symme y
S
S
A icle
Real-Time Con ol o he EHU S ella a o
Izaskun Ga ido * , Ja ie Maseda, I zia Ma ija and Ai o J. Ga ido
Au oma ic Con ol G oup—ACG, Depa men o Au oma ic Con ol and Sys ems Enginee ing, Facul y o
Enginee ing o Bilbao, Uni e si y o he Basque Coun y(UPV/EHU), Po Ra ael Mo eno no3, 48013 Bilbao, Spain;
cja ie [email p o ec ed] (J.M.); i zia [email p o ec ed] (I.M.); ai o [email p o ec ed] (A.J.G.)
*Co espondence: [email p o ec ed]
Recei ed: 24 No embe 2019; Accep ed: 17 Decembe 2019; Published: 19 Decembe 2019
Abs ac :
A p esen , wo main magne ic con inemen usion de ices exis : okamaks and s ella a o s.
Mo eo e , s ella a o s ha e been demons a ed o be a good al e na i e o okamaks, due o hei abili y
o ope a e in con inuous mode, which e en ually ansla es in o a highe comme cial p o i abili y.
In s ella a o s, he magne ic con inemen o he plasma is achie ed exclusi ely by he coils, hus no
elec ic cu en h ough he plasma is needed. In pa icula , his a icle p esen s he Columbia
Non-Neu al To us s ella a o ha is loca ed in he Au oma ic Con ol G oup o Euskal He iko
Unibe si a ea (EHU). This EHU s ella a o main ains symme y in i s s uc u e due o he opology
o he mesh ha is o med by i s coils. A co ne s one o u u e usion eac o s is o ob ain eal- ime
con ol ha enables a sus ained eac ion. In his a icle, a con ol-o ien ed model o he ins alled
magne ic con inemen coils is p esen ed. The model is based on ma ices ha p ese e symme y,
which is de ined om physical p inciples and hen alida ed by di e en se s o expe imen al da a.
Then, based on his model, a no el p edic i e con ol sui ed o his pa icula model wi h symme ic
objec i e unc ion is implemen ed in he nume ical simula ions, and i s esponse is compa ed o
ha o adi ional con olle s. Finally, his con ol is implemen ed in a eal plan and he sa is ac o y
expe imen esul s p o ide alida ion o bo h he nume ical model and p oposed con olle .
Keywo ds: nuclea usion ene gy; magne ic con inemen ; eal- ime con ol; p edic i e con ol
1. In oduc ion
In ecen yea s, he e has been an in e na ional e o o de elop clean ene gy p oduc ion echnology
based on usion ene gy, such as = he In e na ional The monuclea Expe imen al Reac o (ITER) [1].
The ene gy gene a ion in ol es nuclea usion eac ions, whe e wo o mo e ligh elemen ’s
a omic nuclei, usually om deu e ium and i ium ( wo di e en hyd ogen iso opes), combine o
o m di e en a omic nuclei and suba omic pa icles. The eac ion implies a ne loss o mass ha is
ans o med in o ene gy in he o m o gamma ays and kine ic ene gy emi ed by he a o emen ioned
pa icles, as shown in Equa ion (1) [
2
]. A ypical deu e ium– i ium eac ion is supposed o be in
he o m:
2D+3T→4He +n+17.58 MeV (1)
The inal objec i e is o achie e a s a e o sus ained con inuous nuclea usion eac ion.
This objec i e ep esen s a la ge numbe o scien i ic and echnical challenges. In pa icula , he eal- ime
con ol o he plasma by means o he con inemen coils plays a key ole in he pe o mance o he
p ocess and he easibili y o he clean usion echnology. I his sense, i mus be conside ed ha he
main limi ing phenomenon in usion de ices is he p ema u e eac ion decay due o plasma ins abili ies.
Nowadays, wo p incipal app oaches coexis ha y o achie e success ul and comme cially
compe i i e usion p ocesses: ine ial con inemen -based and magne ic con inemen -based app oaches.
Ine ial con inemen usion a emp s o achie e he eac ion by comp essing and hea ing a uel a ge ,
Symme y 2020,12, 11; doi:10.3390/sym12010011 www.mdpi.com/jou nal/symme y
Symme y 2020,12, 11 2 o 15
and i is being s udied in se e al U.S. acili ies. Magne ic con inemen a emp s o achie e and
main ain he eac ion by using magne ically con ined uel wi hin acuum chambe s, and i is he
opology pe used in ITER (In e na ional The monuclea Expe imen al Reac o ), TCV (Tokamak
à
Con igu a ion Va iable), o JET (Join Eu opean To us). I is s ill no clea which app oach will lead o
he desi ed esul s.
A p esen , wo main magne ic con inemen opologies exis o usion de ices: okamaks and
s ella a o s. On he one hand, okamak de ices con ine plasma in a o oidal egion using compound
magne ic ields. The p incipal magne ic ield is usually o oidal, while a poloidal magne ic ield induces
a cu en in o he plasma ha ac s as he seconda y ci cui o an elec ical ans o me . The poloidal
ield lines c ea ed a ound he plasma cu en a e combined wi h he o oidal ield p oducing helical
ield lines, which w ap a ound he o us, p e en ing he plasma displacemen owa ds he essel
walls [
3
]. On he o he hand, s ella a o s consis o a mo e complex helical symme ic coil sys em,
in such a way ha he plasma ollows wis ing magne ic beam line pa hs. In hese kinds o de ices,
he magne ic con inemen is ully achie ed by he coils, so no induced cu en is needed o con ine he
plasma, al hough ohmic, non-induc i e, and boo s ap cu en s may also be p esen [
4
]. In his sense,
s ella a o s a e a g ea al e na i e o okamaks, wi h signi ican esea ch p og ess aking place ega ding
he s udy o magne ically con ined plasma physics on hese de ices du ing ecen yea s. Addi ionally,
he abili y o s ella a o s o ope a e in con inuous mode would allow highe comme cial p o i abili y.
In his con ex , his a icle s udies a eal- ime con ol s a egy o he coils o he EHU (Euskal
He iko Unibe si a ea)s elle a o name he ul a-low-io a supe elonga ed s ella a o (ULISES), ully
designed and buil by he Au oma ic Con ol G oup (ACG) a he Enginee ing Facul y o he Basque
Coun y Uni e si y (UPV/EHU) in collabo a ion wi h CIEMAT (Cen o de In es igaciones Ene g
é
icas,
Medioambien ales y Tecnol
ó
gicas) (see Figu es 1and 2). The nume ical plan model will be o mula ed
based on he symme y o he sys em due o he plan opology and de i ed om physical p inciples
coupled wi h pa ame e es ima ion. The success o he ini ial simula ions pa ed he way o he
eal- ime expe imen al implemen a ion, which demons a es he e ec i eness o bo h he model and
he con ol s a egies [5].
Symme y 2020, 12, 11 2 o 15
Nowadays, wo p incipal app oaches coexis ha y o achie e success ul and comme cially
compe i i e usion p ocesses: ine ial con inemen -based and magne ic con inemen -based
app oaches. Ine ial con inemen usion a emp s o achie e he eac ion by comp essing and
hea ing a uel a ge , and i is being s udied in se e al U.S. acili ies. Magne ic con inemen a emp s
o achie e and main ain he eac ion by using magne ically con ined uel wi hin acuum chambe s,
and i is he opology pe used in ITER (In e na ional The monuclea Expe imen al Reac o ), TCV
(Tokamak à Con igu a ion Va iable), o JET (Join Eu opean To us). I is s ill no clea which
app oach will lead o he desi ed esul s.
A p esen , wo main magne ic con inemen opologies exis o usion de ices: okamaks and
s ella a o s. On he one hand, okamak de ices con ine plasma in a o oidal egion using compound
magne ic ields. The p incipal magne ic ield is usually o oidal, while a poloidal magne ic ield
induces a cu en in o he plasma ha ac s as he seconda y ci cui o an elec ical ans o me . The
poloidal ield lines c ea ed a ound he plasma cu en a e combined wi h he o oidal ield
p oducing helical ield lines, which w ap a ound he o us, p e en ing he plasma displacemen
owa ds he essel walls [3]. On he o he hand, s ella a o s consis o a mo e complex helical
symme ic coil sys em, in such a way ha he plasma ollows wis ing magne ic beam line pa hs. In
hese kinds o de ices, he magne ic con inemen is ully achie ed by he coils, so no induced cu en
is needed o con ine he plasma, al hough ohmic, non-induc i e, and boo s ap cu en s may also be
p esen [4]. In his sense, s ella a o s a e a g ea al e na i e o okamaks, wi h signi ican esea ch
p og ess aking place ega ding he s udy o magne ically con ined plasma physics on hese de ices
du ing ecen yea s. Addi ionally, he abili y o s ella a o s o ope a e in con inuous mode would
allow highe comme cial p o i abili y.
In his con ex , his a icle s udies a eal- ime con ol s a egy o he coils o he EHU (Euskal
He iko Unibe si a ea)s elle a o name he ul a-low-io a supe elonga ed s ella a o (ULISES),
ully designed and buil by he Au oma ic Con ol G oup (ACG) a he Enginee ing Facul y o he
Basque Coun y Uni e si y (UPV/EHU) in collabo a ion wi h CIEMAT (Cen o de In es igaciones
Ene gé icas, Medioambien ales y Tecnológicas) (see Figu es 1 and 2). The nume ical plan model
will be o mula ed based on he symme y o he sys em due o he plan opology and de i ed om
physical p inciples coupled wi h pa ame e es ima ion. The success o he ini ial simula ions pa ed
he way o he eal- ime expe imen al implemen a ion, which demons a es he e ec i eness o
bo h he model and he con ol s a egies [5].
Figu e 1.
EHU (Euskal He iko Unibe si a ea) s elle a o loca ed in he Au oma ic Con ol G oup
(ACG) a he Enginee ing Facul y o he Basque Coun y Uni e si y (UPV/EHU).
Symme y 2020,12, 11 3 o 15
Symme y 2020, 12, 11 3 o 15
Figu e 1. EHU (Euskal He iko Unibe si a ea) s elle a o loca ed in he Au oma ic Con ol G oup
(ACG) a he Enginee ing Facul y o he Basque Coun y Uni e si y (UPV/EHU).
Figu e 2. Dimensions o he eac ion chambe and he coils: he le he acuum chambe and ex e io
coils; he igh he inne coils, shown in a 90° se ing o isualiza ion pu poses.
The es o he manusc ip is o ganized as ollows. Sec ion 2 desc ibes h ee di e en s a egies
o cons uc he nume ical models o he EHU s ella a o . Sec ion 3 desc ibes he no el ad anced
p edic i e con ol laws. Sec ion 4 p esen s he eal- ime expe imen al pe o mance o he p oposed
con olle s. Finally, concluding ema ks a e gi en in Sec ion 5.
2. Da a Acquisi ion Sys em and Model S a emen
In his sec ion, h ee di e en modeling app oaches a e employed o ob ain a eliable model o
he magne ic coils sys em o he EHU s ella a o . An analy ical model ob ained by means o
pa ame e iden i ica ion echniques is compa ed o he p oposed physical equi alen sys em, a pu e
black box model, and a hyb id g ey box model, in which he p elimina y s uc u e o he sys em is
i s es ablished and hen iden i ied.
A e he models ha e been cons uc ed, hese nume ical sys ems will be alida ed
expe imen ally. Tha is, eal expe imen s will be ca ied ou on he eal plan o di e en s udy
cases, so ha he ob ained measu ed ou pu da a can be compa ed wi h hose o he nume ical
model esponse o he same s udy cases.
In o de o con ol he EHU s ella a o , a eedback loop mus be p o ided. In his case, he
eedback consis s o he ol age ou pu V
Ou
and cu en I signal measu emen s, while he inpu
signal V
In
is also being moni o ed. No e ha he main ac ua o o he sys em is composed o a coil
sys em consis ing o wo ex e nal and wo in e nal coils connec ed o a eal- ime ully con ollable
powe sou ce, as shown in Figu es 1 and 2. The esul ing ou pu ol age and cu en s a e, he e o e,
he con olled a iables, and a e measu ed di ec ly om he coils’ coppe wi es by means o physical
esis ance-based and Ohmic induc i e senso s, espec i ely, p o iding he inpu o he con ol
eedback loop h ough he co esponding condi ioning ci cui s shown in Figu es 3 and 4 and he
DAQ (Da a acquisi ion) connec ed o he eal- ime a ge .
Fo his pu pose, a da a acquisi ion sys em has been buil . Using a Na ional Ins umen s
PCI-6221 ins umen o da a acquisi ion, as well as he necessa y elec onic componen s o
condi ion he ci cui , as seen in Figu e 3 o he ou pu ol age, Figu e 4 o he inpu ol age, and
Figu e 5 o he ou pu cu en .
Figu e 2.
Dimensions o he eac ion chambe and he coils: he le he acuum chambe and ex e io
coils; he igh he inne coils, shown in a 90◦se ing o isualiza ion pu poses.
The es o he manusc ip is o ganized as ollows. Sec ion 2desc ibes h ee di e en s a egies
o cons uc he nume ical models o he EHU s ella a o . Sec ion 3desc ibes he no el ad anced
p edic i e con ol laws. Sec ion 4p esen s he eal- ime expe imen al pe o mance o he p oposed
con olle s. Finally, concluding ema ks a e gi en in Sec ion 5.
2. Da a Acquisi ion Sys em and Model S a emen
In his sec ion, h ee di e en modeling app oaches a e employed o ob ain a eliable model o he
magne ic coils sys em o he EHU s ella a o . An analy ical model ob ained by means o pa ame e
iden i ica ion echniques is compa ed o he p oposed physical equi alen sys em, a pu e black box
model, and a hyb id g ey box model, in which he p elimina y s uc u e o he sys em is i s es ablished
and hen iden i ied.
A e he models ha e been cons uc ed, hese nume ical sys ems will be alida ed expe imen ally.
Tha is, eal expe imen s will be ca ied ou on he eal plan o di e en s udy cases, so ha he
ob ained measu ed ou pu da a can be compa ed wi h hose o he nume ical model esponse o he
same s udy cases.
In o de o con ol he EHU s ella a o , a eedback loop mus be p o ided. In his case, he eedback
consis s o he ol age ou pu V
Ou
and cu en Isignal measu emen s, while he inpu signal V
In
is also
being moni o ed. No e ha he main ac ua o o he sys em is composed o a coil sys em consis ing o
wo ex e nal and wo in e nal coils connec ed o a eal- ime ully con ollable powe sou ce, as shown
in Figu es 1and 2. The esul ing ou pu ol age and cu en s a e, he e o e, he con olled a iables,
and a e measu ed di ec ly om he coils’ coppe wi es by means o physical esis ance-based and
Ohmic induc i e senso s, espec i ely, p o iding he inpu o he con ol eedback loop h ough
he co esponding condi ioning ci cui s shown in Figu es 3and 4and he DAQ (Da a acquisi ion)
connec ed o he eal- ime a ge .
Symme y 2020, 12, 11 4 o 15
Figu e 3. Ou pu ol age signal condi ioning ci cui .
Figu e 4. Inpu ol age signal condi ioning ci cui .
As can be seen in he igu es abo e, he ol age ou pu signal is d i en h ough a ol age
di ide due o he high ol age alues in he ou pu poin , which could des oy he PCI (Pe iphe al
Componen In e connec ) ca d. Addi ionally, all o he signals a e d i en h ough a ol age limi e ,
and inally h ough an op amp in bu e con igu a ion be o e hey each he a ge . Wi h his
con igu a ion, he op amp is capable o ollowing he o iginal signal wi h no a enua ion, while
s aying below he maximum ol age alue.
All he addi ional componen s a e ins alled in o de o p o ec he da a acquisi ion ca d, while
main aining adequa e signal acking and wi hou in e e ence wi h he main ci cui o he sys em.
Figu e 5. Cu en signal condi ioning ci cui .
2.1. Analy ical Model
F om he basic physical design o he ULISES desc ibed in Figu e 6, an analy ical plan model is
c ea ed. In pa icula , based on he elec ical elemen s ha compose he de ice, a nume ical model is
ob ained by i ing he pa ame e s o a con ol-o ien ed space–s a e ep esen a ion. Addi ionally, he
pa ame e s a e de ined in Table 1.
Figu e 3. Ou pu ol age signal condi ioning ci cui .
Symme y 2020,12, 11 4 o 15
Symme y 2020, 12, 11 4 o 15
Figu e 3. Ou pu ol age signal condi ioning ci cui .
Figu e 4. Inpu ol age signal condi ioning ci cui .
As can be seen in he igu es abo e, he ol age ou pu signal is d i en h ough a ol age
di ide due o he high ol age alues in he ou pu poin , which could des oy he PCI (Pe iphe al
Componen In e connec ) ca d. Addi ionally, all o he signals a e d i en h ough a ol age limi e ,
and inally h ough an op amp in bu e con igu a ion be o e hey each he a ge . Wi h his
con igu a ion, he op amp is capable o ollowing he o iginal signal wi h no a enua ion, while
s aying below he maximum ol age alue.
All he addi ional componen s a e ins alled in o de o p o ec he da a acquisi ion ca d, while
main aining adequa e signal acking and wi hou in e e ence wi h he main ci cui o he sys em.
Figu e 5. Cu en signal condi ioning ci cui .
2.1. Analy ical Model
F om he basic physical design o he ULISES desc ibed in Figu e 6, an analy ical plan model is
c ea ed. In pa icula , based on he elec ical elemen s ha compose he de ice, a nume ical model is
ob ained by i ing he pa ame e s o a con ol-o ien ed space–s a e ep esen a ion. Addi ionally, he
pa ame e s a e de ined in Table 1.
Figu e 4. Inpu ol age signal condi ioning ci cui .
Fo his pu pose, a da a acquisi ion sys em has been buil . Using a Na ional Ins umen s PCI-6221
ins umen o da a acquisi ion, as well as he necessa y elec onic componen s o condi ion he
ci cui , as seen in Figu e 3 o he ou pu ol age, Figu e 4 o he inpu ol age, and Figu e 5 o he
ou pu cu en .
Symme y 2020, 12, 11 4 o 15
Figu e 3. Ou pu ol age signal condi ioning ci cui .
Figu e 4. Inpu ol age signal condi ioning ci cui .
As can be seen in he igu es abo e, he ol age ou pu signal is d i en h ough a ol age
di ide due o he high ol age alues in he ou pu poin , which could des oy he PCI (Pe iphe al
Componen In e connec ) ca d. Addi ionally, all o he signals a e d i en h ough a ol age limi e ,
and inally h ough an op amp in bu e con igu a ion be o e hey each he a ge . Wi h his
con igu a ion, he op amp is capable o ollowing he o iginal signal wi h no a enua ion, while
s aying below he maximum ol age alue.
All he addi ional componen s a e ins alled in o de o p o ec he da a acquisi ion ca d, while
main aining adequa e signal acking and wi hou in e e ence wi h he main ci cui o he sys em.
Figu e 5. Cu en signal condi ioning ci cui .
2.1. Analy ical Model
F om he basic physical design o he ULISES desc ibed in Figu e 6, an analy ical plan model is
c ea ed. In pa icula , based on he elec ical elemen s ha compose he de ice, a nume ical model is
ob ained by i ing he pa ame e s o a con ol-o ien ed space–s a e ep esen a ion. Addi ionally, he
pa ame e s a e de ined in Table 1.
Figu e 5. Cu en signal condi ioning ci cui .
As can be seen in he igu es abo e, he ol age ou pu signal is d i en h ough a ol age di ide
due o he high ol age alues in he ou pu poin , which could des oy he PCI (Pe iphe al Componen
In e connec ) ca d. Addi ionally, all o he signals a e d i en h ough a ol age limi e , and inally
h ough an op amp in bu e con igu a ion be o e hey each he a ge . Wi h his con igu a ion, he op
amp is capable o ollowing he o iginal signal wi h no a enua ion, while s aying below he maximum
ol age alue.
All he addi ional componen s a e ins alled in o de o p o ec he da a acquisi ion ca d, while
main aining adequa e signal acking and wi hou in e e ence wi h he main ci cui o he sys em.
2.1. Analy ical Model
F om he basic physical design o he ULISES desc ibed in Figu e 6, an analy ical plan model is
c ea ed. In pa icula , based on he elec ical elemen s ha compose he de ice, a nume ical model
is ob ained by i ing he pa ame e s o a con ol-o ien ed space–s a e ep esen a ion. Addi ionally,
he pa ame e s a e de ined in Table 1.
Symme y 2020,12, 11 5 o 15
Symme y 2020, 12, 11 5 o 15
Figu e 6. Pa ame ic elec ical equi alen ci cui o he coil sys em o he EHU s ella a o .
Figu e 6. Pa ame ic elec ical equi alen ci cui o he coil sys em o he EHU s ella a o .
Table 1. Pa ame e s o he elec ical equi alen ci cui o he EHU s ella a o .
Pa ame e Physical Meaning SI uni
VIN Inpu DC ol age Vol (V)
VOUT Measu ed DC ol age Vol (V)
R1Resis ance o i s ou e and inne coil,
plus second inne coil Ohm (Ω)
R2Resis ance o second ou e coil Ohm (Ω)
Le1Induc ance o he i s ou e coil Hen y (H)
Le2Induc ance o he second ou e coil Hen y (H)
Li1 Induc ance o he i s inne coil Hen y (H)
Li2 Induc ance o he second inne coil Hen y (H)
M
Mu ual induc ance (be ween inne coils)
Hen y (H)
Me ging he induc ances and esis ances leads o a simpli ied ci cui wi h educed pa ame e s.
These new pa ame e s a e shown in he ollowing espec i e equa ions o he o al ci cui induc ance
and esis ance:
K=Le1+Li1+Le2+Li2±M(2)
RT=R1+R2(3)
In o de o analyze he ci cui beha io , he equa ions ha go e n he ci cui a e conside ed:
VIN =I(R1+R2)+KdI
d (4)
VOUT =I·R2+Le2
dI
d (5)
whe e I( ) ep esen s he cu en h ough he ci cui .
No e ha bo h Ki chho ’s laws and Ohm’s law pa icula ized o he di e en lumped-pa ame e
ci cui elemen s a e used in Equa ions (2)–(5).
In o de o ob ain a space–s a e ep esen a ion, he ollowing s a e a iables a e chosen, whe e he
usual space–s a e a iable nomencla u e is employed. In his sense, no e ha
x1
and
x2
, he componen s
o he s a e ec o , ha e di e en dimensions:
x1=I(6)
x2=.
x1=dI
d (7)
Replacing Equa ion (4) wi h Equa ion (7), he ollowing exp ession is ob ained:
.
x1=dI
d =−(R1+R2)
KI+1
KVIN (8)
Symme y 2020,12, 11 6 o 15
and he ime de i a i e o Equa ion (8) leads o he exp ession:
.
x2=−(R1+R2)
K
dI
d =−(R1+R2)
Kx2(9)
Thus, all he space–s a e a iables and hei espec i e de i a i es ha e been de ined. Neglec ing
he mu ual induc ance, he educed space–s a e model can be es ablished, whe e he s a e a iables
a e decoupled:
".
x1
.
x2#=
−(R1+R2)
K0
0−(R1+R2)
K"x1
x2#+"1
K
0#VIN (10)
"IOUT
VOUT #="1 0
R2Le2#" x1
x2#(11)
Once he analy ical s a e–space model o m is de ined in Equa ions (10) and(11), i is necessa y
o iden i y he alues o he pa ame e s om he eal expe imen al sys em. These pa ame e s a e
desc ibed and de ined in Figu e 5and Table 1.
Fo pa ame e iden i ica ion, mul iple expe imen al es s a e pe o med on he eal plan , collec ing
ou pu da a h ough he ins alled da a acquisi ion sys em. Besides, an analy ical solu ion o Equa ions
(10) and (11) is compu ed o acili a e he pa ame e iden i ica ion p ocess:
x1( )=VIN
K1−e−RT
K (12)
x2( )=VIN
Ke−RT
K (13)
Taking in o accoun he exp essions gi en in Equa ions (6) and (7), o each gi en inpu hei
esul ing ou pu will be compa e wi h he da a ou pu om he eal EHU s ella a o . Bea ing his
objec i e in mind, a se ies o expe imen al es s a e ca ied ou . The expe imen s consis ing o applying
di e en ol age es inpu signals o he eal sys em. The esul ing da a om he expe imen s a e
hen e ie ed by he ins umen a ion, as de ailed in he p e ious sec ion. Then, he alues o he
pa ame e s o he space–s a e sys em a e app oxima ed by sys em iden i ica ion.
Following his p ocedu e o di e en expe imen s and di e en ol age inpu alues, he esul s
p esen ed in Table 2a e achie ed:
Table 2. Pa ame e alue iden i ica ion o he elec ical equi alen ci cui .
Pa ame e R1R2Le1(=Le2)Li1+Li2+M
Value 426.870 mΩ57.626 mΩ509.990 µH3.268 µH
E en when his iden i ica ion p ocess o he analy ical model is pe o med based on he sys em
physical equa ions, o he app oaches such as pu e black box o g ey box me hods may be also used o
de e mine he model o he sys em. These will be u he explained in he ollowing subsec ions.
2.2. Black Box Model
The black box models ep esen an unknown sys em, whe e only inpu s and ou pu s a e known.
By analyzing hese signals, a ans e unc ion o a space–s a e sys em ha ep esen s he unknown
plan may be c ea ed. Howe e , he s a es o he sys em do no usually co espond wi h any physical
a iables o he eal sys em [
6
]. In pa icula , conside ing he same inpu and ou pu signals as in
Sec ion 2.1, he co esponding black box model o he EHU s ella a o is:
".
x1
.
x2#="−18.67 −17.07
58.12 −43.91 #" x1
x2#+"0.001124
0.535700 #VIN (14)
Symme y 2020,12, 11 7 o 15
"IOUT
VOUT #="−472.70 −10.260
−18.53 7.471 #" x1
x2#(15)
2.3. G ey Box Model
Analogous o he black box models, g ey box models ep esen an unknown sys em. Howe e ,
in his case he inpu and ou pu signals a e known, as well as he s uc u e o he space–s a e sys em.
This means ha he dimensions o he ma ices and some physical es ic ions on he pa ame e s a e
conside ed du ing he iden i ica ion [
7
]. Howe e , some pe u ba ions om highe o de dynamics ha
we e no p e iously aken in o accoun in Sec ion 2.1 a e now allowed in o he sys em. In pa icula ,
conside ing he same inpu and ou pu signals as in Sec ion 2.1, he co esponding g ey box model o
he EHU s ella a o is: ".
x1
.
x2#="−25.90 0
0−1#" x1
x2#+"58.93
0#VIN (16)
"IOUT
VOUT #="−1 0
0.06 1 #" x1
x2#(17)
2.4. Model Valida ion ia Expe imen a ion
In Sec ions 2.1–2.3, h ee di e en nume ical models ha e been p esen ed. In his sec ion,
he esponse o hese es ima ed models will be compa ed o he expe imen al esponse o he eal EHU
s ella a o . This compa ison, as seen in Figu e 7, se es o e i y which one o hese models is he bes
ma ch o he EHU s ella a o [8,9].
Symme y 2020, 12, 11 8 o 15
𝐼
𝑉=−1 0
0.06 1𝑥
𝑥 (17)
2.4. Model Valida ion ia Expe imen a ion
In Subsec ions 2.1–2.3, h ee di e en nume ical models ha e been p esen ed. In his sec ion,
he esponse o hese es ima ed models will be compa ed o he expe imen al esponse o he eal
EHU s ella a o . This compa ison, as seen in Figu e 7, se es o e i y which one o hese models is
he bes ma ch o he EHU s ella a o [8,9].
Figu e 7. Compa ison o he analy ical model, black box model, and he g ey box model esponses in
eal ime: compa ison o ol age ( op) and cu en (bo om).
Taking in o accoun he ol age ou pu signal, he black box model is ou pe o med by bo h he
analy ical model and g ey box model esponses, since bo h o hem p o ide an accu a e es ima ion
o he sys em esponse. On he o he hand, looking in o he cu en ou pu signal, he analy ical
model shows some s eady-s a e e o . In his sense, we no e ha he s eady-s a e e o ep esen s he
di e ence be ween he ou pu signal and he e e ence desi ed one once he sys em has eached a
s a e whe e he ou pu a ia ions emains bounded and limi ed o 2%–5% o i s alue, whe e he
ime ends o be in ini e, conside ing ha he con olled sys em is s able, and hus con e gen .
The e o e, i may be concluded ha he g ey box model is he mos accu a e model ha has been
es ima ed o he EHU s ella a o . Ne e heless, i mus be conside ed ha he di e ences be ween
he g ey box and he analy ical model a e no ema kable, while he analy ical model allows
iden i ica ion o physical magni udes co esponding o i s di e en pa ame e componen s. In o de
o u he con i m hese esul s, he same inpu signal is d i en o he expe imen al sys em and bo h
he black box model and he g ey box model. The esul s o hese compa isons a e shown in Figu e 8.
Figu e 7. Compa ison o he analy ical model, black box model, and he g ey box model esponses in
eal ime: compa ison o ol age ( op) and cu en (bo om).
Symme y 2020,12, 11 8 o 15
Taking in o accoun he ol age ou pu signal, he black box model is ou pe o med by bo h he
analy ical model and g ey box model esponses, since bo h o hem p o ide an accu a e es ima ion
o he sys em esponse. On he o he hand, looking in o he cu en ou pu signal, he analy ical
model shows some s eady-s a e e o . In his sense, we no e ha he s eady-s a e e o ep esen s he
di e ence be ween he ou pu signal and he e e ence desi ed one once he sys em has eached a
s a e whe e he ou pu a ia ions emains bounded and limi ed o 2%–5% o i s alue, whe e he ime
ends o be in ini e, conside ing ha he con olled sys em is s able, and hus con e gen . The e o e,
i may be concluded ha he g ey box model is he mos accu a e model ha has been es ima ed o
he EHU s ella a o . Ne e heless, i mus be conside ed ha he di e ences be ween he g ey box and
he analy ical model a e no ema kable, while he analy ical model allows iden i ica ion o physical
magni udes co esponding o i s di e en pa ame e componen s. In o de o u he con i m hese
esul s, he same inpu signal is d i en o he expe imen al sys em and bo h he black box model and
he g ey box model. The esul s o hese compa isons a e shown in Figu e 8.
Symme y 2020, 12, 11 9 o 15
Figu e 8. Compa ison be ween he eal sys em and he heo e ical model ou pu signals: compa ison
wi h he black box model (le ) and g ey box model ( igh ).
As can be seen in Figu e 7, he p oposed models yield ou pu s ha ma ch hose o he eal
sys em wi h an accu acy o app oxima ely 50%–60% o ol age ou pu and 94%–95% o cu en
ou pu . The la ge e o in he ol age esponse is due o he un il e ed noise c ea ed by he magne ic
ields ha in e e e wi h he ins umen a ion. The e o e, as he magni ude o he noise is a ound 200
mV, bo h he esponses in ol age and cu en signals a e a good ma ch o he expe imen al signal
ou pu . The e o e, bo h he black box and he g ey box models a e alid, and he expe imen al es s
also show ha he g ey box model p esen s a be e ma ch wi h he eal sys em ou pu , al hough he
pa ame e ep esen a i eness is inhe en o he analy ical model.
3. Con ol Design
Once he g ey sys em model is es ablished and e i ied as he mos sui able i wi h he EHU
s ella a o , an adequa e con ol may be designed. The main objec i e o he con ol in he pla o m is
o ensu e ha he plasma inside he ULISES de ice chambe ollows he desi ed ajec o y so ha he
usion eac ion does no degene a e by egula ing he coil inpu ol age. The con ol o he plasma
cu en is indi ec ly achie ed by con olling he inpu ol age, as bo h a e di ec ly ela ed.
Fo his pu pose, di e en con olling echniques ha e been es ed. Fi s , a adi ionally used
PID (P opo ional In eg al De i a i e) con ol is implemen ed and uned in o de o e i y whe he
he sys em can be con olled by a a he simple con olle . Nex , a mo e complex con olle is
de eloped, namely a model p edic i e con ol (MPC), in o de o in es iga e hei ad an ages wi h
espec o he adi ional con olle s.
The de elopmen , implemen a ion, and he sys em ou pu o hese con ols will be explained
in u he de ail in he ollowing subsec ions.
3.1. PID Con olle Implemen a ion
PID con olle s a e e y common, as hey a e simple ye e ec i e in minimizing he e o signal
in addi ion o s abilizing he sys em [10]. Di e en me hods exis o une he con olle [11–13]. In
his pa icula example, he PID has been uned using he closed-loop p inciple o Ziegle –Nichols,
whe e he uning p ocess is subjec ed o he cons ain s o closed-loop s abili y and la ge bandwid h
while main aining dis u bance ejec ion, and enough phase ma gin and gain ma gin o allow o
dis u bances and unmodelled dynamics. A p op ie a y uning p ocedu e ies o comp omise
be ween hose cons ain s. In o de o implemen he esul ing PID in o he sys em, a closed-loop
block diag am is designed ha sends signals o he ac ua o s and collec s signals om he senso s
h ough a DAQ NI-6221 ins umen , as shown in Figu e 9. Conside ing ha only he inpu ol age is
con olled, he ou pu ol age signal loca ed be ween he second se o coils (see Figu e 6) will be
used as eedback o he con olle s.
Figu e 8.
Compa ison be ween he eal sys em and he heo e ical model ou pu signals: compa ison
wi h he black box model (le ) and g ey box model ( igh ).
As can be seen in Figu e 7, he p oposed models yield ou pu s ha ma ch hose o he eal sys em
wi h an accu acy o app oxima ely 50%–60% o ol age ou pu and 94%–95% o cu en ou pu .
The la ge e o in he ol age esponse is due o he un il e ed noise c ea ed by he magne ic ields
ha in e e e wi h he ins umen a ion. The e o e, as he magni ude o he noise is a ound 200 mV,
bo h he esponses in ol age and cu en signals a e a good ma ch o he expe imen al signal ou pu .
The e o e, bo h he black box and he g ey box models a e alid, and he expe imen al es s also show
ha he g ey box model p esen s a be e ma ch wi h he eal sys em ou pu , al hough he pa ame e
ep esen a i eness is inhe en o he analy ical model.
3. Con ol Design
Once he g ey sys em model is es ablished and e i ied as he mos sui able i wi h he EHU
s ella a o , an adequa e con ol may be designed. The main objec i e o he con ol in he pla o m is o
ensu e ha he plasma inside he ULISES de ice chambe ollows he desi ed ajec o y so ha he
usion eac ion does no degene a e by egula ing he coil inpu ol age. The con ol o he plasma
cu en is indi ec ly achie ed by con olling he inpu ol age, as bo h a e di ec ly ela ed.
Fo his pu pose, di e en con olling echniques ha e been es ed. Fi s , a adi ionally used PID
(P opo ional In eg al De i a i e) con ol is implemen ed and uned in o de o e i y whe he he
sys em can be con olled by a a he simple con olle . Nex , a mo e complex con olle is de eloped,
namely a model p edic i e con ol (MPC), in o de o in es iga e hei ad an ages wi h espec o he
adi ional con olle s.
Symme y 2020,12, 11 9 o 15
The de elopmen , implemen a ion, and he sys em ou pu o hese con ols will be explained in
u he de ail in he ollowing subsec ions.
3.1. PID Con olle Implemen a ion
PID con olle s a e e y common, as hey a e simple ye e ec i e in minimizing he e o signal in
addi ion o s abilizing he sys em [
10
]. Di e en me hods exis o une he con olle [
11
–
13
]. In his
pa icula example, he PID has been uned using he closed-loop p inciple o Ziegle –Nichols, whe e
he uning p ocess is subjec ed o he cons ain s o closed-loop s abili y and la ge bandwid h while
main aining dis u bance ejec ion, and enough phase ma gin and gain ma gin o allow o dis u bances
and unmodelled dynamics. A p op ie a y uning p ocedu e ies o comp omise be ween hose
cons ain s. In o de o implemen he esul ing PID in o he sys em, a closed-loop block diag am
is designed ha sends signals o he ac ua o s and collec s signals om he senso s h ough a DAQ
NI-6221 ins umen , as shown in Figu e 9. Conside ing ha only he inpu ol age is con olled,
he ou pu ol age signal loca ed be ween he second se o coils (see Figu e 6) will be used as eedback
o he con olle s.
Symme y 2020, 12, 11 10 o 15
Figu e 9. PID (P opo ional In eg al De i a i e) closed-loop block diag am.
Once he closed loop has been designed and es ablished, a se ies o beha io condi ions will be
imposed, which he con olle mus ul il [14]. Fo his se ing, he PID pa ame e alues will be
uned o achie e he ollowing condi ions:
• Quick esponse. Since he sys em will ha e o handle he con inemen o a apidly a ying
plasma cu en , he con ol o e he coil ol age will ha e o be as as as possible.
• Low o e shoo . Excessi e o e shoo ansla es in o a mo e powe ul magne ic ield, which
can lead o unexpec ed beha io and ul ima ely cause in e nal damage o he de ice, which
mus be a oided.
• Minimal s eady-s a e e o . A a ying signal o ol age applied o coils c ea es magne ic
ields ha can change bo h in di ec ion and in magni ude. This a iable magne ic ield will
induce a leaking ol age in o he conduc i e ma e ials. The leaking cu en s can in e e e
wi h he plasma inside he de ice chambe and he ins umen a ion signals, and can also
al e he empe a u e condi ions.
Using he obus s ep- esponse op imiza ion algo i hm o a a ge phase ma gin o 60°, he
alues o he PID pa ame e s a e ob ained. The PID con olle wi h he alues shown in Table 3
does achie e he desi ed pe o mance, as will be seen in Sec ion 4.
Table 3. Tuned PID pa ame e s.
Pa ame e 𝑲𝒑 𝑲𝒊 𝑲𝒅
Value 14.7180 357.55 0.0018
3.2. Model P edic i e Con ol Design
Model p edic i e con ol (MPC) elies on he idea o a mo e complex op imiza ion-based
scheme, which akes in o accoun he u u e s a es o he sys em. In a ew wo ds, using an accu a e
dynamic ma hema ical model o he eal sys em and di e en measu emen s o he sys em, his
con olle p edic s he u u e beha io o he sys em in o de o g an he bes con ol signal [15–16].
The eal sys em has a ime cons an in he o de o milliseconds, so ha sys em equa ions
(Equa ions (16) and (17) a e disc e ized wi h a ime s ep o ha o de o magni ude o ob ain an
accep able di e ence be ween he con inuous and he disc e ized op imal con ol p o iles. Howe e ,
such a small disc e iza ion ime s ep c ea es a need o signi ican ly educe he compu a ion ime a
Figu e 9. PID (P opo ional In eg al De i a i e) closed-loop block diag am.
Once he closed loop has been designed and es ablished, a se ies o beha io condi ions will be
imposed, which he con olle mus ul il [
14
]. Fo his se ing, he PID pa ame e alues will be uned
o achie e he ollowing condi ions:
•
Quick esponse. Since he sys em will ha e o handle he con inemen o a apidly a ying plasma
cu en , he con ol o e he coil ol age will ha e o be as as as possible.
•
Low o e shoo . Excessi e o e shoo ansla es in o a mo e powe ul magne ic ield, which can
lead o unexpec ed beha io and ul ima ely cause in e nal damage o he de ice, which mus
be a oided.
•
Minimal s eady-s a e e o . A a ying signal o ol age applied o coils c ea es magne ic ields ha
can change bo h in di ec ion and in magni ude. This a iable magne ic ield will induce a leaking
ol age in o he conduc i e ma e ials. The leaking cu en s can in e e e wi h he plasma inside
he de ice chambe and he ins umen a ion signals, and can also al e he empe a u e condi ions.
