation of the other currents. Figure 3.15 shows

instead the negligible difference in shape between the reference pulse (in

blue) and the one with the CLA enabled (in red). Notice in particular

how the X-point position is kept fixed (as been programmed in the CLA

configuration). A detail of the movements of the top-right gap (GAP2) and

of the internal and external position of the plasma (RIG and ROG GAPs)

is reported in Figure 3.17.

33


(a)

(b)

Fig

ure

3.15

:JE

Tp

uls

e#

8171

0(b

lue)

and

#81

715

(red

)w

ith

CL

Aen

able

d.

Sh

ape

erro

r(a

)an

dd

etail

(b).

34


61 61.2 61.4 61.6 61.8 62 62.2 62.4 62.6 62.8 63−4000

−3000

−2000

Time [s]

Cu

rre

nt

[A]

Current on ID1

#81710

#81715

61 61.2 61.4 61.6 61.8 62 62.2 62.4 62.6 62.8 63−1.05

−1

−0.95x 10

4

Time [s]

Cu

rre

nt

[A]

Current on ID2

#81710

#81715

61 61.2 61.4 61.6 61.8 62 62.2 62.4 62.6 62.8 63−1.2

−1.15

−1.1

−1.05x 10

4

Time [s]

Cu

rre

nt

[A]

Current on ID3

#81710

#81715

61 61.2 61.4 61.6 61.8 62 62.2 62.4 62.6 62.8 635500

6000

6500

7000

Time [s]

Cu

rre

nt

[A]

Current on ID4

#81710

#81715

Figure 3.16: Comparison of currents on the divertor colis for JET pulses#81710 and #81715.

35


61 61.2 61.4 61.6 61.8 62 62.2 62.4 62.6 62.8 63

0.08

0.09

0.1

0.11

0.12

0.13

0.14

Time [s]

GA

P [

m]

RIG Measure

#81710

#81715

61 61.2 61.4 61.6 61.8 62 62.2 62.4 62.6 62.8 630

0.02

0.04

0.06

Time [s]

GA

P [

m]

ROG Measure

#81710

#81715

61 61.2 61.4 61.6 61.8 62 62.2 62.4 62.6 62.8 630.18

0.2

0.22

0.24

0.26

Time [s]

GA

P [

m]

GAP2 Measure

#81710

#81715

Figure 3.17: Comparison of GAP measures for GAP2 (top right of thevacuum vessel) and RIG/ROG (Radial Inner/Outer GAP) for the JETpulses #81710 and #81715.

36

3 Plasma control problems and solutions 3.3 Power supplies related problems

3.3 Power supplies related problems

Due to the high fields required for magnetic control and heating of plasmas,

Tokamak power supplies tend to be very complex machines, usually custom

built for the experiment at hand.

In this section two examples of some of the most common difficulties

concerning Tokamak power amplifiers are reported, namely the manage-

ment of problems when driving amplifiers outside their standard operating

point, and the overcome of power supplies limits due to their embedded

controllers. The former problem has been addressed in FTU, where low

current requests on the AL-F amplifier led to oscillating behavior, while

the latter concerned the improvement of the performances of an old ampli-

fier for the EFCC coils at the JET Tokamak.

3.3.1 Induced plasma oscillations: the AL-F amplifier

IP

IV

Figure 3.18: Control system block diagram of horizontal position.

In FTU, the desired horizontal plasma position is regulated thanks to a

pair of coils named V (vertical field) and F (feedback). The former provides

most of the energy needed for the horizontal stabilization and is generally

driven in feedforward mode due to its severe bandwith limitations. The

latter, instead, is dedicated to an accurate regulation of the horizontal

plasma position and is driven by a PID controller working in feedback

mode plus a possible feedforward preprogrammed term.

37


A feedback PID controller uses as input the difference between the mag-

netic flux measured at the two desired plasma boundaries ∆Ψ. This mea-

surement resembles the horizontal position error because a horizontal mis-

placement causes a difference between the flux values at the two desired

boundaries. The whole F coil control loop is sketched in Figure 3.18, where

the AL-F block is a thyristor-based converter receiving a reference signal

coming from the PID controller, corresponding to the requested F coil cur-

rent.

38


Figure 3.19: Electrical scheme of the AL-F converter.

39


The schematic of the AL-F converter is shown in Figure 3.19; the circuit

can be however well represented by the simplified electrical scheme shown

in Figure 3.20.

I1

I2

IF

L L

V1

V2

LF

RF

Figure 3.20: Simplified electrical scheme of the thyristor bridges of theAL-F converter.

In this scheme, each thyristor has a minimum current threshold of

1.2 kA below which no conduction is possible. Therefore, any requested

current level below this threshold has to be obtained by an adequate bal-

ance among the currents flowing through the 2 bridges. Unfortunately,

the PID controller was not designed to deal with nonlinear components, so

that instability phenomena occur when it is forced to act with F currents

below the 1.2 kA threshold. In fact, the algorithm generally works fine

for standard plasma discharges, but it often results inadequate during the

plasma startup or in particular experimental circumstances such as when,

due to the first wall impurity’s release, the kinetic pressure of the plasma

is lower than the expected one. In many of such cases, strong oscillations

are experienced and the experiment (shot) is often terminated.

40


3.3.1.1 Model of the AL-F feedback

The first step in trying to reproduce the oscillations seen during experi-

ments was to develop a simplified model of the AL-F circuit derived from

the scheme of Figure 3.20, where each one of the left and right branches

represents two pools of thyristors (exactly sixteen of them, in parallels of

pairs).

Each branch can generate pulsing voltages on the F coil, which is repre-

sented by the central branch and its inductance LF and resistance RF . The

two inductances L are saturated inductances (namely variable inductances

whose value depends on the current level) used to limit sudden current

variations in low current operation. A hardware control system (not shown

in the figure), called PHSC (Programmable High Speed Controller), is em-

bedded into the AL-F circuitry. This control system has authority over

the switching angles of each thyristor within each one of the two external

branches of Figure 3.20. In particular, each thyristor transfers some quan-

tity of the alternate power supply to the load according to the switching

angle allocation.

Since the load is highly inductive (with time constant LF /RF ), from

the point of view of the currents I1(t) and I2(t) flowing in the circuit, what

matters most is the equivalent average voltage applied to each branch within

one period of the alternate power supply (this is roughly 60 Hz). According

to Figure 3.20, denote by V1(t) and V2(t), respectively, the average voltage

applied to the left and right branches of the figure.

Then, also taking into account the constant voltage drop VT around each

conducting thyristor, the equations describing the circuit in Figure 3.20,

neglecting the presence of the two diodes, correspond to (dependence from

time has been omitted for space constraints):V1 = L

dI1

dt+ LF

d(I1 − I2)

dt+RF (I1 − I2) + 8VT

V2 = LdI2

dt− LF

d(I1 − I2)

dt−RF (I1 − I2) + 8VT ,

(3.23)

41


where the constant voltage drop VT is multiplied by 8 because each branch

consists of a series of 8 thyristors.

Equations (3.23) can be used to derive two coupled differential equations

allowing to compute I1(t) and I2(t) from the equivalent average voltages

V1(t) and V2(t) applied by the thyristors. These equations are reported

in (3.24). Note that in (3.24) the presence of the diodes of Figure 3.20 is

embedded in the fact that with non positive currents, the current variation

is not allowed to be negative, so that the non-negative semiaxis is positively

invariant.

dI1dt =

max

0, (L+LF )V1+LFV2+LRF (I2−I1)−8(2LF +L)VT

L2+2LLF

, if I1 ≤ 0

(L+LF )V1+LFV2+LRF (I2−I1)−8(2LF +L)VTL2+2LLF

, otherwise

dI2dt =

max

0, (L+LF )V2+LFV1+LRF (I1−I2)−8(2LF +L)VT

L2+2LLF

, if I2 ≤ 0

(L+LF )V2(t)+LFV1+LRF (I1−I2)−8(2LF +L)VTL2+2LLF

, otherwise

(3.24)

Clearly, from equations (3.24) one can easily compute the current flow-

ing in the F coil by IF (t) = I1(t)− I2(t).

The hardware PHSC unit (whose block diagram is reported in Figure

3.21) controls the voltages V1(t) and V2(t) so that two requirements are

fulfilled: 1) the output current IF (t) is close (as close as possible) to the

requested current IF,req(t) coming from the PID controller (see Figure 3.18);

2) both currents I1(t) and I2(t) never drop below the minimum conduction

current characterizing the thyristors if IF,req(t) is below that threshold.

Since the thyristors are paired and each thyristor has a minimum current

of 600A, the total minimum current is given by Imin = 1200A.

To fulfill the above mentioned goals, the PHSC follows a PID strategy

42


++PHSC

PID

AL-FBridges

_ _IF,req PHSC

Logic

IFIreg

I1

I2

I2

I1V1

V2

eI

Figure 3.21: Block diagram of the PHSC.

with an error feedback from the F coil current error:

Ireg(t) = KpeI(t) +KIxc(t) +KdeI(t)

xc(t) = eI(t)(3.25)

Moreover, based on the output Ireg(t) of the PID controller, the PHSC

imposes the voltages V1(t) and V2(t) as

V1(t) = σV (Imin − 1.8I2(t) + σM (Ireg(t)))

V2(t) = σV (Imin − 1.8I1(t)− σM (Ireg(t)))(3.26)

where σs(·) is the scalar symmetric saturation function having saturation

level s, and M = 12500A and V = 5000V .

This control strategy ensures that for any current request IF,req(t), the

PHSC will regulate I1(t) and I2(t) so that, after a reasonable transient,

IF (t) = IF,req(t) and, moreover, both I1(t) and I2(t) will be either zero or

larger than Imin. This type of behavior is inevitable with circuits relying

on thyristors which can be thought of as some very powerful diodes and,

as such, are inevitably characterized by a minimum current to be able

43


to polarize the P/N junction. The larger the maximum current of the

thyristor, the larger the minimum allowable current must be. Hence, when

low currents are requested from IF,req(t), the PHSC will need to enforce

two currents in the left and right branches of Figure 3.20, both of them

larger than Imin and such that their difference (which flows in the load)

corresponds to IF,req(t). Note that in the model we completely disregard

the effects of the switching angles of each thyristor: the filtering action of

the highly inductive load makes it unnecessary to model all the switches

happening in the bridge and the pulsed voltage waveforms arising on the

load. The averaged representation of this model is sufficient to reproduce

the experimental behavior.

0.4 0.6 0.8 1 1.2 1.4

−1000

0

1000

2000

Time [s]

Cu

rre

nt

[A]

Experimental and simulated currents on F coil (shot #20838)

Experimental

Simulated

Figure 3.22: Shot number #20838. Open-loop simulation of the AL-Fmodel.

Figure 3.22 reports on an open-loop simulation where the model given

by (3.24), (3.25) and (3.26) has been implemented in Matlab/Simulink using

the experimental time history of IF,req(t) from the unstable shot #20838

as an input. According to the PHSC datasheet, the parameters in the PID

controller (3.25) have been selected as

Kp = 1.5, Ki = 37.5, Kd = 0.75.

44


Moreover since the small nonlinearity of L causes negligible effects on the

closed-loop behavior, it has been considered as a linear inductance. Finally,

according to the experimental equipment, the other components have been

selected with the values reported in Table 3.1. In Figure 3.22 the solid

curve represents the experimental measurement of IF (t) while the dashed

curve represents the simulation output.

L LF RF VT2mH 9mH 8mΩ 1.8V

Table 3.1: Values of the electrical components of the AL-F model.

Altogether, the model in Figure 3.21 consisting of (3.24), (3.25) and

(3.26) with:

eI(t) = IF,req(t)− IF (t) = IF,req(t)− (I1(t)− I2(t)) (3.27)

corresponds to a strongly nonlinear closed-loop relating the requested cur-

rent IF,req(t) to the actual F coil current IF (t).

Considering the systems (3.24), (3.25), (3.26) and (3.27) under the ac-

tion of an input IF,req(t) = I0+I(t) with I(t) sufficiently small in magnitude

and rate it is possible to show [45] that the solution of the systems coincides

with the one of (3.25) and (3.27) interconnected with the linear filter:

IF (t) = αIF (t) + βIreg(t) (3.28)

If |I0| is sufficiently large (but |I0| < |M |) the system (3.28) is stable with:

α = − LRFL2 + 2LLF

= −0.28, β =L+ LF

L2 + 2LLF= 67.4

called, from now on, High Current (HC) model; while if |I0| is sufficiently

45


small, system (3.28) becomes unstable with:

α =L(1.8− 2RF )

L2 + 2LLF= 63.53, β =

2L

L2 + 2LLF= 71.22

defined as Low Current (LC) model.

This interesting feature means that before the stabilizing action per-

formed by the PID controller (3.25) in the feedback loop of Figure 3.21,

the core linear dynamics of the system ranges from exponentially unstable

behaviors to exponentially stable ones, thus resulting in a highly nonlinear

response for large ranged signals. Despite the unstable small signal be-

havior of (3.24) and (3.26), the PID controller (3.25) manages to stabilize

both linearized dynamics (even though with poor performance in the small

signal range -see the upper plot of Figure 3.23).

Indeed, when closing the loop with the PID controller (3.25), the poles

of the linearized AL-F transfer function from If,req(t) to If (t) are (−4103,

−77, −21) in the first case, i.e. with the HC model, and (−4107,−21±j36)

with the LC model.

Figure 3.23 shows the simulation response IF (t) to a triple step input

IF,req(t) when using the closed-loop of the PID with the LC linear model

(solid curve in the upper plot) and the response to the same input when

closing the loop with the HC linear model (solid curve in the lower plot).

In both plots the nonlinear response obtained by closing the loop with the

nonlinear model corresponds to the dashed curves. Note that in the first

step, where I0 is very small, the response matches that one of the LC model,

in the second step it sits somewhere between the two models and in the

third step, where I0 is sufficiently large, it matches the HC model response.

Once established this peculiar feature of AL-F, also the other compo-

nents of the feedback system were modeled in order to be able to run a

closed-loop simulation of the control system in Figure 3.18.

46


0 0.5 1 1.5 20

500

1000

1500

2000

Time [s]

Curr

ent [A

]

Step response of the high current (HC) model

Reference

Nonlinear AL/F model

Linear HC model

0 0.5 1 1.5 20

500

1000

1500

2000

Time [s]

Curr

ent [A

]Step response of the low current (LC) model

Reference

Nonlinear AL/F model

Linear LC model

Figure 3.23: Linear LC and HC models behavior compared to the nonlinearresponse.

The PID controller on the left is completely known because it is dis-

cretized and implemented in the real-time control code running on the

Linux-RTAI platform controlling the plasma during the experiment [46].

In particular, the controller obeys the following standard law:

yPID(t) = Kp(t)uPID(t) +Ki(t)xc(t) +Kd(t)uPID(t)

xc(t) = uPID(t)(3.29)

where Kp(t), Ki(t), Kd(t) are time variant gains which are preprogrammed

and usually uniformly ramp up during the startup phase, are constant

47


during the flattop phase and ramp down during the final phase of the shot.

The constant values at the flattop, Kp = 0.15, Ki = 25, Kd = 4.5 · 10−4,

have been used as this is the most interesting part of the experiment, and

the one in which the oscillations are most evident. Mimicking the FTU

control system, the controller (3.29) has been introduced in the simulation

diagram in its discretized form with the sampling period Ts = 0.5 ms used

at FTU. Its approximate discrete-time transfer function corresponds to:

yPID(z) =− 1

2 · 10−5

(Kp +Ki

Ts2

(z + 1

z − 1

)+Kd

z − 1

(τ + Ts)z − τ

)uPID(z)

with the time constant value τ = 4 ms.

The external signals acting on the diagram of Figure 3.18 correspond to

the preprogrammed feedforward profiles for the F coil (called IF,pre), for the

V coil (called IV,pre) and for the plasma current (called IP,pre). In particular,

the equivalent effect of these currents at the plasma input is computed by

suitably weighting each contribution according to their equivalent steady-

state effect on the plasma position and corresponds to selecting the signal

acting before AL-F in Figure 3.18 as w1(t) = IF,pre(t), and to selecting the

signal acting after AL-F as w2(t) = gV IV,pre(t) + gP IP,pre(t), with gV =

4.317 and gP = 4.717 · 10−2. Then the controller (3.29) is interconnected

to the closed-loop via the equations IF,req(t) = IF,pre(t) + yPID(t) and

uPID(t) = ∆Ψ(t).

The plasma model in Figure 3.18 is crudely represented as a simple linear

dynamical system capturing the gross horizontal motion of the plasma. The

model adopted has been identified by manually adjusting the parameters

48


in a first order continuous time filter with the following transfer function:

∆Ψ(s) = P (s)(IF (s) + w2(s))

:= −10−7 3.4375s

0.008s+ 1(IF (s) + w2(s))

(3.30)

mapping IF (t) + w2(t) into ∆Ψ(t).

0.4 0.6 0.8 1 1.2 1.4

−0.1

−0.05

0

0.05

0.1

Time [s]

Ma

gn

etic f

lux [

Wb

]

Experimental and simulated magnetic flux (shot #20838)

Experimental

Simulated

Figure 3.24: Shot number #20838. Open-loop simulation of the plasmamodel.

Figure 3.24 shows a comparison between the experimental data from

the same unstable shot #20838 used in Figure 3.22 and the simulated

data obtained from the model (3.30) driven by the experimental signals

IF,supplied(t)+w2(t). Some differences between the experimental data (solid)

and the simulated data (dashed) occur, especially with large signals, for the

fact that the linearity of plama behaviour is guaranteed only for very small

variations around the equilibrium. However, the small signal fidelity of the

model is satisfactory.

49


0 0.5 1 1.5

−1000

0

1000

2000

Time [s]

Cu

rre

nt

[A]


Experimental

Simulated

0 0.5 1 1.5

0

2000

4000

6000

Time [s]

Cu

rre

nt

[A]


Experimental

Simulated

Figure 3.25: IF response for shots number #28000 (upper plot) and #20838(lower plot) in solid lines. Corresponding closed-loop simulations in dashedlines.

In Figure 3.25 two closed-loop simulations5 are reported: one corre-

sponding to a standard experiment (where the F coil current was monoton-

ically increasing and significantly higher than the circulating current Imin),

and an oscillating one.

5Closed-loop simulations of previous experiments are carried out by closing the AL-Floop while considering the other signals (such as the currents on the other coils, etc.)as external disturbances and directly feeding them to the simulink model as downloadedfrom the FUT experimental database. This, while not being completely accurate, as itdisregard some phenomena such as mutual inductances, can give an insight of problemsand performances of the solutions proposed, and it is a mandatory step before closingthe loop on the actual machine.

50


The upper plot shows the IF (t) response simulating the stable shot

#28000. The initial mismatch between the experimental data (solid) and

the simulated response (dashed) depends on possible different initial con-

ditions and the fact that the linear plasma model (3.30) certainly cannot

capture the highly nonlinear plasma behavior during the breakdown phase.

The lower plot of Figure 3.25, instead, shows the simulated IF (t) response

for the unstable shot #20838. Note that the simulated F current is correctly

mapped within the critical range between ±Imin and the closed-loop sys-

tem exhibits an undesirable oscillation, mimicking the twofold behavior of

the actual experiments. Once again, the simulated behavior in Figure 3.25

(as well as the experimental behavior), reveals that the only possible cause

of this twofold behavior can be the nonlinear model of the AL-F circuit.

Indeed, all the other components of the closed-loop simulation (correspond-

ing to the diagram of Figure 3.18) are linear and cannot cause instability

for small signals and stability for large ones.

As a further confirmation of this fact the poles of the linear closed-

loops between the PID controller (3.29) and the plasma model (3.30) via

the two linear approximate behaviors HC and LC for the AL-F system have

been studied. With the HC model, the closed-loop is exponentially stable

with a maximum real part of the stable closed-loop poles corresponding to

λMAX = −7.5. With the LC model, the closed-loop is, instead, unstable,

with λMAX ' 34. This property explains, to a certain extent, the oscil-

latory behaviour experienced in experiments and simulations in the small

signals regime.

3.3.1.2 Anti-windup solution

Once the cause of instability is recognized, the anti-windup scheme of [47]

(see also [48]) can be applied by treating the nonlinear dynamic behavior

of AL-F as a sort of undesired (dynamical) input nonlinearity. Indeed, the

basic calculations carried out in [48, 47] still apply to this case and conver-

51


gence properties can be established because the plasma model (3.30) is lin-

ear and exponentially stable. The arising closed-loop scheme is represented

in Figure 3.26, where the supplied current in the F coil is not measured

from the field but is computed using the model illustrated6. In particular,

the faithfulness of the computed current with respect to the experimental

one has been confirmed by real-time simulations running exactly the same

real-time code prepared for the experimental controller (see [49] for details

on the underlying architecture).

AL-Fmodel

PLASMAmodel

–+

++

Anti-windup compensator

.

PID PLASMA++++

ΔΨ. AL-F

Preprogrammed

V and P current

F,reqIFI

Preprogrammed

F current

FÎ

Targetmodel I F,T F-Î

v =ΔΨ

++

.

++

.

T-ΔΨ2

v =KΔI1Kaw

ΔΨ

~

Figure 3.26: Anti-windup solution.

The proposed anti-windup solution consists in adding extra dynamic

components to the closed-loop, that generate two compensation signals

6Note that the current could be measured directly from the field, but this wouldoverload the input signals to the real-time controller; therefore computing an estimate ofit from the model has been the preferred solution. Moreover, as the anti-windup solutionis robust (as shown in [47]) and the nonlinear AL-F model developed is quite realistic,using the model to compute IF has the beneficial side effect of avoiding the introductionof any noise in the system that, instead, a real sensor inevitably has.

52


v1(t) and v2(t) (as in Figure 3.26), where v1(t) is added to the AL-F input

and v2(t) is added to the plant output ∆Ψ(t). In particular, the controller

(3.29) is interconnected to the closed-loop via:

IF,req(t) = yPID(t) + IF,pre(t) + v1(t)

uPID(t) = ∆Ψ(t) + v2(t)(3.31)

Regarding v1(t) and v2(t), they are selected in such a way that the com-

pensation action aims at reproducing as much as possible the closed-loop

response arising when the AL-F dynamics is replaced by the “target model”

in Figure 3.26, which is selected to be linear. Defining IF,T (t) as the output

of said “target model”, IF (t) as the estimated value of IF (t) arising from

the nonlinear model, Kaw as a positive constant (tuning parameter for the

antiwindup system), and ∆ΨT (t) and ∆Ψ(t) as, respectively, the (linear)

plasma model response to IF,T (t) and IF (t), then the v1(t) and v2(t) signals

are selected as:

v1(t) = Kaw(IF,T (t)− IF (t))

v2(t) = ∆ΨT (t)−∆Ψ(t)(3.32)

It is possible to show [45] that for small enough values of Kaw ≥ 0, and

under the action of limited signals, the anti-windup closed-loop generates

limited responses and that for any trajectory of the target closed-loop such

that the response of the target model coincides with that of the nonlinear

AL-F model (3.25), (3.26), (3.27), the response ∆Ψ(t) of the anti-windup

closed-loop from the same initial conditions and with the same inputs con-

verges to the response ∆Ψ(t) of the target closed-loop.

Note that according to the robustness analysis carried out in [47] (see

also [50]), the overall scheme is robust with respect to variations of the

plant parameters (as compared to the model). This robustness follows

from a small gain reasoning (see [47] for details) under the assumption that

the controller is incrementally stable, which holds as shown before.

53


0 0.5 1 1.5

−1000

0

1000

2000

Time [s]

Cu

rre

nt

[A]

Simulated currents on F coil (shot #20838)

Without AW

With AW

Figure 3.27: Shot number #20838. Anti-windup simulation.

Figure 3.27 shows a simulation of the same shot #20838 illustrated in

the lower plot of Figure 3.25 when the target model is selected as the HC

model previously characterized. This selection of the target model also

allows to achieve an automatic and smooth shutdown of the anti-windup

compensation when the F current becomes large enough, i.e. when the

response of the nonlinear model coincides with the one of the target (HC)

model. It can be seen that the oscillations caused by the AL-F nonlin-

earities (solid curve) are completely removed by the anti-windup scheme

(dashed curve). Note also that the oscillations during the initial transient

are still present but those, as mentioned above, should be interpreted as

an effect of the linear model of the plasma behavior, which is inaccurate

during the startup phase. Note also that this startup phase is basically

the same for the solid and dashed curves, revealing that the anti-windup

compensation is not doing much in that initial transient.

The proposed solution, whose block diagram representation is shown in

Figure 3.26, has been implemented on the FTU feedback system and tested

with various values for the gain Kaw.

54


First of all a simpler version of the anti-windup system has been de-

ployed at FTU in order to have a benchmark and test the system software-

wise. This preliminary version consisted of the scheme of Figure 3.26 with

Kaw = 0 (thus turning off the signal v1) and the target model chosen as

an identity (thus forcing the system to behave like an ideal amplifier). The

drawback of this solution, however, was that, since the AL-F model never

acts like an identity, the anti-windup action would enforce closed-loop cor-

rections also in operating conditions where the F current is large enough not

to require any correction. Therefore, in order to forcibly avoid any interven-

tion of the controller when large currents were requested, a dead-zone-like

nonlinearity was added at the input of the anti-windup system.

The FTU experimental response with this solution is shown in Figure

3.28 (shots #31621 and #31626). Notice how the oscillations have been

greatly damped.

0.35 0.4 0.45 0.5 0.55 0.6 0.65−1000

0

1000

2000

Time [s]

Cu

rre

nt

[A]

Comparison of the same pulse with and without antiwindup system

#31621 (AW off)

#31626 (AW on)

Figure 3.28: Shots #31621 and #31626: same shot type. In the latter theanti-windup system was turned on.

Following the success of this preliminary version, the development of the

anti-windup system has been completed and the final controller deployed

in the plant. In Figure 3.29, a comparison between two shots, one with

the anti-windup system turned off (#32784) and the other with the system

active and tuned with the target model coinciding with the HC model and

Kaw = 1 (#32786) is reported. In Figure 3.30 the values of the signals v1(t)

55


and v2(t) are also shown. It is evident that the damping of the oscillations

was worse than what expected from the simulations, and in particular from

what was obtained with the simplified system deployed previously.

0.4 0.5 0.6 0.7 0.8 0.9 1

1000

1500

2000

2500

Time [s]

Cu

rre

nt

[A]

Comparison of the same pulse with and without antiwindup system

#32784 (AW off)

#32786 (AW on)

Figure 3.29: Shots #32784 and #32786: same shot type. In the latter theanti-windup system is turned on.

To verify this issue, a further test has been carried out and is reported

in Figure 3.31, where the same experiment has been repeated twice, first

using the “HC-target” anti-windup compensation (shot #32959) and then

using the simplified one (shot #32960). This test further confirmed the

better behaviour of the less elegant solution.

Considering the high level of accuracy of the implemented nonlinear

model of the AL-F amplifier (and thus of its HC linearization), the simple

plasma model used in the anti-windup system is probably the cause of the

bad behaviour of the HC-target anti-windup solution. This theory is further

confirmed by inspecting the experimental data corresponding to the signal

∆Ψ(t) of Figure 3.26 where the closed-loop oscillations are clearly visible.

As currently no fast plasma boundary reconstruction algorithms are

deployed at FTU, it is not possible to have a better plasma model for

the anti-windup system. For this reason the simplified scheme is the one

active by default during experimentation at FTU. With this solution in

place, the previous undesired oscillations occasionally happening and pos-

56


0.4 0.5 0.6 0.7 0.8 0.9 1−400

−200

0

200

400

Time [s]

v1 s

ignal

v1 signal in pulse #32786

0.4 0.5 0.6 0.7 0.8 0.9 1

−5

0

5

x 10−3

Time [s]

v2 s

ignal

v2 signal in pulse #32786

Figure 3.30: Shot #32786: signals v1 and v2 of the anti-windup system.

0.35 0.4 0.45 0.5 0.55 0.6 0.65

1000

2000

3000

4000

Time [s]

Cu

rre

nt

[A]

Comparison between complete and simplified anti−windup

#32959 (complete AW)

#32960 (simplified AW)

Figure 3.31: Shots #32959 and #32960: same shot type. The completeanti-windup code ran on the former. The simplified code shows smalleroscillations.

sibly compromising the experiment have not been seen again during all the

subsequent experimental campaigns.

57


3.3.2 The JET EFCC Coils control system

Magnetic field perturbations which break the toroidal symmetries are in-

evitable in tokamaks due to imperfections in magnetic field coils and to the

presence of magnetic materials. Magnetic islands arising from these asym-

metries can cause the appearance of locked modes which, if uncontrolled,

frequently lead to disruptions [6, 5]. One of the main goals of the Error

Field Correction Coil (EFCC) systems in modern tokamaks is to alleviate

this effect by applying magnetic perturbations that compensate the natu-

ral error field at the plasma boundary. In JET the EFCC are a set of 4

non-axisymmetric coils distributed around the Tokamak as by Figure 3.32

Figure 3.32: The EFCC coils at the JET Tokamak.

Recently at JET, performance issues and practical limitations led to the

decision of replacing the EFCCs voltage amplifiers by using the old Vertical

Stabilisation amplifier (named FRFA) which was decommissioned around

the same period.

The opportunity was also taken to reformulate and improve the con-

troller application by incorporating it into a new realtime software frame-

work, developing a new control algorithm and revising the time synchro-

nization mechanism whilst maintaining essentially the same VME based

hardware components [51].

58


It has been observed during JET operations that there is a decrease in

the performance of this simple PID controller as the frequency of the current

reference waveform increases. Furthermore, it is inevitable that inherent

plant non-linearities such as component saturations and, in particular, the

amplifier’s switching of the thyristor bridge restricts the performance of the

(linear) PID controller to a limited operational space.

New controller

Originalcurrentreference

AnticipationAnticipatedreference

InverseModel

DirectModel

Newreference

PID

Innerdelay

adaptation

Plant(EFCCs)

VCVS

Feedforwardvoltage

Feedbackvoltage

Outerdelay

adaptationMeasuredcurrent

+-

JG10.250-1c

Figure 3.33: The proposed advanced controller block diagram.

This has motivated the design and development of a new non-linear and

adaptive controller scheme (for a primer on adaptive control see for instance

[52]) with the clear aim of improving the system’s overall bandwidth [51].

The new controller (Figure 3.33) is based on the idea of shifting the current

reference in time (Anticipation block) in order to compensate for circuit

delays and the dynamics of the coils. The Inverse Model block calculates

the inverse dynamics of the system (amplifier and coils) thus supplying the

feedforward component of the control voltage. Also, the Direct Model block

is used in order to calculate the new reference for the PID which takes into

account the anticipation mechanism. The anticipation mechanism is, in

turn, driven by two different loops: the internal one, which attempts to

synchronize the original reference with the newly calculated one (i.e. the

one modified by the plant dynamics), and the outer one, which does the

59


same with the new reference and the measured coil current.

The new controller algorithm has been developed and tested in Matlab

Simulink environment and simulation results are presented in Figure 3.34.

This figure shows a comparison between the experimentally achieved EFCC

current and the predicted one by simulating the new controller algorithm

for JET Pulse #79777. Furthermore, as a validation cross-check of the

plant model used in the new controller algorithm, the simple PID behavior

of the present controller has also been simulated revealing good agreement

with the experimentally obtained current, thus, providing a clear indication

of the accuracy of the model. The current reference used in this pulse is a

40Hz sinusoidal waveform and it can be seen that the simulation with the

new controller scheme predicts an overall system bandwidth increase once

it is implemented in the online system.

Pulse No: 79777

-1500

-2000

-1000

-500

0

19.70 19.72 19.74 19.7619.68 19.78

Cu

rre

nt (

A)

Time (s)

JG

10

.25

0-3

c

Figure 3.34: Comparison of simulated and experimental results for theEFCC advanced controller. Solid black line represents the reference wave-form, dashed black line represents the simulated current obtained with thenew controller, dark gray line represents the current experimentally ob-tained with the present PID controller and the light gray line representsthe simulated current obtained with the present PID controller using theplant model.

60

Chapter 4

Technical solutions and

implementation

4.1 The MARTe Framework

MARTe (Multithreaded Application Realtime executor) is a framework

recently developed at the JET Tokamak while working with the PPCC

(Plasma Position and Current Control) Group. The main aim of this frame-

work is to simplify the development and deployment of control systems with

strict hard-realtime requirements by being easily portable (thanks to the

underlying library BaseLib2) and by giving to the control system engineer

a simple environment in which to deploy the control law, completely hiding

to him the implementation details.

MARTe received a warm acceptance by the fusion community, and is

now used in various machines throughout Europe (JET, FTU, ISTTOK,

COMPASS...). In particular FTU is carrying out a complete revamping of

its old control system in order to port it to the new framework.

61

4 Technical solutions and implementation 4.1 The MARTe Framework

4.1.1 The BaseLib2

MARTe is built upon a C++ multi-platform library named BaseLib2. The

first key feature of the library is the ability to run the same code in different

operating systems (OS). It is organized in consecutive layers (Figure 4.1)

where the lowest level implements the different calls for each of the available

systems. In order to guarantee portability, the remaining layers and the

end-user code must use the functionalities provided by the library, avoiding

OS dependent calls. This layered scheme provides a logical organization

on how the code is distributed. Top layers have a broader view over the

library functionality and tend to accommodate code that is less critical for

the operation of a system, granting at the same time a set of tools that

greatly eases the development of applications. When porting the library to

a new OS only the lowest layer needs to be adjusted.

Level 0

Threading

Semaphores

Memory

...

Files

Sockets

Strings

Level 1

Garbage Collection

Named objects

Object Database

...

Level 2

Advanced streaming

Data types definition

Level 3

Configuration DB

Data driven support

Build objects by name

...Level 4

Built-in HTTP server

Object introspection

Level 5

Dynamic Data Buffer

Message interfaces

Data driven interfaces

... Level 6

Matrices

RT Matrices

Basic filters

...

Figure 4.1: The layered structure of BaseLib2.

The layer closest to the operating system provides all the abstrac-

tion regarding the interaction with the file system, networking, threading,

semaphores, atomic operations and operating system dependent optimiza-

tions. BaseLib2 was already ported to the following OS: VxWorks, Linux,

Linux RTAI, Solaris, Mac OS X and Microsoft Windows. The possibility

62


of running the same code in different systems allows developers to write

and debug code using tools that might not be available in the target archi-

tecture. This is even more important when the final environment has no

memory protection (such as Linux RTAI), making the debug of algorithms

particularly difficult.

BaseLib2 tries to maximize the concept of reference and to dissuade as

much as possible the use of pointers. For this purpose a garbage collector

and a special root garbage-collectable object is available (GCNamedObject).

Objects inheriting from this class can be automatically constructed by the

library and are destroyed by the garbage collector when they are no longer

required by any external reference. These objects are also allowed to have

a name and are, upon construction, automatically added to an internal

database (GlobalObjectDataBase). By simply searching for an object

name in this database a reference to it can be later obtained.

In order to automatically create objects the library provides a standard

configuration language. This configuration is provided to the library as a

stream and analyzed by a parser that instantiates the objects based on the

requested classes. If the object is successfully created, its self-configuration

function (ObjectLoadSetup) is called with the subtree of the configuration

file relative to the object passed as a parameter. Listing 4.1 and Figure

4.2 show an example of a possible configuration. In order to guarantee

real-time efficiency, the object is expected to perform the majority of the

required validations and all memory allocations at this stage. Once the

object is successfully built it is added to the previously described database.

A garbage collectable container object is also provided, allowing to recur-

sively create new nodes in the internal database (GCReferenceContainer).

63


+HttpServer = Class = HttpServ ice

Port = 8084

+MARTe =

Class = MARTeContainer

+RTThread1 = Class = RealTimeThread

+Cont ro l l e r = Class = ControllerGAM

NoPlasmaCurrentGain = 40.0

IPWaveform = Times = 0 120Amplitudes = 0.5 0 .5

+DAM =

Class = DAMGAM

Project ionMatr ix = 0 = 1 .0 0 .0 0 .0 0 .0 1 = 0 .0 1 .0 0 .0 0 .0 2 = 0 .0 0 .0 1 .0 0 .0 3 = 0 .0 0 .0 0 .0 1 .0

. . .

. . .

. . .

Listing 4.1: An example of a BaseLib2 configuration.

A series of classes are dedicated to strings and data streaming. These

permit to perform a series of advanced operations in character sequences,

Figure 4.2: Example of a BaseLib2 CDB. The library is data driven using asyntax that allows to automatically create and configure objects. Once cre-ated these are added to an internal tree database which can later be used tosearch and retrieve references. This figure corresponds to the configurationpresented in listing 4.1

64


and to perform input/output (I/O) operations without requiring the con-

cept of beginning and end of transmission. Most of the I/O classes are

abstracted to a level where the knowledge of the target media (file, socket,

memory, etc.) is not required.

Live introspection and analysis of objects is provided by the CINT C++

interpreter1, which permits to verify objects internal states and expected

behaviors. Due to its wide availability and simplicity the Hypertext Trans-

fer Protocol (HTTP) has been chosen as the standard transfer mechanism

of information when querying objects. BaseLib2 provides an internal multi-

threaded HTTP server which can browse any objects that inherit the ap-

propriate interface (HttpInterface). The internal object database is also

browsable and is rendered as a recursive tree with links to all the objects

which have the HTTP interface implemented. This scheme allows library

users to have a standard user-interface for all the application built with

the library. The GET and POST HTTP requests are also implemented

providing a way to actively interact with the objects. Multiple servers can

coexist at the same time, by using different ports.

Object oriented languages provide a very good programming paradigm

when designing an application. The concepts of data abstraction, inheri-

tance and modularity permit to define and even impose how the different

pieces of the application should interact. Sometimes, and particularly true

when providing a library, one cannot fully constrain or predict how some-

thing is going to behave. In order to decouple concepts higher level pro-

tocols are usually used. Applications developed using the BaseLib2 library

can use a series of message classes that allow objects to communicate in

a Smalltalk fashion. These messages contain a sender and a receiver ob-

ject address, specified as a unique path in the internal tree configuration

database. A network based message server enables the interaction between

1http://root.cern.ch/drupal/content/cint

65


applications living in different machines. The library automatically searches

for the object address in its database and if found calls the appropriate func-

tion (ProcessMessage). Messages can also be sent in synchronous mode

where the sender expects a reply from the receiver. The content of the

messages is free and they are routinely used inside the library to start and

stop services and by some objects to update their internal behavior.

One example of such an object is the state machine class. It is updated

by changing its internal states accordingly to the messages received and

upon state changing it broadcasts new messages to registered listeners. Be-

ing structured using the aforementioned named objects, the State Machine

(and the content of the messages sent when changing states) is completely

configurable at runtime.

The library also provides a series of algebraic and mathematical tools.

The widest range is in matrix calculations where several matrix decompo-

sition methods, like the single value decomposition (SVD) and LU decom-

position, are available.

In order to assure the correct function of a system, a logger mechanism

is of huge importance. A good logging scheme permits to expeditiously

analyze any problems that may arise during operation. On the other side

the logger should not compromise the real-time performance.

BaseLib2 provides a series of logging functions with which it is possible

to automatically append to a desired logging string, information like the

name of the object, its location in memory, the time when the message

was issued, the thread and process identifiers, as well as the name of the

machine where it was generated.

A minimum impact on the system is guaranteed by the use of a con-

sumer/producer scheme. The process wishing to write a log message ap-

pends it to a FIFO queue. A consumer, running with very low priority,

processes the messages in the queue when processor time is available. This

66


permits to even report information from an interrupt service routine where

the scheduler is usually frozen.

The library makes no assumptions about how messages are consumed.

The default behavior is to send it using the User Datagram Protocol (UDP)

to a stated address. Using this scheme a relay logger mechanism was devel-

oped, allowing to combine, collect and store messages arriving from different

machines. Figure 4.3 shows a design where messages are produced in a pri-

vate network and subsequently broadcasted to a data persistence node and

a live information system.

Since a system can produce hundreds, or even thousands, of information

messages per day, a Java application that organizes messages accordingly

to user defined criteria has been developed. Messages are grouped first by

producer, where each machine has a node in a tree, and inside every node,

messages are grouped by: severity, thread and object producer name. Fil-

tering enables control room users to follow only a narrow subset of messages

(e.g., messages with a particular alarm level from a specific object in a sub-

system).

4.1.2 Multithreaded Application Realtime executor (MARTe)

MARTe is a modular collection of a series of components that permits the

system to work as a whole [4]. Some of the blocks are intended to be further

adapted to the target application, while others are expected to be used as

provided.

4.1.2.1 Generic Application Module

The atomic element of MARTe is named Generic Application Module (GAM)

and all applications built using the framework are designed around these

components. A GAM is a class inheriting an interface specified in the

BaseLib2 library. Each GAM contains three communication points: one

for configuration and two for data input and output. GAMs are setup us-

67


Figure 4.3: Relay logger mechanism. Messages are automatically relayedacross networks, allowing to add new logger nodes as required. In thisfigure messages are produced in the acquisition network and further re-layed to a node responsible for data persistence and another node for livevisualization.

ing the standard BaseLib2 configuration syntax described in the previous

section. The core of a typical GAM processes the input accordingly to how

it was configured and outputs the modified information.

Conceptually GAMs are equivalent to a “block” in a standard block

diagram Figure 4.4.

During initialization the modules declare what data they expect to re-

ceive and what information is going to be produced in output. Each type of

input or output is declared as a configurable named signal with a data type

associated. This is the only available way to chain GAMs and provides a

clear boundary in the system: GAMs are not aware of the presence of other

68


C P

H

u y

v

D

D

B

GAM

C

read(v)

read(u)

read(y)

wri te(u)

wri te(y)

wri te(v)

TIMEGAM

P

GAM

H

Figure 4.4: Conceptual passage from a block diagram to a MARTe archi-tecture.

modules.

The GAMs which interface with hardware are named IOGAMs and pro-

vide a unique high level interface. The connection between the IOGAM and

69


the specific low level code responsible for driving the hardware is performed

through the specialization of a high level class named Generic Acquisition

Module. This interface requires the number of hardware inputs and outputs

to be specified and forces the existence of a reading and a writing function.

These functions must be implemented for each kind of I/O device, although

it is common that devices belonging to the same family are able to share

a common acquisition module. These high level interfaces to the hardware

can usually be configured to return the latest acquired value or to wait for

a new sample to arrive (at the cost of delaying the execution), depending

on the requirements of the application.

Another important feature in MARTe is the ability to perform simula-

tion without interfering with the plant. Although this greatly depends on

the target project, it is usually possible to model up to some extent the

process to be controlled, and a GAM can be used to simulate the inputs

(possibly using real signals saved beforehand) and another to predict the

output of the system. This arrangement permits to debug and tune all the

other modules, or to test the possible effects that a change in a module

configuration will produce. On the live system the simulation modules can

later be swapped with the real interface to the hardware. This technique

has been used for instance in the development of a simulator for the JET

Vertical Stabilization system [53].

Data is transferred between GAMs by using an optimized memory bus

named Dynamic Data Buffer (DDB). The first role of this entity is to en-

sure coherency across the system, verifying if all the signals requested by

each of the GAMs are produced by one module and in case of any inconsis-

tency issue an error during the initialization phase. Although it is not the

default behavior, a GAM may write over a signal already produced by an-

other module. This process, named patching, must be explicitly requested

otherwise it is assumed as an error.

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MARTe also provides a collection of GAMs to send signals between

different systems, even in different machines. Depending on the system,

real-time may only be guaranteed on the producer, unless using a realtime

network such as RTNet [54, 55].

The RealTimeThread is a container of GAMs and acts as a GAM micro-

scheduler being responsible for their sequential execution. The thread can

be configured to run on a specific processors and can be assigned to a spec-

ified priority. It also tracks execution times and keeps a series of internal

timing information about each of the GAMs for which it is responsible. The

list of GAMs that are executed can be changed accordingly to the state of

the system as provided by a BaseLib2 State Machine as described earlier.

Depending on the severity of an error, the RealTimeThread can be config-

ured to take an action, which could be the complete stop of execution, or

to switch the execution to a series of “safety” GAMs.

MARTe must contain at least one real-time thread. When designing a

new system one of the major challenges is to decide what GAMs, and in

what order, are to be executed. Figure 4.5 depicts a possible set of modules

that start by acquiring signals from an hardware device, then processing

and taking decisions upon this data, and finally outputting the signals to

both a device and a storage scheme. Threads can be configured to run at

a specific frequency and all the GAMs are expected to execute within this

time. A warning or an error is issued everytime the execution time is larger

than the specified cycle period.

MARTe requires the existence of at least a timing source. A shared

variable in the RealTimeThread tracks the absolute time in microseconds.

Depending on the project, this time is usually expected to be updated by an

external hardware through an IOGAM, although sometimes the CPU clock

can be used, particularly when developing and debugging a new project.

71


Figure 4.5: The RealTimeThread acts a module micro-scheduler. In thisfigure a group of seven GAMs is executed at each cycle. The first GAMacquires data from a device and outputs it to the memory data buffer. Onceprocessed some of the data is written back to the hardware.

MARTe provides ready made high precision time emulators, based on the

CPU time and optimized for each of the supported operating systems. A

new control cycle is started when the absolute time is a multiple of the

requested cycle period.

The previously described acquisition module also forces the presence

of a synchronization function. When configuring MARTe one chooses if

this synchronization module has to work in interrupt or polling mode. In

the first case the execution of MARTe is arrested up to the arrival of an

external interrupt. If polling is selected the system will continuously query

the interface until an answer is provided. In both cases when an answer

72


arrives the absolute time is updated and the framework checks if a new

cycle is to begin.

As this is one of the most delicate parts of the system a series of checks

and timeouts can be configured. The system designer must decide what

actions to perform when a timeout or error occurs.

MARTe is also able to handle a collection of RealTimeThreads. These

can either be configured to run concurrently on the same processor or in

parallel. The only way of sharing data between threads is to use a special

IOGAM (provided by the framework) as the output of the thread producing

data, connected to an input acquisition module in the thread consuming

it. For MARTe these two synchronization GAMs emulate the presence of a

physical hardware which would produce and consume the data, allowing to

have the two threads completely decoupled. The output module can also

be used as the timing source for the driven thread and can be configured

to send undersampled filtered data, allowing to specify different running

frequencies.

MARTe can send and receive messages using the BaseLib2 message pro-

tocol described earlier. MARTe internal services are started and stopped

upon the reception of a specific message. The interface is designed to be

connected to an external object that is able do decode an external con-

figuration protocol, for instance from a human machine interface, into a

MARTe recognized message. This is the preferred way to change the list of

modules to be executed and to update GAMs parameters. After receiving a

message, the framework verifies its validity and forwards it internally. If re-

configuration is required the threads being executed are eventually stopped.

MARTe uses the HTTP server provided by BaseLib2 and supplies a

collection of HTTP based components that allow to setup a communica-

tion channel with all the internal elements. Examples of these utilities are

73


a remote configuration file upload and a signal server to download data

acquired during a certain period of time in CSV or MATLAB binary for-

mat. Live diagnosis of threading and memory activity are also available,

together with the list of all the registered objects. All the GAMs that

expose information are also highlighted.

74


4.1.3 Code generation via SysML

Modeling languages, such as the Unified Modeling Language (UML), help

the designers to foster the design and understanding of complex systems.

The Systems Modeling Language (SysML) [56] extends the UML, in-

tending to unify the various modeling languages used by systems engineers.

In particular, SysML extends the application of UML to systems which are

not purely software based, and can in particular be applied to design hetero-

geneous embedded systems. SysML also introduces a requirement diagram

to structure the requirements and link these to the system architecture and

test procedures.

During the last decade UML and SysML have been used to promote

model–driven development in different fields, such as manufacturing sys-

tems [57, 58], electronic systems [59], embedded systems [60, 61, 62], and

automotive [63].

In particular in [57], Thramboulidis extends the UML to define the

Model–Integrated–Mechatronics paradigm. Such a paradigm supports the

model–driven development of complex mechatronic systems, and it has been

used to develop a system platform called Archimedes that permits to au-

tomate the development process of manufacturing systems. A recent ex-

tension that uses SysML to model industrial automation control systems is

presented in [64], while [61] also deals with an application of model–driven

engineering to real-time automation systems.

Furthermore, SysML has been adopted in [58] to formally specify mecha-

tronics systems; such a description is then used to generate models to be

used for the verification of the automatically generated embedded control

code. A similar approach to automatically generate models from a SysML

description has been presented also in [65].

More recently, the authors of [62] have used UML to propose model–

driven approach for the analysis of the so-called dynamically partially re-

configurable systems (DPRS), which are embedded system realized with an

75


FPGA device with the capability of being partially reconfigurable. These

systems enables more applications to be accelerated in hardware, making

possible to reduce the overall system execution time.

Due to all this interest in the SysML language it was decided to develop

an automatic model-to-MARTe system. In fact GAM configurations can

be easily stored into text-file, as well as a number of makefiles that are

needed to compile the real-time application on different targets. Moreover

by using SysML a better system documentation is achieved.

It was decided to use a subset of the diagrams SysML provides, in

particular:

• internal block diagrams are used to specify the internal structure of

GAMs; this allows to explicitly show the distinction between GAM

internal parameters and input/output signals, which enhance the self-

documentation of the project;

• interdependency among GAMs is explicitly represented by means of

block definition diagram that show the interconnections between the

various module, also enhancing the overall project documentation.

Having proposed a model–driven approach to design a MARTe applica-

tion, is then possible to use model–2–text tools to automatically generate

part of the real-time code and of the configuration data, together with make

files for the compilation on different platforms. To this aim Topcased has

been adopted as modeling tool, since it integrates the model–2–text tool

Acceleo. Topcased is a system/software engineering toolkit which complies

with the requirements of critical and embedded applications [66].

First of all a BaseLib2 model containing all the common definitions

(classes, types, etc.) needed to model GAMs (see Figure 4.6) has been

developed.

76


(a) Excerpt of the BaseLib2 modeled classes.

(b) Excerpt of the BaseLib2 modeled data types.

Figure 4.6: Block definition diagrams used to model the BaseLib2 library.

Once the BaseLib2 model has been imported in a new Topcased project,

the first step to model GAMs is to define them by using a BDD. An ex-

ample is shown in Figure 4.7, where three GAMs are defined: a simple

77


Figure 4.7: Example of GAMs modeling. The block definition diagramreported in this figure is used to define three GAMs and to add to themthe HTTP server, which is implemented by the HttpInterface block.

PID controller, a WaveformGenerator that generates the control reference,

and a Plant block, which simulates the plant behavior and can be used to

perform offline tuning and validation of the controller.

The three GAMs reported in Figure 4.7 inherits also from the HttpInter-

face abstract class; this block is included in the BaseLib2 library and is used

to add HTTP user interface capabilities to a generic block. This scheme

enables GAMs to publish run-time execution information about the inter-

nal state of algorithms and data. When modeling a GAM it is possible to

add internal parameters (e.g., controller gains for the PID in the proposed

78


Figure 4.8: Internal block diagram used to define input and output signalsfor the PID GAM shown in Figure 4.7.

example) and to extend the interface (e.g., the GenerateReference() func-

tion for the WaveformGenerator GAM).

The definition of the internal parameters can be easily done by using an

IBD, as shown in Figure 4.8, where the internal structure of the PID GAM

is modeled. Moreover IBDs are also used to model input and output signals

of a given GAM. Input and output names shall match channel names into

the DDB, while the distinction between inputs and outputs allows to clearly

identify the producers and consumers of each signal.

By using the Topcased modeling tool, it is also easy to add comments

and expression objects to a GAM model, in order to add comments to

GAM parameters and signals, and to specify initial values, respectively

(see Figure 4.9). This feature is also exploited to add comments and initial

values to the automatic generated code.

Once all the GAMs within a project have been modeled, BDDs can be

used also to define interconnections between them. Such interconnection

implicitly defines the execution order of the GAMs chain by the Real-time

Thread..

Figure 4.10 shows the GAMs chain for the simple example described in

the previous section. In particular, two additional GAMs (ADC and DAC)

have been added to model the data acquisition boards of this simple real-

time control system. In Figure 4.10 the Plant GAM has not been chained,

79


Figure 4.9: Topcased hierarchical view of the model of the PID GAM blockshown in Figure 4.7.

Figure 4.10: Block definition diagram used to model the connections be-tween GAMs.

80


since this BDD models the behavior of the real system to be deployed,

which therefore does not include the plant simulation.

Starting from the SysML model of the MARTe application to be de-

ployed, which consists of the definition of the GAMs and of the GAMs

chain, the Acceleo tool can be exploited to automatically generate a large

part of the whole real-time source code, configuration and makefiles for

multi-platform compilation.

Acceleo is a code generator tool which transforms models into code, and

it has been designed to improve software development productivity. Its ap-

proach deals with many concepts grouped together under the name Model

Driven Architecture (MDA), which is obviously coherent with mode–driven

approach proposed in this work. Although MDA is currently being stan-

dardized by the Object Management Group, there is a lack of effective and

operational tools. Acceleo results from the best practices and experience

feedbacks from the use of MDA in the industry, and it is fully integrated

into Topcased. In particular, it is easy to develop Acceleo plug-ins for

Topcased.

By using the Acceleo plug-in, the SysML model is parsed and the fol-

lowing files are produced for each GAM, each one in its own subdirectory:

• the GAM C++ source files (.h and .cpp);

• the header files containing the input and output signals for easier

interfacing with the DDB;

• additional files for multi-platform compilation (including make files);

• the GAM configuration file.

Moreover, the top level MARTe configuration file (including all the

GAM-relevant configurations previously generated) is also produced.

81


4.1.3.1 Sample application to the FTU Tokamak

As an example of application of the model–driven approach, the plasma

control system of FTU has been modeled, and a large part of the code for

the real-time system has been automatically generated.

The Frascati Tokamak Upgrade is a medium size Tokamak (minor and

major radius of the chamber are, respectively, 0.31 and 0.935 meters) op-

erating since 1990 at the ENEA laboratories of Frascati, in the south of

Rome (Italy). FTU is capable of discharges of up to 1.5 seconds of length

with a toroidal field of 8T .

The magnetic field responsible for plasma shaping and current drive, is

generated by four different amplifiers that feed a coils system that surrounds

the tokamak vacuum chamber. In particular, two amplifiers, named AL-F

and AL-V, are used for the horizontal position control (the former, faster,

is in closed loop, while the latter is usually operated in feed-forward), while

the AL-H amplifier for the vertical one, and AL-T for the plasma current.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

T1

T2

T3

V

FI

FE

HIHE

T2

T3

V

FI

FE

HIHE

Figure 4.11: Cross section of the FTU Tokamak.

82


Figure 4.11 and Figure 4.12 show a cross section of the FTU tokamak

toroidal vessel. The vacuum chamber sits in the middle of the figure, while

the coils lay around it, named following the amplifier to which they are

connected (F, V, H and T).

Figure 4.12: FTU vacuum chamber.

The block diagram of the plasma control system of FTU is reported

in Figure 4.13. The blocks in light grey represent the actuators and the

plant, the white one is the algorithm which reconstructs the plasma shape

from the magnetic measurements, the oval blocks are the references and the

feedforwards for the actual control systems, whose main blocks are depicted

in dark grey.

The plasma control system is divided in two main parts: the gas control

system, which regulates the density of the plasma; and the plasma current

and position control system, which is made by three PIDs (the vertical

83


Plant

Gas Valves

Current

Amplifiers

Density

Controller

Gas preprog.

value

I preprog.

values

H

Controller

F

Controller Allocator

PlasmaShape

ExtremumSeeking

Algorithm

Direct/Reflected Power

Pos. ref.

values

LLL Temp.

Controller

F H V T

LLL Temps

Magnetics

z r

r*

z,r

T

Controller

Ip

Figure 4.13: Block diagram of the FTU plasma control system.

position feedback, which uses the AL-H amplifier, the horizontal one, which

uses the AL-F amplifier, and the AL-T controller which drives the plasma

current to the requested value). The AL-V amplifier is operated in open-

loop2. The feedback quantities for AL-F and AL-H (called DEP and DEZ)

are the flux errors measured on the horizontal and vertical axis of the

vacuum chamber, and are proportional to the plasma position error. Those

quantities are evaluated from the magnetic measurements by the realtime

Last Closed Magnetic Surface estimation algorithm, “Plasma Shape” in

Figure 4.13 (see Tutorial 7 in [67]).

The plasma current and position control system is also augmented by

three nonlinear controllers: the temperature controller for the experimen-

tal liquid lithium limiter (in development), an extremum seeking algorithm

2It should be noticed that “open loop” is intended only concerning the FTU FeedbackSystem: in fact all the amplifiers have an internal control system which drives the outputcurrent to the reference value, so, strictly speaking, no one of them is actually operatedin open-loop.

84


for LH power optimization [68], and an allocator algorithm used to control

plasma elongation [44].

Figure 4.14: BDD of the FTU plasma control system.

In order to revamp and improve the FTU control systems, it was decided

to reimplement it from scratch leveraging the MARTe Framework [4]. To

do so the PCS has been “packaged” in small self-contained pieces which

could be wrapped as GAMs. The final result of this packetization is shown

in Figure 4.14. Note that the PCS reported in the figure is a simplified

version, as the safety and scheduling modules which had to be produced

for a reliable operation of the device were added at a later stage. Each block

85


in Figure 4.13 has been translated in a single GAM. As the AL-F PID has a

different behavior than the other ones (more precisely it has been upgraded

with an antiwindup system in order to avoid low current oscillations [69]),

instead of using various instances of a single and standard PIDGAM, it has

been decided to develop three different PID-based controllers to leave room

for future improvements.

Figure 4.15: Auto-generated files for the FTU Plasma Control System.

The BDD diagram shown has been then fed to the developed Accelleo

plugin in order to generate the boilerplate code. In Figure 4.15 we show

the amount of files automatically produced. The vast majority of standard

code, as well as a simple master configuration file, has been generated,

greatly reducing development time. In particular about 60% of the code

has been automatically generated, most of which was the one relative to

the initialization and visualization of each GAM’s parameters (i.e. the most

error-prone code). The only code which had to be actually written was the

“scientific” one, i.e. the algorithms themselves.

86

4 Technical solutions and implementation 4.2 The JET systems

4.2 The JET systems

4.2.1 The Vertical Stabilisation system

As shown in a previous chapter, in order to obtain better fusion perfor-

mances the plasma is forced to be vertically elongated, unfortunately be-

coming unstable [70], thus needing closed loop control. The aim of the

Vertical Stabilisation (VS) system is to control the instability by driving

the current in a set of Poloidal Field (PF) coils so that a radial magnetic

field is produced. The lose or erroneous control of the instability can have

huge negative impacts, as plasma disruptions (complete loss of thermal and

magnetic energy) may occur, inducing large currents and forces in the ma-

chine vessel.

An international project for the upgrade of the JET plasma control

(Plasma Control Upgrade, PCU) [71, 72] allowed to greatly enhance the

current VS system. The project has seen the development of new modeling

techniques for the analysis of the vertical instability, as well as numerous

technological improvements, concerning in particular the control system

(with a complete upgrade using the MARTe Framework) and the new power

supply ERFA (Enhanced Radial Field Amplifier).

The hardware-software requirements for the upgrade were the execu-

tion of the closed loop cycle within 50 µs with a maximum jitter of 2.5 µs,

including the interface with hardware and data processing. An application

fulfilling these requirements was designed using the MARTe framework,

where a multi-disciplinary team contributed to the different parts of the

system: hardware and software engineers developed the integration with

hardware and the overall setup of the system, while control engineers pro-

duced the GAMs for modeling and control.

Although JET is a pulsed machine, with experiments that can last up to

2 minutes and where the presence of the VS system is vital, it was decided

from the beginning to have the vertical stabilization always running and

87


guaranteeing real-time, making no distinction between operational phases.

This is particularly relevant for future fusion devices like ITER [73], where

subsystems will have to adapt to a steady state operation reality. This

was also only possible since no pulse-based assumptions were made in the

design of the framework.

4.2.1.1 The Vertical Stabilization hardware

The system runs on a Intel Quad-Core processor and uses the RTAI im-

plementation [74], with a standard Linux kernel option (isolcpus) to ex-

plicitly assign interrupts and Linux tasks to a single core, breaking the

symmetric multiprocessor scheduler decisions. All MARTe threading activ-

ity is placed on the remaining three cores, allowing one to be completely

dedicated to the RealTimeThread. This single feature immediately guar-

antees that no external activity or spurious interrupts will deviate the real-

time system from its high priority activities. It is important to notice

that all these configurations are completely transparent to MARTe and no

code modifications had to be performed, not even to change in which cores

threads should run or how memory should be arranged. The downside

of this implementation is that, living in kernel space, software faults have

large impacts on the system, making it very hard to debug problems that

are not closely related to the framework, mainly in the GAMs algorithms.

This is where the multi-platform configuration proves to be a powerful

mechanism as all the code can be tested as is in more friendly environment

like userspace Linux or MS Windows.

The hardware of the data acquisition system is based on the PICMG 3.0

Advanced Telecommunications Computing Architecture (ATCA) standard

and contains 6 data acquisition cards. Each board comprises 32 18-bit res-

olution analog to digital converters acquiring at 2Msamples/s. The cards

are connected to the controller computer using the Peripheral Component

88


Figure 4.16: Photo of the backpane of the VS5 ATCA crate.

Interconnect Express (PCIe) point-to-point links through the ATCA back-

plane [75]. A rear transition module (RTM) connects the system to the

radial field amplifier ERFA (for a picture of the crate see Figure 4.16).

When designing the hardware interface driver for the data acquisition

system it was decided to use an interrupt-less environment with a data

polling scheme, but without compromising the other interfaces to the com-

puter, e.g., network access. The data acquisition boards, map in the con-

troller computer memory a set of four buffers as described in Figure 4.17.

The selected buffer is consecutively cycled every 50 µs by the firmware. The

first value written is the header and contains the absolute time since the

89


last trigger, followed by the values of the ADCs and finally by the footer

containing the same value as the header. The driver continuously queries

the value of next header to be written and as soon as it changes, it starts to

check the footer. When these two values are the same, the driver signals the

high level IOGAM, which in turn broadcasts and updates MARTe absolute

internal time. The framework uses the values provided by the high resolu-

tion timers of the processor to measure the performance of the system and

to keep track of the jitter associated with the synchronization mechanism.

The firmware also assures synchronization between all boards.

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10

0 u

s a

go

32 A

DC

s

50

us a

go

32 A

DC

s

20

0

us a

go

32 A

DC

s

15

0 u

s a

go

18050 17900 1795018000

18050 17900 1795018000

32 A

DC

s

10

0 u

s a

go

32 A

DC

s

50

us a

go

32 A

DC

s

20

0

us a

go

32 A

DC

s

15

0 u

s a

go

18050 17900 1795018000

18050 17900 1795018000

10

0 u

s a

go

50

us a

go

20

0

us a

go

15

0 u

s a

go

18050 17900 1795018000

Core #1

Linux

Core #2

MARTe

Services

Core #3

MARTe

Services

Core #4

RT-Thread

network

and other

I/O interrupts

HTTP server

Logger

...

CPU

Master board

Figure 4.17: Data synchronization of the ATCA boards is performed in themaster board, which is guaranteed by the firmware to be the latest to havedata available. Once new data is available it is collected and a new MARTecycle starts. The CPU core isolation scheme allows to protect the real-timeenvironment from spurious and undesired interrupt sources.

4.2.1.2 Interfacing with JET

The JET Control and Data Acquisition System (CODAS) [76] is the en-

tity responsible for providing control, monitoring and data acquisition to

all the existent subsystems. As a JET subsystem, the vertical stabiliza-

tion uses the tools provided by CODAS, both for plant configuration and

90


data retrieval. Between pulses, experts are allowed to change the system

configuration by mainly updating values in the different GAMs. This is

performed using the standard user interface of JET (Figure 4.18) which

contains several access layers and where expert users and engineers are al-

lowed to upload configuration files for each of the modules. VS operators

are expected to act on a upper layer where atomic values are validated and

have already a unique and direct physical meaning. As of today and with

configuration files that can easily have more than 7000 lines, the require-

ment for an advanced user-interface was almost compulsory, allowing to

capitalize all the VS experimental advanced features [13], minimizing the

risks of configuration and regression faults.

4.2.1.3 Vertical Stabilization GAMs

The design of the new system has been carried out following a model–based

approach [9], which turns out to be essential when high performance and

robustness are required. In particular, such an approach has been adopted

for:

• the design of the new power supply for the RFA circuit, called En-

hanced Radial Field Amplifier (ERFA), to assess the system perfor-

mance for different choices of the amplifier’s maximum voltage and

current [72];

• the assessment of the best choice for the turns setup of the RFA coils;

• the design of the new VS control algorithm, to optimize the controller

parameters for the different operative scenarios.

Thanks to the availability of reliable linear models for the plasma mag-

netic behavior [36, 37], a validation phase has been carried out for each

design step, from conceptual design to implementation.

Scenarios with highly elongated plasmas in presence of large ELM per-

turbations are envisaged to achieve better fusion performance in tokamaks.

91


Figure 4.18: JET LEVEL1 interface for the new Vertical Stabilisation Sys-tem 5.

In these extreme scenarios a general purpose controller3 cannot guarantee

the requirements. Hence, to push the performance up to the desired level,

it is usual to rely on a model–based design approach [9], which assures the

needed control performance. In particular, for each plasma scenario, it was

envisaged that the JET VS system could potentially use different estima-

tions of the plasma vertical velocity, as well as different adaptive algorithms

for the controller gains, in order to optimize the system behavior.

3We refer to general purpose controller as a controller which is robust enough to satis-factory work under any envisaged operational scenario, without pushing the performanceto the best. In particular a general purpose controller should at least do not disrupt theplasma for almost all the possible operational scenarios.

92


The architecture proposed for the VS system is similar to the one

adopted for the eXtreme Shape Controller at JET [31, 34, 30]. In particu-

lar, it permits to face with different scenarios during the same experiment in

a simple manner. However, since the controllers are optimized, there must

be a safety logic that, in case of unexpected dangerous events, switches to

the general purpose controller, in order to get a safe termination of the

experiment.

Since control algorithms are usually developed in a modeling and sim-

ulation environment (e.g. Matlab/Simulink), another requirement for the

new VS software architecture concerns the possibility to check and vali-

date the whole real-time code (including both the control algorithm and

the auxiliary code, i.e. communication interface with other systems, data

acquisition, etc.) before testing it on the plant. To perform this offline

validation real-time computational model of the plant, based on detailed

plasma linearized models [36, 37] are needed.

It turns out that the adoption of a flexible and modular software archi-

tecture is mandatory for the VS implementation, in order to successfully

cope with the functional requirements summarized above. Indeed, the old

VS system, based on 4 Texas Instruments DSPs (TMS320C40), was not

flexible enough to satisfy the requirements. As an example, the present

control system has been used to carry out some preliminary experiments

aimed to confirm the simulation results. To perform these tests the needed

modification had been applied as patches to the normal control mode, since

it was not possible to isolate the control algorithm from the remaining part

of the software. It turned out that, given the limitations of the present

architecture, anytime a new functionality was required its implementation

was not straightforward, mostly due to this lack of modularity, which is

always needed in a real world control application.

The overall system is composed of a collection of 18 modules. The

first GAM synchronizes and retrieves data from 192 ADC channels which

93


are then written into the DDB. Using some of these signals, the second

GAM produces a series of synthetic data, like threshold detection and linear

combinations of magnetic signals. ObserverGAM subsequently provides an

estimate of the plasma vertical velocity, followed by a scheduler module

deciding which of the following GAMs must be executed.

Four controller GAMs are then sequentially executed and only the one

previously selected by the scheduler, through a signal in the DDB, per-

forms real work. Two modules, named vertical and divertor amplifier, are

allowed to override the output of the controller with some special features,

like dither or hysteresis, and are run before calling the module responsible

for writing the output back to the DAC and close the loop. A collection

of 6 different GAMs acquire in memory the data for each type of signal:

ADC, controller, debug, performance, waveforms and asynchronous. Fi-

nally, a module performing live statistics of configured signals is executed.

The scheme is depicted in Figure 4.19 and mean values for the time of ex-

ecution of these application modules, reported in Table 4.1.

The architecture of the new JET VS system has been conceived to oper-

ate in advanced plasma scenario, where different estimations of the plasma

vertical velocity must be available in order to optimize system performance.

For these reason, the ObserverGAM has been designed as a container of

ten different observers which computes different estimations of the plasma

vertical velocity.

An observer receives as input a set of measurements and a transfor-

mation matrix. The resulting outputs can be used as inputs for other

observers, in a daisy chain design, enabling the eventual reuse and opti-

mization of some calculations.

The observer computational interface can be extended and specialized

in order to meet and model specific requirements, loosing in flexibility but

leveraging configuration and functionality. One example is the state space

model observer [77], where instead of specifying one anonymous matrix, the

94


Figure 4.19: All the modules executed for each control cycle by theRealTimeThread. The first module provides the synchronization with thehardware. All the code must be executed in less than 50 µs.

end-user is expected to provide the matrices with a direct correspondence

to the observer dynamic model.

As for the ObserverGAM, the Controller GAM has been conceived as

a container of four different control algorithms which are available during

whole pulse. Thanks to this choice, it is possible to meet the requirements

in terms of disturbances rejection and thermal losses in the RFA circuit,

by selecting the optimal controller in each phase of the pulse. Furthermore

this architectural choice permits to safely validate new control algorithms

on the plant by running them in open–loop during the experiments.

95


0

1

2

3

4

5

6

7

8

9

10

Execution tim

e (

us)

GAM Execution times (#78210)

AT

CA

AD

Cand s

ynchro

nis

ation

Sig

nal P

rocessin

g

Observ

er

Schedule

r

Contr

olle

r 1

Contr

olle

r 2

Contr

olle

r 3

Contr

olle

r 4

Vert

ical A

mp. M

odule

Div

ert

or

Am

p. M

odule

AT

CA

Outp

ut

AD

C C

olle

ction

Contr

olle

r C

olle

ction

Debug C

olle

ction

Perf

orm

ance

Colle

ction

Async. C

olle

ction

Wavefo

rm C

olle

ction

Web−

sta

tistics

Maximum

Minimum

Mean

Figure 4.20: Maximum, minimum and mean execution times for all VS5GAMs.

There are a number of inputs that are common to all the control algo-

rithms (i.e. the plasma velocity estimations and the current in the RFA

circuit). Moreover, each algorithm can have its own input signals. The

selection of the plasma vertical velocity to be used for the control is made

on the basis of the scheduling signal provided by the Scheduler GAM.

The control algorithms can implement any linear or nonlinear control

algorithm, provided that the computational effort is achievable. However

each control algorithm must satisfy two basic requirements:

• control of the plasma vertical velocity, in order to achieve vertical

stabilization;

• control the current in the RFA circuit to avoid current saturation and

96


Table 4.1: The execution times of the VS application modules.

GAM Mean (µs) Std. dev. (µs)

ADC 2.43 0.26

Signal processing 5.14 0.01

Observer 4.00 0.04

Scheduler 0.37 0.01

Controller 1 1.01 0.02




Vertical amplifier 0.85 0.03

Divertor amplifier 0.59 0.02

DAC 0.39 0.02

Data collection 1 2.83 0.07






Statistics 1.24 0.02

to reduce the thermal losses in the coil.

In the current version of the JET VS system the plasma velocity regulator

is a proportional controller while a proportional–integral regulator is used

for the current in the RFA circuit. The controller gains are varied during

the experiment on the basis of some additional signals (e.g. the tempera-

ture in the ERFA).

97


The VAMGAM is executed immediately after the controllers and se-

lects the desired controller output, on the basis of the scheduling signals.

Before sending it to the ERFA, the selected voltage request can be further

processed by a series of components: a Dither module, a Delay module, a

Kicks module and a Relay Characteristic.

The Dither component adds a sawtooth waveform to the selected volt-

age request. This feature is used to reduce the effect of the voltage quan-

tization. Indeed ERFA is composed of four units each rated 3 kV, 5 kA,

which can be configured to deliver 12 kV, 5 kA [78].

The Delay module is used to delay the voltage request by a given num-

ber of time samples. The resulting delay introduced in the system has been

used to estimate stability margins during dedicated tests [79].

The Kicks module is the most innovative component of the VAMGAM.

It implements all the various types of “kicks”, voltage pulses of a given

length and amplitude, used mostly to drive Vertical Displacement Event

(VDE) or for ELM pacing.

Each kick is made by a “kick waveform” and of a “kick type”. The

former describes the voltage waveform to be applied by the kick component,

while the latter decides when to apply the waveform itself.

A kick waveform is defined as a sequence of time windows, each one

specifying the following parameters:

• the duration (in seconds) of the time window;

• the amplitude (in volts) of the window;

• the kick modality which can be set either equal to

– ON, to apply in feed-forward the amplitude of the current time

window, substituting the value calculated by the controller;

98


– OFF, to ignore the amplitude specified and to turn off the kick

logic in the current time window;

– ADD, to add the amplitude specified to the value calculated by

the controller);

• the time, which can set equal to

– DEFAULT, to use the value specified by the length parameter

as duration of the current time window;

– WAVEFORM, to use the values specified by a given waveform

as duration of the current time window.

By using the kick waveform and the kick type parameter a very high

level of customization is achieved, allowing the user to specify:

• timed kicks which are kicks applied at a precise time during the exper-

iment, and which are used to simulate Vertical Displacement Events

(VDEs) and to perform halo currents studies [80];

• periodic kicks, used for ELM pacing [81];

• Hα kicks which are triggered at the occurrence of an ELM, and which

are used to switch off the controller during an ELM phase;

• saturation kicks, which are used as protection system when the am-

plifier current reaches the safety threshold, i.e. when the current is

close to the saturation. If this is the case the current is moved far

from saturation by using voltage kicks.

Finally the Relay Characteristic module implements the same variable

hysteresis logic of the power supply ensuring that the correct voltage is

applied by the amplifier even in presence of noise or not perfect calibrated

DACs.

99


The DAMGAM is a module created in order to let the VS system act on

the divertor coils, which are normally controlled by the Shape Controller [3].

In particular the DAMGAM made possible the application of voltage kicks

to the divertor coils.

SC request for D1

JG09.365-6c

Voltage request for D1




SC request for D2

SC request for D3

SC request for D4

Transformed (P) space

Divertors space

Figure 4.21: The internal logic of the DAM.

A block diagram of the DAMGAM is shown in Figure 4.21, where P is

a 4-by-4 invertible matrix which defines a linear transformation that maps

the four divertor voltage requests received from the Shape Controller into a

custom P-space. In this space a gain and a saturation can be applied to each

signal, and the transformed signals pass also through a kick controller which

works in almost the same way as the VAMGAM module. Eventually the

signals are transformed back in voltage requests to the divertor amplifiers.

Thanks to its highly configurable structure the DAMGAM can be effec-

tively used to explore all the possible interactions and advantages of using

also the divertors for the task of the vertical stabilization.

4.2.1.4 User Interface

Two main graphical interfaces are available, namely the Level 1 Interface

(L1-Interface), provided by CODAS, and the Web Interface. The former

allows the user to setup all the VS system parameters before the experi-

ment, while the latter permits to monitor the state of the system during

the experiment.

100


The structure of the L1-Interface is made of several graphical layers,

each one corresponding to a different level of abstraction. Such layers are

organized in two levels:

• Real-time executor level, which allows the user to load the MARTe

configuration. In particular, the user can specify the GAMs to be

executed together with their parameters, specifying them by means

of text files. It is important to note that this level is common to all

MARTe-based applications.

• Application level, which is customized for the VS system. This level

is designed to allow the user to set each controller parameter before

the experiment.

The Real-time executor level is made of three different graphical pages:

• the MARTe Layer page, which is used to setup the interfaces between

MARTe and the other external systems;

• The MARTe Thread Layer page, where the user can load all the

GAMs that make up the real-time system to be deployed. In par-

ticular for the VS system all the GAMs are loaded from this page,

together with their configuration files.

• The Patch page, which is used to change the default values of the

system parameters.

The Application level deployed for the VS system is made of two graph-

ical pages:

• The General page, which is used to set the parameters of the con-

troller. In particular this page is organized in four subsections, each

one corresponding to one of the following module: SPGAM, Observer

GAM, Controller GAM and VAMGAM.

101


• The Scheduler page. This page is dedicated to the Scheduler GAM

and allows the user to plan the experiment by setting the VS behavior

in each of the 25 available time windows. For example, in each time

window the user can choose the estimation of the plasma vertical

velocity to be controlled together with the desired control algorithm.

This page permits also to set the behavior of both the VAMGAM and

the DAMGAM, and to switch on the kicks performed by these two

modules.

The Web Interface is based instead on the MARTe framework and it

is automatically generated by the real-time application. This graphical

interface allows the user to navigate into the GAMs structure and check

the value of the parameters loaded in the VS system.

A sample screenshot of the Vertical Stabilization Web Interface is re-

ported in Figure 4.22.

4.2.1.5 First Results

CODAS is collecting an average of 320 signals per pulse, amounting to

several hundred of megabytes of data. The data collection modules can be

configured to acquire several windows at different frequencies, but higher

importance is given to the data acquired by the ADCs, as the magnetic

signals can be used later for simulation and modeling purposes.

The new vertical stabilization architecture has been running in parallel

with the previous version of the system since the summer of 2008 and it was

already used several times to control the machine in closed loop. Several

consecutive weeks of operation are regularly achieved, with the system run-

ning and in real-time 24 hours per day. During these long operation periods

the configuration was changed by the operators a considerable amount of

times and the system proved to have the capacity to withstand and react

to it with remarkable effectiveness.

One of the major accomplishments regarding the software side of the

102


Figure 4.22: A screenshot of the VS5 Web Interface: the VAMGAM.

project was the achievement of jitters well under 1 µs, as shown in Figure

4.23 where the standard deviation is 0.12 µs . These figures are always true,

not only during the pulse, and were only possible due to key design deci-

sions in the VS configuration, mainly the interrupt and processor isolation.

Again, this was only possible due to the uncommitted way MARTe was

designed, allowing to configure the system (e.g. threading) in a completely

transparent way.

The commissioning of the new VS system has been carried out at JET

during the C26 experimental campaign. During the commissioning period

the old control algorithm has been implemented on the new system, and

ran in parallel with the old one.

The first tests consisted in comparing the voltages requested made by

the new VS controller with the ones provided by the old system, in or-

103


Figure 4.23: The system is continuously is real-time with a jitter inferior to1 µs. In this figure 105 control cycles were performed and the error relativeto the 50 µs is due to the imprecision on the time measurement (usingthe processor timers) and to the natural jitter associated with accessing amemory location.

der to check the accuracy of the new references, and to verify if all the

experimental features were being activated when requested. After gaining

some confidence on the validity of the acquired data and on the software

modules, the new VS started to close the loop in plasma during the ramp

down phase, where the plasma current is smaller and the risk of actually

endangering the machine very small.

Finally, the first plasmas were controlled using the new VS system in

different operational scenarios. No software failures were ever observed

during the execution of an experiment.

After this phase the new system has been employed during the C27

experimental campaign for the commissioning of the ERFA amplifier, and

also to choose the optimum number turns for the coils in the RFA circuit.

For this purpose, the performance of the vertical controller has been as-

sessed not only with plasmas of varying vertical instability growth rate,

104


but also with different plasma–wall clearance, q-profiles [6], etc. This has

been achieved by means of the analysis of the response to controlled per-

turbations (vertical and divertor kicks) in as wide a range of configurations

as possible.

In order to avoid disruptions, the kicks durations have been assessed by

means of closed–loop simulations.

As an example, in Figure 4.24 a comparison between experiment and

simulation is shown.

1.0

VERFA

Experimental

Simulated

0.5

0

-0.5

-1.0

23.10 23.15 23.2023.05 23.25

Vo

lta

ge

(V

)(1

04)

Time (s)

JG

09

.36

5-8

a

(a) Amplifier voltage. Note that af-ter each positive kick there is a neg-ative counter kick due to controllerreaction

1000

2000IERFA

Experimental

Simulated

0

-1000

-200023.10 23.2023.00 23.30

Am

pe

re (

A)

Time (s)

JG

09

.36

5-8

b

(b) Amplifier current.

0

2

Experimental

Simulated

-2

-4

-623.10 23.15 23.2023.05 23.25

Ve

rtic

al ve

locity e

stim

atio

n (

10

7)

Time (s)

JG

09

.36

5-8

c

(c) Vertical velocity estimation.

Figure 4.24: Experimental (solid black lines) and simulated values (dashedred lines) for 12 kV positive kicks applied during JET pulse #78376 startingfrom t = 23 s.

105

4 Technical solutions and implementation 4.3 The new FTU Feedback System

4.3 The new FTU Feedback System

Recently effort has been put on the reengineering and porting of the old

FTU feedback under the MARTe Framework. Considering the structure of

the feedback system shown in Figure 4.13 in the previous chapter, a more

organic structure for the system using various GAMs and limiting as much

as possible the responsabilities of each one of them has been envisaged. The

proposed GAM subdivision is reported in in Figure 4.25.

Three GAMs manage the communication with the sensors and actuators

(ADC and DAC), and generate the preprogrammed references requested by

the users. The SignalProcessingGAM then verifies the plasma presence and

diagnoses problems such as plasma runaway, gas immission failures, and so

on. The 32 magnetic measures, together with the toroidal current an the

Vloop integral, are passed to the MomentGAM, which first evaluates and

removes the pick-up toridal field offset from the acquired data, and then

preforms the toridal multipolar expansion described in [82]. The 12 out-

put signals (external and internal moments) are part of the inputs for the

LCMSGAM and are also sent via RTNet [54, 55] to a satellite station whose

aim is the evaluation of the plasma equilibrium using a realtime version of

the ODIN code [83, 84]. The LCMSGAM calculates the poloidal flux on

the limiter contact points, mixing the moments to the geometrical functions

that describe the mesh4. The absolute maximum value for the flux among

the contact points is the one of the last magetic surface. The reconstruc-

tion of the LCMS is then carried out by iterating this process for all mesh

points and stopping each time that the evaluated flux is greater or equal

to the contact point one. The last set of inputs of the LCSMGAM are the

preprogrammed radiuses5, which are used to calculate the plasma position

error in terms of ∆Ψ (DEP and DEZ signals, for horizontal and vertical

position error respectively). These two signals, together with the plasma

4The actual mesh is made of 128 steps along the radius and 64 steps along the poloidalsection

5Internal, external, upper and lower desidered plasma radius

106


current, are the inputs for the CoilsControllerGAM, which holds the con-

trollers for the three poloidal field amplifiers, and the plasma current one.

Before executing this GAM, however, the ExtremuumSeekingGAM, if ac-

tive, optimises via an extremum seeking algorithm the plasma position, in

order to maximise the coupling with the LH antenna [68]. The CoilsCon-

trolGAM is made by four PID controller objects6.

In FTU, the gas control is independent from the described process and

is made by four GAMs: the PrefillControlGAM , the PlasmaDensityCon-

trolGAM, the SwapSignalGAM and the FluxVoltageGAM. The first two

GAMs generate the gas flux request for the valves in the prefill and in the

plasma phase respectively. The SwapSignalGAM schedules the control sig-

nals of the previous two GAMs, and finally the FluxVoltageGAM translates

the flux request into the voltage reference for the valves amplifier using a

nonlinear calibration curve.

In FTU MARTe is being deployed using USB pendrives with a live linux

distribution. This allowed to test and deploy different systems without

needing to reinstall anything on the VME stations.

4.3.1 Experimental results

The completed feedback system is being currently tested in the backup sta-

tion, running in parallel with the previous feedback system. A comparison

some produced signal of the old and new systems is shown in in Figures 4.26

and 4.27, while Figure 4.28 shows the behavior of the gas control system

(in closed loop).

6Note that it was necessary to merge the PIDs and the various nonlinear controllersin a single GAM, as their signals were heavily intertwined.

107


ElongationController

PlasmaState &SecurityCheck

Signal Proc.&

OffsetRemoval

Scheduler AntiwindupSystem

PIDController

FluxVoltageGasControl

On-Off GasControl

PIDController

PIDController

RTNET IN

ExtremumSeeking

Algorithm

DAC

&

NONRTSTREAMING

Main FeedBack System

ODIN Satellite NodeLH Satellite Node

ADC

LHTubeDAC

LLL Temp.Controller

ADC

&

WAVEFORM

GENERATION

TControl

HControl

F and VControl

Vacuum Moment

RTNETOut

LCMS

Mesh0Mesh0

Mesh0Mesh0

Mesh0

Odin

Figure 4.25: Block diagram of the MARTe FTU feedback system.

108


0 0.5 1 1.50.646

0.648

0.65

0.652

0.654

0.656

Time [s]

Po

sitio

n [

m]

RS1 − MARTe

0 0.5 1 1.50.646

0.648

0.65

0.652

0.654

0.656

Time [s]

Po

sitio

n [

m]

RS1 − Current System

0 0.5 1 1.5

1.21

1.215

1.22

1.225

1.23

1.235

Time [s]

Po

sitio

n [

m]

RS2 − MARTe

0 0.5 1 1.5

1.21

1.215

1.22

1.225

1.23

1.235

Time [s]

Po

sitio

n [

m]

RS2 − Current System

Figure 4.26: Reconstructed internal and external radiuses for the presentcontroller and the MARTe-based one.

109


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6−0.04

−0.02

0

0.02

0.04

0.06

Time [s]

∆Ψ

[W

b]

DEP − MARTe

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6−0.04

−0.02

0

0.02

0.04

0.06

Time [s]

∆Ψ

[W

b]

DEP − Current System

Figure 4.27: Magnetic flux measurement ∆Ψ, used as horizontal positionerror for the coils control.

110


−10 −8 −6 −4 −2 0 20

0.5

1

1.5

2

2.5

3

x 10−5

Time [s]

Pre

ssu

re [

mb

ar]

Prefill

−10 −8 −6 −4 −2 0 20

10

20

30

40

50

60

Time [s]

De

nsity [

ele

ctr

on

s/m

3]

Plasma density

−10 −8 −6 −4 −2 0 20

2

4

6

8

Time [s]

DA

C v

olta

ge

[V

]

Valve control voltage

Figure 4.28: Pressure and pressure prefill reference , plasma density refer-ence and interferometer density average, valve amplifier request.

111

Chapter 5

Conclusions and future work

In this Thesis various control problem in the field of nuclear fusion research

have been illustrated, such as the Vertical Stabilization and the Shape

Control problem. In particular work has been carried out on:

• The problem of vertical instability of elongated plasmas, which has

been illustrated from a general perspective as well by detailing the

solution to the issue carried out in the JET Tokamak, showing the

control loop of the european Tokamak, and how the whole system has

been revamped in the framework of the european PCU project;

• The MARTe Framework, developed in the same PCU project as the

new JET Vertical Stabilization system;

• The JET Shape Controller, previously augmented with the eXtreme

Shape Controller (XSC), which has been furtherly upgraded with a

Current Limit Avoidance (CLA) module, capable of moving poloidal

field currents away from saturations without excessive modifications

of the plasma shape;

• The Frascati Tokamak Upgrade (FTU), in particular concerning the

solution to the AL-F amplifier oscillating current output problem, and

112

5 Conclusions and future work

on the revamping of the feedback system by porting it to the MARTe

Framework).

Most of the work done on the FTU Tokamak is still work in progress,

and as such will be furtherly developed in the following years. This, together

with a better documentation, improvements, and the ideation of tools for

rapid control system development related to the MARTe Framework is of

evident ITER-relevance, and the accumulated know-how will be reused as

much as possible in the future development of the next fusion machines.

113

Bibliography

[1] L. Giancarli, V. Chuyanov, M. Abdou, M. Akiba, B. Hong, R. Lsser,

C. Pan, and Y. Strebkov, “Breeding Blanket Modules testing in ITER:

An international program on the way to DEMO,” Fusion Engineering

and Design, vol. 81, no. 1-7, pp. 393 – 405, 2006.

[2] F. Piccolo, JET Vertical Stabilization System: Modelling and Control.

PhD thesis, 2007.

[3] F. Sartori, G. De Tommasi, and F. Piccolo, “The Joint European

Torus, Plasma Position and Shape Control in the World’s Largest

Tokamak,” IEEE Control Systems Magazine, vol. 26, no. 2, pp. 64–

78, 2006.

[4] A. Neto, F. Sartori, F. Piccolo, R. Vitelli, G. D. Tommasi, L. Zabeo,

A. Barbalace, H. Fernandes, D. F. Valcarcel, and A. J. N. Batista,

“MARTe: a Multi-Platform Real-Time Framework,” IEEE Transac-

tions on Nuclear Science, 2010.

[5] J. Wesson, Tokamaks. Clarendon Press - Oxford, 3 ed., 2004.

[6] J. Freidberg, Plasma Physics and Fusion Energy. Cambridge Univer-

sity Press, 2007.

[7] J. D. Lawson., “Some criteria for a power producing thermonuclear

reactor,” in Proceedings of the Physical Society, vol. 70, p. 6, 1957.

114

Bibliography

[8] H. Alfven, “Existence of Electromagnetic-Hydrodynamic Waves,”

vol. 150, pp. 405–406, 1942.

[9] M. Ariola and A. Pironti, Magnetic Control of Tokamak Plasmas.

Springer, 2008.

[10] A. Pironti and M. Walker, “Fusion, tokamaks, and plasma control,”

IEEE Control Systems Magazine, vol. 25, pp. 30–43, Oct. 2005.

[11] J. Wesson, The science of JET. Abingdon, Oxon: JET Joint Under-

taking, 2000.

[12] F. Romanelli and R. Kamendjeon, “Overview of JET results,” Pro-

ceedings of the 22st IAEA Fusion Energy Conference Geneva, 2008.

[13] F. Romanelli, J. Pamela, R. Kamendje, M. Watkins, S. Brezinsek,

Y. Liang, X. Litaudon, T. Loarer, D. Moreau, D. Mazon, G. Saibene,

F. Sartori, and P. de Vries, “Recent contribution of JET to the ITER

physics,” Fusion Engineering and Design, vol. 84, no. 26, pp. 150 –

160, 2009.

[14] N. Holtkamp, “An overview of the ITER project,” Fusion Engineering

and Design, vol. 82, no. 514, pp. 427 – 434, 2007.

[15] N. Holtkamp, “The status of the ITER design,” Fusion Engineering

and Design, vol. 84, no. 26, pp. 98 – 105, 2009.

[16] S. Konishi, S. Nishio, and K. Tobita, “DEMO plant design beyond

ITER,” Fusion Engineering and Design, vol. 6364, no. 0, pp. 11 – 17,

2002.

[17] R. Andreani, E. Diegele, W. Gulden, R. Lasser, D. Maisonnier, D. Mur-

doch, M. Pick, and Y. Poitevin, “Overview of the European Union

fusion nuclear technologies development and essential elements on the

way to DEMO,” Fusion Engineering and Design, vol. 81, no. 1-7, pp. 25

– 32, 2006.

115

Bibliography

[18] V. D. Shafranov and L. E. Zakharov, “Equilibrium of toroidal plasma

with no circular cross section,” Sov. Phys. Tech, vol. 18, pp. 151–156,

1967.

[19] Y. Liang, “Overview of Edge-Localized Mode Control in Tokamak

Plasmas,” Fusion Science and Technology, vol. 59, no. 3, pp. 586–601,

2011.

[20] A. W. Degeling, Y. R. Martin, P. E. Bak, J. B. Lister, and X. Llobet,

“Dynamics of edge localized modes in the TCV tokamak,” Plasma

Physics and Controlled Fusion, vol. 43, no. 12, p. 1671, 2001.

[21] P. T. Lang, A. W. Degeling, J. B. Lister, Y. R. Martin, P. J. M. Carthy,

A. C. C. Sips, W. Suttrop, G. D. Conway, L. Fattorini, O. Gruber,

L. D. Horton, A. Herrmann, M. E. Manso, M. Maraschek, V. Mertens,

A. Mck, W. Schneider, C. Sihler, W. Treutterer, H. Zohm, and A. U.

Team, “Frequency control of type-I ELMs by magnetic triggering in

ASDEX Upgrade,” Plasma Physics and Controlled Fusion, vol. 46,

no. 11, p. L31, 2004.

[22] S. H. Kim, M. M. Cavinato, V. Dokuka, A. A. Ivanov, R. R. Khayrut-

dinov, P. T. Lang, J. B. Lister, V. E. Lukash, Y. R. Martin, S. Y.

Medvedev, and L. Villard, “Comparing magnetic triggering of ELMs

in TCV and ASDEX Upgrade,” Plasma Physics and Controlled Fu-

sion, vol. 51, no. 5, 2009.

[23] F. Sartori, P. Lomas, F. Piccolo, M. Zedda, and J.-E. Contributors,

“Synchronous elm pacing at jet using the vertical stabilisation con-

troller,” Proocedings of the 35th EPS Conference con Plasma Physics,

June 2008.

[24] G. Ambrosino, M. Ariola, G. De Tommasi, A. Pironti, F. Sartori,

E. Joffrin, and F. Villone, “Plasma Strike-Point Sweeping on JET

116

Bibliography

Tokamak with the eXtreme Shape Controller,” IEEE Transactions on

Plasma Science, vol. 36, no. 3, 2008.

[25] A. Cenedese and F. Sartori, “Plasma position and current control man-

management at JET,” in 42nd IEEE Conference on Decision and Con-

trol, vol. 5, pp. 4628–4633, 2003.

[26] L. Zabeo, G. Artaserse, A. Cenedese, F. Piccolo, and F. Sartori, “A

new approach to the solution of the vacuum magnetic problem in fusion

machines,” Fusion Engineering and Design, vol. 82, no. 5-14, pp. 1081–

1088, 2007.

[27] F. Sartori, A. Cenedese, and F. Milani, “JET real-time object-oriented

code for plasma boundary reconstruction,” Fusion Engineering and

Design, vol. 66-68, pp. 735–739, 2003.

[28] A. Beghi and A. Cenedese, “Advances in Real-Time Plasma Boundary

Reconstruction,” IEEE Control Systems Magazine, vol. 25, pp. 44–64,

Oct. 2005.

[29] G. Ambrosino, M. Ariola, A. Pironti, and F. Sartori, “A new shape

controller for extremely shaped plasmas in JET,” Fusion Engineering

and Design, vol. 66-68, pp. 797–802, 2003.

[30] M. Ariola and A. Pironti, “The design of the eXtreme Shape Con-

troller for the JET tokamak,” IEEE Control Systems Magazine, vol. 25,

pp. 65–75, Oct. 2005.

[31] R. Albanese, G. Ambrosino, M. Ariola, A. Cenedese, F. Crisanti, G. De

Tommasi, M. Mattei, F. Piccolo, A. Pironti, S. F., and F. Villone,

“Design, implementation and test of the XSC extreme shape controller

in JET,” Fusion Engineering and Design, vol. 74, no. 1-4, pp. 627–632,

2005.

117

Bibliography

[32] M. Shimada, V. Mukhovatov, G. Federici, Y. Gribov, A. Kukushkin,

Y. Murakami, A. Polevoi, V. Pustovitov, S. Sengoku, and M. Sugihara,

“Performance of ITER as a burning plasma experiment,” Nuclear Fu-

sion, vol. 44, no. 2, pp. 350–356, 2004.

[33] J. Lister, A. Portone, and Y. Gribov, “Plasma control in ITER,” IEEE

Control Systems Magazine, vol. 26, no. 2, pp. 79–91, 2006.

[34] G. De Tommasi, R. Albanese, G. Ambrosino, M. Ariola, M. Mattei,

A. Pironti, and F. Sartori, “XSC Tools: A Software Suite for Tokamak

Plasma Shape Control Design and Validation,” IEEE Transactions on

Plasma Science, vol. 35, no. 3, pp. 708–723, 2007.

[35] G. Ambrosino and R. Albanese, “A survey on modeling and control of

current, position and shape of axisymmetric plasmas,” IEEE Control

Systems Magazine, vol. 26, no. 5, pp. 76–91, 2005.

[36] R. Albanese and F. Villone, “The linearized CREATE-L plasma re-

sponse model for the control of current, position and shape in toka-

maks,” Nuclear Fusion, vol. 38, pp. 723–738, May 1998.

[37] R. Albanese, G. Calabro, M. Mattei, and F. Villone, “Plasma response

models for current, shape and position control at JET,” Fusion Engi-

neering and Design, vol. 66–68, pp. 715–718, 2003.

[38] G. De Tommasi, S. Galeani, A. Pironti, G. Varano, and L. Zaccar-

ian, “Trading output performance for input allocation: application to

the JET tokamak shape controller,” in Proceedings of the 48th IEEE

Conference on Decision and Control, December 2009.

[39] G. Varano, G. Ambrosino, G. De Tommasi, S. Galeani, A. Pironti, and

L. Zaccarian, “Performance assessment of a dynamic current allocator

for the jet extreme shape controller,” in in 26th Symposium on Fusion

Technology (SOFT10), Porto, Portugal, September 2010.

118

Bibliography

[40] G. Ambrosino, G. De Tommasi, S. Galeani, A. Pironti, G. Varano,

and L. Zaccarian, “On dynamic input allocation for set-point regula-

tion of the JET tokamak plasma shape,” in 2011 IEEE International

Conference on Control Applications (CCA), September 2011.

[41] G. De Tommasi, S. Galeani, A. Pironti, G. Varano, and L. Zaccarian,

“Nonlinear dynamic allocator for optimal input/output performance

trade-off: Application to the JET tokamak shape controller,” Auto-

matica, vol. 47, no. 5, pp. 981–987, 2011.

[42] L. Zaccarian, “Dynamic allocation for input redundant control sys-

tems,” Automatica, vol. 45, no. 6, pp. 1431 – 1438, 2009.

[43] L. Boncagni, S. Galeani, G. Granucci, G. Varano, V. Vitale, and L. Za-

ccarian, “Using dynamic input allocation for elongation control at

FTU,” Fusion Engineering and Design, 2010, to appear.

[44] L. Boncagni, S. Galeani, G. Granucci, G. Varano, V. Vitale, and L. Za-

ccarian, “Plasma position and elongation regulation at ftu using dy-

namic input allocation,” IEEE Transactions on Control Systems Tech-

nology, 2011. accepted for publication.

[45] R. Vitelli, L. Boncagni, F. Mecocci, S. Podda, V. Vitale, and L. Zaccar-

ian, “An anti-windup-based solution for the low current nonlinearity

compensation on the FTU horizontal position controller,” Proceedings

of the 49th IEEE Conference on Decision and Control, December 2010.

[46] V. Vitale, C. Centioli, F. Iannone, G. Mazza, M. Panella, L. Pan-

gione, S. Podda, and L. Zaccarian, “Real-time Linux operating sys-

tem for plasma control on FTU: implementation advantages and

first experimental results,” Fusion Engineering and Design, vol. 71,

no. 1[U+FFFD], pp. 71 – 76, 2004.

[47] A. Teel and N. Kapoor, “The L2 anti-windup problem: Its definition

and solution,” in Proc. 4th ECC, (Brussels, Belgium), July 1997.

119

Bibliography

[48] L. Zaccarian and A. Teel, “A common framework for anti-windup,

bumpless transfer and reliable designs,” Automatica, vol. 38, no. 10,

pp. 1735–1744, 2002.

[49] L. Boncagni, C. Centioli, L. Fiasca, F. Iannone, M. Panella, V. Vi-

tale, and L. Zaccarian, “Introducing a Virtualization Technology for

the FTU Plasma Control System,” in Proceedings of the 18th topical

meeting on the technology of fusion energy (TOFE), (San Francisco

(CA), USA), Sept. 2008.

[50] A. Bemporad, A. Teel, and L. Zaccarian, “Anti-windup synthesis via

sampled-data piecewise affine optimal control,” Automatica, vol. 40,

no. 4, pp. 549–562, 2004.

[51] D. Alves, R. Vitelli, L. Zaccarian, L. Zabeo, A. Neto, F. Sartori, P. Mc-

Cullen, and P. Card, “The new Error Field Correction Coil controller

system in the Joint European Torus tokamak,” Fusion Engineering

and Design, vol. 86, no. 6-8, pp. 1034–1038, 2011.

[52] S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence,

and Robustness. Prentice-Hall, 1994.

[53] T. Bellizio, G. De Tommasi, N. Risoli, R. Albanese, and A. Neto, “A

MARTe based simulator for the JET Vertical Stabilization system,”

Fusion Engineering and Design, vol. 86, pp. 1026–1029, October 2011.

[54] L. Boncagni, Y. Sadeghi, D. Carnevale, G. Mazzitelli, A. Neto,

D. Pucci, F. Sartori, S. Sinibaldi, V. Vitale, R. Vitelli, L. Zaccarian,

S. Monaco, and G. Zamborlini, “First steps in the FTU migration to-

wards a modular and distributed real-time control architecture based

on MARTe and RTNet,” in 17th Real Time Conference, (Lisbona, Por-

tugal), May 2010.

[55] L. Boncagni, A. Barbalace, Y. Sadeghi, M. Pompei, L. Zaccarian,

and F. Sartori, “Switched Ethernet in Synchronized Distributed Con-

120

Bibliography

trol Systems Using RTnet,” IEEE Transactions on Nuclear Science,

vol. 58, pp. 1793–1799, August 2011.

[56] T. Weilkiens, Systems Engineering with SysML/UML – Modeling,

Analysis, Design. Morgan Kaufmann, 2006.

[57] K. Thramboulidis, “Model-integrated mechatronicstoward a new

paradigm in the development of manufacturing systems,” IEEE Trans-

actions on Industrial Informatics, vol. 1, pp. 54–61, Feb. 2006.

[58] M. Foeken, M. Voskuijl, A. Cabrera, and M. van Tooren, “Model

generation for the verification of automatically generated mecha-

tronic control software,” in IEEE/ASME International Conference on

Mechtronic and Embedded Systems and Applications, pp. 275–280, Oc-

tober 2008.

[59] Y. Vanderperren, W. Mueller, and W. Dehaene, “UML for electronic

systems design: a comprehensive overview,” Design Automation for

Embedded Systems, vol. 12, no. 4, pp. 261–292, 2008.

[60] R. Kawahara, H. Nakamura, D. Dotan, A. Kirshin, T. Sakairi, S. Hi-

rose, K. Ono, and H. Ishikawa, “Verification of embedded system’s

specification using collaborative simulation of SysML and simulink

models,” in International Conference on Model-Based Systems Engi-

neering, pp. 21–28, March 2009.

[61] G. Doukas and K. Thramboulidis, “A Real-Time-Linux-Based Frame-

work for Model-Driven Engineering in Control and Automation,”

IEEE Transactions on Industrial Electronics, vol. 58, pp. 914–924,

Mar. 2011.

[62] C. Huang and P. Hsiung, “Model-based verification and estimation

framework for dynamically partially reconfigurable systems,” IEEE

Transactions on Industrial Informatics, vol. 7, pp. 287–301, May 2011.

121

Bibliography

[63] Y. Guo and R. Jones, “A study of approaches for model based devel-

opment of an automotive driver information system,” in 3rd Annual

IEEE Systems Conference, pp. 267–272, March 2009.

[64] K. Thramboulidis and A. Buda, “3+1 SysML view model for IEC61499

Function Block control systems,” in 8th International Conference on

Industrial Informatics, pp. 175–180, July 2010.

[65] T. Johnson, C. Paredis, J. Jobe, and R. Burkhart, “Modeling contin-

uous system dynamics in SysML,” in Proceedings of the ASME Inter-

national Mechanical Engineering Congress and Exposition, (Seattle,

Washington), November 2007.

[66] N. Pontisso and D. Chemouil, “TOPCASED Combining Formal

Methods with Model-Driven Engineering,” in Proceedings of the 21st

IEEE/ACM International Conference on Automated Software Engi-

neering, pp. 359–360, September 2006.

[67] A. Beghi and A. Cenedese, “Advances in Real-Time Plasma Boundary

Reconstruction,” IEEE Control Systems Magazine, vol. 25, pp. 44–64,

Oct. 2005.

[68] D. Carnevale, A. Astolfi, C. Centioli, S. Podda, V. Vitale, and L. Zac-

carian, “A new extremum seeking technique and its application to max-

imize RF heating on FTU,” Fusion Engineering and Design, vol. 84,

pp. 554–558, Jun. 2009.

[69] L. Zaccarian, L. Boncagni, D. Cascone, C. Centioli, S. Cerino, F. Gra-

vanti, F. Iannone, F. Mecocci, L. Pangione, S. Podda, V. Vitale, and

R. Vitelli, “Nonlinear instabilities induced by the F coil power ampli-

fier at FTU: modeling and control,” Fusion Engineering and Design,

vol. 84, no. 7–11, pp. 2015–2019, 2009.

122

Bibliography

[70] R. Albanese, E. Cocorrese, and G. Rubinacci, “Plasma modeling

for the control of vertical instabilities in tokamaks,” Nuclear Fusion,

vol. 29, no. 6, pp. 1013 – 1023, 1989.

[71] F. Sartori, F. Crisanti, R. Albanese, G. Ambrosino, V. Toigo, J. Hay,

P. Lomas, et al., “The JET PCU project: An international plasma con-

trol project,” Fusion Engineering and Design, vol. 83, no. 2-3, pp. 202

– 206, 2008. Proceedings of the 6th IAEA Technical Meeting on Con-

trol, Data Acquisition, and Remote Participation for Fusion Research.

[72] F. Sartori, A. Barbalace, A. J. N. Batista, T. Bellizio, P. Card, G. D.

Tommasi, P. M. Cullen, A. Neto, F. Piccolo, R. Vitelli, and L. Zabeo,

“The PCU JET Plasma Vertical Stabilisation Control System,” Fusion

Engineering and Design, 2010.

[73] F. Perkins, D. Post, N. Uckan, M. Azumi, D. Campbell, N. Ivanov,

N. Sauthoff, M. Wakatani, W. Nevins, M. Shimada, et al., “Chapter

1: Overview and summary,” Nuclear Fusion, vol. 39, pp. 2137–2174,

Dec 1999.

[74] A. Neto, F. Sartori, F. Piccolo, A. Barbalace, R. Vitelli, and H. Fer-

nandes, “Linux real-time framework for fusion devices,” Fusion Engi-

neering and Design, vol. 84, no. 711, pp. 1408 – 1411, 2009.

[75] A. J. N. Batista, J. Sousa, and C. A. F. Varandas, “ATCA digital

controller hardware for vertical stabilization of plasmas in tokamaks,”

Review of Scientific Instruments, vol. 77, Oct 2006.

[76] J. G. Krom, “The evolution of control and data acquisition at JET,”

Fusion Engineering and Design, vol. 43, no. 3-4, pp. 265 – 273, 1999.

[77] D. G. Luenberger, Introduction to Dynamic Systems: Theory, Models,

and Applications. John Wiley and Sons, 1979.

123

List of Figures

[78] V. Toigo, L. Zanotto, M. Bigi, E. Gaio, J. Hay, R. Piovan, and S. Shaw,

“Conceptual design of the enhanced radial field amplifier for plasma

vertical stabilisation in JET,” Fusion Engineering and Design, vol. 82,

pp. 1599–1606, Oct. 2007.

[79] G. Franklin, J.D. Powell, and A. Emami-Naeini, Feedback Control of

Dynamic Systems. Prentice Hall, 5th ed., 2006.

[80] V. Riccardo, T. C. Hender, P. J. Lomas, B. Alper, T. Bolzonella,

P. de Vries, and G. P. Maddison, “Analysis of JET halo currents,”

Plasma Physics and Controlled Fusion, vol. 46, no. 6, pp. 925–934,

2004.

[81] E. De la Luna, F. Sartori, P. Lomas, G. Saibene, T. Eich, G. Arnoux,

L. Barrera, M. Beurskens, J. Lonnroth, V. Parail, C. Perez von Thun,

R. Sartori, E. Solano, L. Zabeo, and M. Zedda, “Magnetic ELM trig-

gering using the vertical stabilization controller in JET,” in Proceedings

of the 36th EPS Conference on Plasma Physics, (Sofia, Bulgaria), Jun.

2009.

[82] F. Alladio and F. Crisanti, “Analysis of MHD equilibria by toroidal

multi-polar expansions,” Nuclear Fusion, vol. 26, p. 1143, 1986.

[83] F. Alladio and P. Micozzi, “Experimental plasma equilibrium recon-

struction from kinetic and magnetic measurements in the FTU toka-

mak,” Nuclear Fusion, vol. 35, no. 3, p. 305, 1995.

[84] Y. Sadeghi, G. Ramogida, L. Boncagni, C. D’Epifanio, V. Vitale,

F. Crisanti, and L. Zaccarian, “Experimental plasma equilibrium re-

construction from kinetic and magnetic measurements in the FTU

tokamak,” IEEE Transactions on Plasma Science, vol. 38, no. 3,

pp. 352–358, 2010.

124

List of Figures

2.1 Structure and scale of a Tokamak: the JET (Joint European

Torus). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Differences between a limiter and a divertor plasma (JET

pre-divertor and JET as of today). . . . . . . . . . . . . . . 7

2.3 Structure of the JET Tokamak divertor region. . . . . . . . 9

2.4 3D model of the ITER Tokamak. . . . . . . . . . . . . . . . 9

3.1 The mechanism of plasma elongation and resulting vertical

instability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 The JET Vertical Stabilisation controller. . . . . . . . . . . 15

3.3 Photo of an internal discrete coil. . . . . . . . . . . . . . . . 17

3.4 Position of the magnetic sensors in the JET Tokamak. . . . 18

3.5 Position of the saddle coils in the JET Tokamak. . . . . . . 19

3.6 JET weights for Mirnov coils and saddle loops. . . . . . . . 20

3.7 JET Vertical Stabilization system, pulse #79632. . . . . . . 21

3.8 JET Vertical Stabilization system, pulse #79698. . . . . . . 22

3.9 Collapse of pedestal causes ELMs. . . . . . . . . . . . . . . 23

3.10 Example of ELM pacing via vertical kicks in pulse #78422. 24

3.11 JET circuits generating the poloidal field. . . . . . . . . . . 25

3.12 Main Gaps in the JET Tokamak. . . . . . . . . . . . . . . . 27

3.13 Block diagram of the Shape Controller system augmented

with the XSC. . . . . . . . . . . . . . . . . . . . . . . . . . . 30

125

List of Figures

3.14 Block diagram of the control system with the insertion of the

allocator block. . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.15 JET pulse #81710 (blue) and #81715 (red) with CLA en-

abled. Shape error (a) and detail (b). . . . . . . . . . . . . 34

3.16 Comparison of currents on the divertor colis for JET pulses

#81710 and #81715. . . . . . . . . . . . . . . . . . . . . . . 35

3.17 Comparison of GAP measures for GAP2 (top right of the

vacuum vessel) and RIG/ROG (Radial Inner/Outer GAP)

for the JET pulses #81710 and #81715. . . . . . . . . . . . 36

3.18 Control system block diagram of horizontal position. . . . . 37

3.19 Electrical scheme of the AL-F converter. . . . . . . . . . . . 39

3.20 Simplified electrical scheme of the thyristor bridges of the

AL-F converter. . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.21 Block diagram of the PHSC. . . . . . . . . . . . . . . . . . . 43

3.22 Shot number #20838. Open-loop simulation of the AL-F

model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.23 Linear LC and HC models behavior compared to the nonlin-

ear response. . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.24 Shot number #20838. Open-loop simulation of the plasma

model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.25 IF response for shots number #28000 (upper plot) and #20838

(lower plot) in solid lines. Corresponding closed-loop simu-

lations in dashed lines. . . . . . . . . . . . . . . . . . . . . . 50

3.26 Anti-windup solution. . . . . . . . . . . . . . . . . . . . . . 52

3.27 Shot number #20838. Anti-windup simulation. . . . . . . . 54

3.28 Shots #31621 and #31626: same shot type. In the latter

the anti-windup system was turned on. . . . . . . . . . . . . 55

3.29 Shots #32784 and #32786: same shot type. In the latter

the anti-windup system is turned on. . . . . . . . . . . . . . 56

3.30 Shot #32786: signals v1 and v2 of the anti-windup system. 57

126

List of Figures

3.31 Shots #32959 and #32960: same shot type. The complete

anti-windup code ran on the former. The simplified code

shows smaller oscillations. . . . . . . . . . . . . . . . . . . . 57

3.32 The EFCC coils at the JET Tokamak. . . . . . . . . . . . . 58

3.33 The proposed advanced controller block diagram. . . . . . . 59

3.34 Comparison of simulated and experimental results for the

EFCC advanced controller. . . . . . . . . . . . . . . . . . . 60

4.1 The layered structure of BaseLib2. . . . . . . . . . . . . . . 62

4.2 Example of a BaseLib2 CDB. . . . . . . . . . . . . . . . . . 64

4.3 Relay logger mechanism. . . . . . . . . . . . . . . . . . . . . 68

4.4 Conceptual passage from a block diagram to a MARTe ar-

chitecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.5 The RealTimeThread acts a module micro-scheduler. . . . . 72

4.6 Block definition diagrams used to model the BaseLib2 library. 77

4.7 Example of GAMs modeling. . . . . . . . . . . . . . . . . . 78

4.8 Internal block diagram used to define input and output sig-

nals for the PID GAM shown in Figure 4.7. . . . . . . . . . 79

4.9 Topcased hierarchical view of the model of the PID GAM

block shown in Figure 4.7. . . . . . . . . . . . . . . . . . . . 80

4.10 Block definition diagram used to model the connections be-

tween GAMs. . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.11 Cross section of the FTU Tokamak. . . . . . . . . . . . . . 82

4.12 FTU vacuum chamber. . . . . . . . . . . . . . . . . . . . . . 83

4.13 Block diagram of the FTU plasma control system. . . . . . 84

4.14 BDD of the FTU plasma control system. . . . . . . . . . . . 85

4.15 Auto-generated files for the FTU Plasma Control System. . 86

4.16 Photo of the backpane of the VS5 ATCA crate. . . . . . . . 89

4.17 Data synchronization of the ATCA boards. . . . . . . . . . 90

4.18 JET LEVEL1 interface for the new Vertical Stabilisation

System 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

127

List of Acronyms

4.19 All the modules executed for each control cycle. . . . . . . . 95

4.20 Maximum, minimum and mean execution times for all VS5

GAMs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.21 The internal logic of the DAM. . . . . . . . . . . . . . . . . 100

4.22 A screenshot of the VS5 Web Interface: the VAMGAM. . . 103

4.23 The system is continuously is real-time with a jitter inferior

to 1 µs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.24 Experimental (solid black lines) and simulated values (dashed

red lines) for 12 kV positive kicks applied during JET pulse

#78376 starting from t = 23 s. . . . . . . . . . . . . . . . . 105

4.25 Block diagram of the MARTe FTU feedback system. . . . . 108

4.26 Reconstructed internal and external radiuses for the present

controller and the MARTe-based one. . . . . . . . . . . . . 109

4.27 Magnetic flux measurement ∆Ψ, used as horizontal position

error for the coils control. . . . . . . . . . . . . . . . . . . . 110

4.28 Pressure and pressure prefill reference , plasma density ref-

erence and interferometer density average, valve amplifier

request. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

128

List of Acronyms

ADC Analog to Digital Converter.

ASDEX Axially Symmetric Divertor EXperiment.

ATCA Advanced Telecommunications Computing Architecture.

CDB Configuration DataBase.

CLA Current Limit Avoidance.

CODAS COntrol and Dta Acquisition System.

COMPASS COMPact ASSembly.

CSV Comma Separated Values.

D-T Deuterium-Tritium.

DAC Digital to Analog Converter.

DAM Divertor Amplifier Module.

DDB Dynamic Data Buffer.

DSP Digital Signal Processor.

EFCC Error Field Correction Coils.

129

List of Acronyms

ELM Edge Localised Mode.

ERFA Enhanced Radial Field Amplifier.

ETB Edge Transport Barrier.

FRFA Fast Radial Field Amplifier.

FTU Frascati Tokamak Upgrade.

GAM Generic Application Module.

IDC Internal Discrete Coils.

IOGAM Input/Output Generic Application Module (GAM).

ISTTOK Instituto Superior Tecnico TOKamak.

JET Joint European Torus.

JPF Jet Pulse File.

L1 Level-1.

LCMS Last Closed Magnetic Surface.

MARTe Multithreaded Application RealTime executor.

MHD MagnetoHydroDynamics.

MIMO Multiple Input Multiple Output.

NIF National Ignition Facility.

PCU Plasma Control Upgrade.

PDE Partial Differential Equation.

130

List of Acronyms

PF Poloidal Field.

PHSC Programmable High Speed Controller.

PID Proportional Integral Derivative.

PPCC Plasma Position and Current Control.

RFA Radial Field Amplifier.

RIG Radial Inner Gap.

ROG Radial Outer Gap.

RTAI Real-Time Application Interface.

RTM Rear Transition Module.

SC Shape Controller.

SVD Singular Value Decomposition.

TCV Tokamak a Configuration Variable.

TF Toroidal Field.

VAM Vertical Amplifier Module.

VME VERSABUS Module Eurocard.

VS Vertical Stabilisation.

XSC eXtreme Shape Controller.

131

phd thesis in control engineering - ce.uniroma2.it

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