P edic i e con ol o a sola ai condi ioning plan
wi h simul aneous iden ifica ion
A.N´
u˜
nez-Reyes and C.Bo dons
Abs ac — This pape p esen s he applica ion o a p edic i e
con olle wi h simul aneous iden ifica ion o a sola ai con-
di ioning plan . The ime a ying na u e o he p ocess makes
necessa y an adjus men o he con olle pa ame e s o he
a ying ope a ional condi ions. The main no el y wi h espec
o classic adap i e MPC scheme is o penalize he iden ifica ion
e o in he cos unc ion used o con ol. The beha iou o he
con olle is illus a ed by simula ions and expe imen al esul s.
The in eg a ion o iden ifica ion and con ol a oids he edious
iden ifica ion p ocedu e ha is necessa y be o e he s a -up
o any p edic i e con olle . This new adap i e MPC scheme
shows i s e ec i eness in con olling he ou le empe a u e in
he sola he mal plan .
I. INTRODUCTION
Model P edic i e Con ol (MPC) has de eloped conside-
ably o e he las yea s, bo h wi hin he esea ch con ol
communi y and in indus y [1]. This success can be a ibu ed
o he ac ha MPC is, pe haps, he mos gene al way o
posing he p ocess con ol p oblem in he ime domain. MPC
o mula ion in eg a es op imal con ol, s ochas ic con ol,
con ol o p ocesses wi h dead ime, mul i a iable con ol
and u u e e e ences when a ailable. Ano he ad an age
o MPC is ha because o he fini e con ol ho izon used,
cons ain s and, in gene al nonlinea p ocesses which a e
equen ly ound in indus y, can be handled.
Howe e , one o he majo d awbacks o his ype o
con ol s a egy is he need o ob ain a dynamic model o he
plan . Mos o he success o comme cial p edic i e con o-
lle s such as Dynamic Ma ix Con ol DMC [2] comes om
i s abili y o use a s ep esponse model o he plan , which
can be easily iden ified wi h expe imen al es s. Howe e ,
he iden ifica ion phase needs a lo o expe ise and ime o
pe o m he expe imen s and his is usually done only once,
a he p ocess s a -up. The model is no upda ed equen ly
e en i p ocess dynamics changes along ime.
Model upda ing is pa icula ly impo an in p ocesses
wi h changing ope a ing condi ions, whe e he p ocess pa-
ame e s a e con inually e ol ing. In p ocesses in ol ing
mass anspo a ion (as he one con olled in his wo k),
he cha ac e is ic ime cons an and delay a e a ec ed by
flow changes, gi ing ise o a p ocess dynamics ha changes
du ing a iable ope a ing egimes.
This wo k was pa ially suppo ed by Spanish Minis y o Science and
Technology unde g an DPI2004-07444-C04-01 and by HYCON Ne wo k
o Excellence, con ac numbe FP6-IST-511368
A.N´
u˜
nez-Reyes and C.Bo dons a e wi h Dp o. de Ingenie ´
ıa de
Sis emas y Au om´
a ica. Escuela Supe io de Ingenie os. Uni e sidad
de Se illa. Camino de los Descub imien os s/n. 41092 Se illa. Spain
(ampa o,bo dons)@ca uja.us.es
Model unce ain y and dis u bances a e impo an con-
ce ns in MPC and ha e been ho oughly s udied in ecen
yea s. The main app oaches o he subjec appea in he
fields o adap i e con ol and obus con ol. The e is a lo o
wo k done in obus MPC, wi h significan con ibu ions in
he min-max en i onmen which, in spi e o hei heo e ical
impo ance, a e di ficul o be implemen ed in p ac ice [3].
Adap i e MPC has also been widely s udied by a numbe
o au ho s, o example [4] [5]. The applica ion o a sel -
uning con olle wi h a ecu si e leas squa es iden ifica ion
algo i hm gi es ise o a solu ion ha is easily implemen able
bu shows nume ical p oblems when he exci a ion anishes
[6]. A supe iso y le el is needed which makes he p ocedu e
mo e complex. This can be sol ed wi h he me hodology
p oposed by Shouche e al. [7], Model P edic i e Con ol and
Iden ifica ion MPCI, which is an adap i e MPC scheme ha
employs he pe sis en exci a ion condi ion [8] o gua an ee
iden ifiabili y. The main d awback o his me hod is ha
he use o he pe sis en exci a ion condi ion de e io a es he
con ol pe o mance. Al hough he iden ifica ion capabili ies
o he me hod a e e y good, he ac ha he con ol
signals a e calcula ed in o de o gua an ee exci a ion gi es
poo con ol ea u es. In addi ion, he e a e no epo s o
applica ions o eal plan s. The me hod p esen ed he e ies
o o e come his p oblem.
Sola he mal plan s a e usually di ficul o con ol because
he ene gy sou ce (sola adia ion) is no manipulable [5] and
is con inually changing. This makes cons an flow changes
necessa y o e e ence acking, p o oking sudden p ocess
dynamics changes. Lo s o con ol s a egies ha e been
applied o hese plan s, anging om classical PIDs oMPC
[9]. In his pape , a me hod ha uses p edic i e con ol and
iden ifica ion simul aneously has been es ed on a sola ai
condi ioning plan .
The p oposed me hod makes use o a cos unc ion ha
includes acking e o and con ol e o (as any p edic i e
con olle ) as well as he iden ifica ion e o in a pas ece-
ding ho izon. This is a combina ion o he con ol p oblem
and he iden ifica ion p oblem in jus one cos unc ion. This
me hod is in he amewo k o he dual con ol [10]. The
p oblem is no oo cos ly and has been implemen ed on an
indus ial low-cos SCADA.
The pape is o ganized as ollows. In sec ion II a desc ip-
ion o he sola plan is p esen ed. Sec ion III desc ibes he
p oposed con ol s a egy, which is es ed unde simula ion
and compa ed o a sel - uning MPC in sec ion IV. The esul s
o applying he p oposed con olle o he eal plan a e
shown in sec ion V and finally he conclusions a e d awn.
P oceedings o he
44 h IEEE Con e ence on Decision and Con ol, and
he Eu opean Con ol Con e ence 2005
Se ille, Spain, Decembe 12-15, 2005
MoIB20.5
0-7803-9568-9/05/$20.00 ©2005 IEEE 1355
II. PLANT DESCRIPTION
The sola ai condi ioning plan is loca ed in Se ille
(Spain). I is used o cool he Labo a o ies o he Sys em
Enginee ing and Au oma ic Con ol Depa men o he Uni-
e si y o Se ille. I consis s o a sola field ha p oduces
ho wa e which eeds an abso p ion machine gene a ing
chilled wa e and injec s i in o he ai condi ioning sys em,
achie ing a cooling powe o 35 kW.
Accumula ion
sys em
B1
Sola sys em
VM1
CC1 CC2 CC3 CC4
Tac
I
T o
Accumula ion
sys em
Fig. 1. Plan desc ip ion
The sola plan can be analyzed as an ai condi ioning
ins alla ion ha uses he mal ene gy o p oduce cold ai . A
comple e desc ip ion o he plan can be ound in [9].
The o e all con ol objec i e is o supply chilled wa e o
he ai dis ibu ion sys em a he equi ed empe a u e. This
is accomplished by con olling he empe a u e o he ho
wa e supplied by he sola field. Since he p ima y ene gy
(sola adia ion) is no manipulable, he desi ed empe a u e
is achie ed by ac ing on he ci cula ing flow. The sola
con ibu ion, in addi ion o adia ion seasonal and daily cy-
clic a ia ions, is also dependen on a mosphe ic condi ions
such as cloud co e , humidi y, and ai anspa ency. I is
impo an o main ain a cons an ou le empe a u e as he
sola condi ions change, and he only means a ailable o
achie ing his is ia adjus men o he fluid flow.
The con ol p oblem add essed in his pape is he e-
gula ion o he sola field ou le empe a u e (T o). Figu e
1 shows he main componen s o he plan , which a e he
ollowing:
a) Sola sys em, composed o a se o fla sola collec o s.
The p ima y sou ce o ene gy is sola adia ion which is
used by he sola collec o s o inc ease he empe a u e
o he ci cula ing wa e . The sola field is composed o
151 m2o fla collec o s which wo k wi hin he ange
o 60 o 100 ◦Cand supply a nominal powe o 50 kW.
b) Accumula ion sys em, composed o wo 2500-li e anks
wo king in pa allel. This sys em ac s as a bu e , s o ing
ho wa e o be used in ansien si ua ions whe e he
sola adia ion does no allow he desi ed empe a u e
o be ob ained a he end o he ho wa e ci cui .
The objec i e o he con ol sys em is o main ain he
ou le oil empe a u e T o a a desi ed le el in spi e o
dis u bances such as changes in he sola i adiance le el
(caused by clouds), mi o eflec i i y o inle wa e em-
pe a u e. This is accomplished by a ying he flow o he
fluid h ough he field manipula ing he h ee-way al e
(VM1). The field exhibi s a a iable delay ime ha de-
pends on he con ol a iable (flow). The ans e unc ion
o he p ocess a ies wi h ac o s such as i adiance le el
o wa e inle empe a u e. The main enance o a cons an
ou le empe a u e h oughou he day as he sola condi ions
change equi es a wide a ia ion in he ope a ional flow le el.
This leads o subs an ial a ia ions in he gene al dynamic
pe o mance and in pa icula , om he con ol iewpoin ,
gi es ise o a sys em ime delay which a ies significan ly.
The con olle pa ame e s need o be adjus ed o sui he
ope a ing condi ions, and he p oposed me hod o e s one
app oach which can accommoda e such a equi emen .
The p oposed con ol s a egy is implemen ed on a small-
size Dis ibu ed Con ol Sys em (DCS) as a ou ine ha
communica es h ough he s anda d in e ace OLE o P ocess
Con ol (OPC). OPC acili a es he in e ope abili y be ween
au oma ion and con ol applica ions.
III. CONTROL STRATEGY
This sec ion is dedica ed o desc ibing he p oposed con-
ol s a egy. The p edic i e con olle wi h simul aneous
iden ifica ion on-line is based on Gene alized P edic i e
Con ol (GPC), ha consis s o applying a con ol sequence
ha minimizes a mul is age cos unc ion ha conside s bo h
acking e o and con ol e o .
Fo con ol pu poses a simple, linea model is equi ed
which ela es changes in fluid flow o changes in ou le
empe a u e. In his sec ion he heo e ical de elopmen o
n-o de sys ems is shown and he use o fi s -o de sys ems
is jus ified.
A. n-o de sys ems
The p oposed con olle ex ends he cos unc ion o he
o iginal GPC ([11]) wi h an iden ifica ion e o e m added
in he ollowing way:
min
xJ=
N2

j=N1
δ(j)[ˆy( +j| )−w( +j)]2+(1)
+
Nu

j=1
λ(j)[∆u( +j−1)]2+
+
N3

j=1
γ(j)[y( −j+1| )−φθ]2
s. ∆umax ≤∆u≤∆umin,u
max ≤u≤umin
ymax ≤y≤ymin,a
imax ≤ai≤aimin
bkmax ≤bk≤bkmin ,d
max ≤d≤dmin
1356
∀i=1...na and ∀k=1...nb, whe e N1and N2a e
he minimum and maximum p edic ions ho izons ( aken
as N1=d+1 and N2=d+N), Nuis he con ol
ho izon and N3is he iden ifica ion ho izon, dis he delay
o he inpu -ou pu p ocess model and δ(j),λ(j)and γ(j)
a e weigh ing sequences. w( +j)is a u u e se -poin o
e e ence sequence, u( )is he inc emen al con ol ac ion
(u( )=u( )−u( −1)),ˆy( +j| )is he j-s ep ahead
p edic ion o he sys em ou pu on da a up o ime and
y( −j+1| )is he j-s ep backwa ds o he sys em eal
ou pu on da a up o ime .φis he eg ession ma ix, θis
he pa ame e ec o o be iden ified and finally ai,bi,d,a e
he ans e unc ion pa ame e s o he disc e e polynomials
o deg ee na and nb as shown below.
I a CARIMA model is used o model he andom dis u -
bances in he sys em and he noise polynomial is chosen o
be 1, he ollowing equa ions a e ob ained1:
A(z−1)y( )=z−dB(z−1)u( )+( )
∆(2)
Whe e Aand Ba e he ollowing polynomials in he
backwa d shi ope a o z−1:
A(z−1)=1+a1z−1+a2z−2+...+anaz−na (3)
B(z−1)=b0+b1z−1+b2z−2+...+bnbz−nb
hen he bes expec ed alue o he ou pu p edic ion ˆy( +
d+j| )is gi en by,
ˆy( +d+j| )=(1−a1)ˆy( +d+j−1| )+ (4)
(a1−a2)ˆy( +d+j−2| )+...+
ana ˆy( +d+j−na −1| )+b0∆u( +j−1) +
b1∆u( +j−2) + ...+bnb∆u( +j−1−nb)
I equa ion (4) is applied ecu si ely o j=1,2,...,N,
he p edic ion ec o is gi en by he ollowing equa ion
exp essed in condensed o m as:
ˆy=Gu++Sˆy−+Hu−(5)
Whe e ˆy,u+,ˆy−and u−a e ec o s o sizes N×1,Nu×1,
(na +1)×1and nb ×1 espec i ely.
ˆy=
⎡
⎢
⎢
⎣
ˆy( +d+1| )
ˆy( +d+2| )
...
ˆy( +d+N| )
⎤
⎥
⎥
⎦
u+=
⎡
⎢
⎢
⎣
∆u( )
∆u( +1)
...
∆u( +Nu−1)
⎤
⎥
⎥
⎦
ˆy−=
⎡
⎢
⎢
⎣
ˆy( +d| )
ˆy( +d−1| )
...
ˆy( +d−na | )
⎤
⎥
⎥
⎦
u−=
⎡
⎢
⎢
⎣
∆u( −1)
∆u( −2)
...
∆u( −nb)
⎤
⎥
⎥
⎦
And G,Sand Ha e ma ices o dimensions N×Nu,N×
(na +1)and N×nb, espec i ely. The ollowing equa ions
show how he ma ices G and S can be ob ained o n-o de
sys ems in a s anda d o m.
1Pa ame e s ai,biand da e ime-dependan .
Gis a lowe iangula ma ix which akes he o m:
G=
⎡
⎢
⎢
⎢
⎣
g00... 0
g1g0... 0
.
.
..
.
..
.
..
.
.
gNgN−1... g
0
⎤
⎥
⎥
⎥
⎦
and hei elemen s a e gi en by
g0=b0
gj=
j

i=1
aigj−i+
j−1

i=0
bij=1,...,N (6)
I j< 0⇒gj=0
Sis gi en by
s1,j =−˜aj+1,j=1,...,n˜a
si,j =
i−1

k=1
s1,ksi−k,j (7)
i=2,...,N;j=1,...,n˜a
Whe e ˜aand n˜aa e he elemen s and deg ee espec i ely
o he polynomial ˜
A(z−1), ha is, ˜
A(z−1)=∆A(z−1)=
(1 −z−1)A(z−1).
His gi en by
h1,j =bj,j=1,...,nb
hi,j =
i−1

k=1
(˜ak+1hi−k,j)+h1,i+j−1(8)
i=2,...,N;j=1,...,nb
And finally φis he eg ession ma ix o dimension N3×
(na +nb +1)and θis he pa ame e ec o o be iden ified
o dimension (na +nb +1)×1, which is calcula ed a e e y
sampling ime using he eceding ho izon iden ifica ion.
φ=[y( −j| )y( −j−1| )...y( −j−na | )
∆u( −d−j| )... ∆u( −d−j−nb | )] (9)
θ=[ 1−a1( )a1( )−a2( )... a
na( )(10)
b0( )... b
nb( )]T
The decision a iables o he p oblem p oposed a e he
ollowing:
x=[a1( )... a
na( )b0( )... b
nb( )d( )(11)
∆u( )∆u( +1)... ∆u( +Nu−1) ]T
The algo i hm complexi y g ows wi h ega d o o de
sys em and con ol ho izon.
B. Fi s -o de sys ems
Mos p ocesses in indus y, when conside ing small chan-
ges a ound an ope a ing poin can be desc ibed by a linea
model o , no mally, e y high o de . This is because mos in-
dus ial p ocesses a e composed o many dynamic elemen s,
usually fi s o de , so he ull model is o an o de equal
o he numbe o elemen s. In ac , each mass o ene gy
s o age elemen in he p ocess p o ides a fi s -o de elemen
1357
in he model. Conside , o ins ance, a long pipe used o hea
exchanging pu poses, as he case o sola collec o . The pipe
can be modelled by b eaking i in o a se o small pieces,
each o which can be conside ed a fi s -o de sys em. The
esul ing model will ha e an o de equal o he numbe o
pieces used o model he pipe, ha is, a e y high-o de
model. These e y high-o de models would be di ficul o
use o con ol pu poses bu , o una ely, as shown in [12], i
is possible o app oxima e he beha iou o such high-o de
p ocesses by a sys em wi h one ime cons an and a dead
ime.
The plan o be con olled can be desc ibed by his kind
o model. I he sampling ime is an in ege mul iple o he
delay, he disc e e ans e unc ion is gi en by:
G(z−1)= bz−1
1−az−1z−d
In his case na =1and nb =1and he me hodology
shown abo e is educed conside ably. The e o e φand θa e
educed o dimensions N3×3and 3×1 espec i ely:
φ=[y( −j−1| )y( −j−2| )∆u( −d−j| )] (12)
θ=1−a( )a( )b( )T(13)
And he decision a iables numbe becomes 3+Nu:
x=[a( )b( )d( )∆u( )∆u( +1)(14)
... ∆u( +Nu−1) ]T
Consequen ly he op imiza ion p oblem is also educed
and now he algo i hm complexi y g ows linea ly wi h he
con ol ho izon. The algo i hm complexi y is independen on
he sys em pa ame e s.
C. Op imiza ion p oblem
The op imiza ion p oblem is composed o a bilinea ob-
jec i e unc ion (con ol and es ima ion canno be designed
sepa a ely, he es ima ion is a ec ed by he con ol) subjec
o inequali y cons ain s ( he ones ha can be handled by
any MPC plus hose imposed on model pa ame e s) in he
p esence o con inuous and in ege a iables (dead ime
d). The e o e i is a non-con ex Mixed In ege Non-Linea
P og amming (MINLP) p oblem.
This kind o p oblem has a high compu a ional bu den,
mainly i he global minimum wan o be ound. The e a e
B anch&Bound algo i hms a ailable in he ma ke ha sol e
his op imiza ion p oblem wi h he help o he use , who
can influence he choice o b anching a iable by p o iding
p io i ies o he in ege a iables. Anyway, his is no an
easy p oblem o be sol ed on-line.
In o de o simpli y he me hod so ha can be used in eal
ime, wo app oxima ion ha e been used:
a) A simple op imiza ion algo i hm has been used. The
Ma lab Op imiza ion Toolbox unc ion ( mincon) has
been used o sol e he p oblem. mincon uses de i a i e-
based sea ch algo i hm and do no gua an ee a glo-
bal minimum. All he pa ame e s o he op imiza ion
unc ion can be modified in o de o each an accep a-
ble comp omise be ween execu ion ime and he sub-
op imal solu ion o he algo i hm.
b) On he o he hand, he p oblem has been elaxed ea ing
he in ege a iable as eal, ha is, i is con e ed in o
Non-Linea P og amming wi h eal a aibles. The alue
gi en by he algo i hm is unca ed in o de o sa is y
he equi emen s o he sys em.
The only uning pa ame e s o he con olle a e:
1) Con ol ho izon: Nu.
2) P edic ion ho izon: N1=d+1,N2=d+N.
3) Iden ifica ion ho izon: N3.
4) Ou pu weigh ing ac o : δi.
5) Inpu weigh ing ac o : λi.
6) Iden ifica ion weigh ing ac o : γi.
IV. SIMULATIONS RESULTS
In o de o es he p oposed me hod be o e he final
implemen a ion and o compa e i wi h o he s con olle s,
a simula ion s udy was made. This sec ion shows simula ion
o he p oposed con olle compa ed o a s anda d app oach
using an sel - unig GPC wi h RLS iden ifica ion and o he
MPCI p oposed by Shouche e al. [7].
The nominal model used o he design is he ollowing
fi s o de linea sys em wi h a dead ime o h ee sampling
pe iods:
Gm(z−1)= −0.009546z−1
1−0.89654z−1z−4(15)
The ollowing figu es show he beha iou o he p ocess
ou pu , which is he sola field ou le empe a u e (T o) and
he manipula ed a iable, which is al e opening (VM1)as
well as model pa ame e s a,band d. The uning alues o
he p edic i e con olle s a e: Nu=10,N=60,N3=60,
λ=1,δ=1,γ= 1000, being he sampling ime Ts=40s.
All he decision a iables ha e an ini ial alue equal o ze o,
ha is, he con olle does no know he p ocess model. And
he maximum and minimum alues o he a iables a e 100
and −100.
Fig 2 shows a compa ison o he e olu ion o he p o-
cess ou pu esponses unde a sel - uning GPC wi h a RLS
iden ifica ion p ocedu e ( hin solid line) and he p oposed
me hod GPC wi h simul aneous iden ifica ion (bold line).
This simula ion was pe o med in o de o illus a e he
beha iou o bo h con olle s unde changes in he ope a ing
poin and se -poin . Ini ially, he model pa ame e s a e a=
−0.89654,b=−0.009546 and d=3. They a e changed
om hei nominal alues a = 159, aking he new alues
a=−0.627,b=−1. The dead ime was no changed so ha
bo h con olle s could wo k in he same condi ions, since he
sel - uning con olle does no es ima e his alue.
As can be seen, bo h con olle s beha e well in he
nominal case, bu he p oposed con olle is able con go on
con olling wi h he new alues o he pa ame e s while he
sel - uning GPC beha es wo s . The RLS finds new alues o
he pa ame e s ha make he sel - uning con olle beha e
well, al hough hey a e no he ue ones. A = 340, he
1358
050 100 150 200 250 300 350 400 450
−2
0
2
4
T o(ºC)
Simula ion I
50 100 150 200 250 300 350 400 450
−5
0
5
10
15
VM1(%)
50 100 150 200 250 300 350 400 450
−1
−0.5
0
pa ame e ,a
50 100 150 200 250 300 350 400 450
−1.5
−1
−0.5
0
pa ame e ,b
50 100 150 200 250 300 350 400 450
0
5
Samples ime
pa ame e ,delay
p oposed MPC
MPC wi h adap a ion
se poin
Fig. 2. Simula ion I
MPC wi h adap a ion modifies he alues pa ame e s. This
e ec is based on he absence o Pe sis en Exci a ion in
closed loop iden ifica ion [13]. A = 351, whe e a s ep
change in he e e ence is pe o med, he p oposed s a egy
gi es a good closed loop esponse while he MPC wi h
adap a ion is fluc ua ing du ing 100 samples.
The ollowing simula ion (figu e 3) p esen s he esul s o
a es pe o med o show how he p oposed s a egy is able
o iden i y he plan dead ime, apa om he o he model
pa ame e s.
050 100 150 200 250 300 350 400 450
0
0.5
1
1.5
T o(ºC)
Simula ion II
50 100 150 200 250 300 350 400 450
−1
−0.5
0
0.5
VM1(%)
50 100 150 200 250 300 350 400 450
−1
−0.5
0
pa ame e ,a
50 100 150 200 250 300 350 400 450
−1
−0.5
0
pa ame e ,b
50 100 150 200 250 300 350 400 450
0
5
Samples ime
pa ame e ,delay
GPC
p oposed MPC
se poin
Fig. 3. Simula ion II
In his case he compa ison has been ca ied ou wi h a
fixed GPC.TheGPC logically beha es wo s , since i is no
able o adap o his change. The model used in he simula ion
has been changed om he one in equa ion (15) o
Gm(z−1)= −0.9z−1
1−0.6723z−1z−1
No e how, in spi e o he g ea a ia ion o he pa ame e s
(e en dead ime), he s a egy desc ibed in his pape is able
o mee he new model pa ame e s wi hou he need o a
Pe sis en Exci a ion. I is able o ack he se -poin in s eady
s a e and when i is changed. The s anda d GPC is no able
o mee hese changes.
The las simula ion compa es he p oposed me hod wi h
he MPCI p oposed by Shouche e al.. The model is aken
om case s udy (B) o [7] and is gi en by:
y( )=ay( −1) + bu( −1) + e( )
Whe e he ini ial model pa ame e s a e a=0.4,b=0.4and
e=−0.05. The ue pa ame e s a e a=0.6,b=0.2and
e=0, which pe ec ly iden ified by bo h con olle s.
Table I shows he acking capabili ies o bo h con olle s
quan ified as IAE (In eg al o Absolu e E o ) and ISE (In e-
g al o Squa e E o ). Bo h con olle s find good es ima es o
he ue alues, bu MPCI imposes cons ain s on he inpu in
o de o ha e Pe sis en Exci a ion, de e io a ing he acking
capabili ies o he con olle . The di e ence in con olle s
pe o mance is clea ly shown.
TABLE I
MPCI VS PROPOSED MPC
Con olle IAE ISE
MPCI 0.0817 2.5017 ×10−5
P oposed MPC 1.3279 ×10−46.6304×10−11
V. EXPERIMENTAL RESULTS
Se e al expe imen s ha e been pe o med on he sola
plan o show he beha iou o he p oposed con olle . The
uning alues used a e: Nu=10,N=60,N3= 150,
λ=1,δ=10,γ= 100. All he decision a iables
s a wi h a ini ial alue equal o ze o, ha is, he e is no
p e ious knowledge o he plan dynamics. The bounds o
all he a iables a e 100 and −100 excep ∆umax =20and
∆umin =−20. The ollowing g aphics show he ac ual sola
field ou le empe a u e (T o) oge he wi h i s e e ence,
al e opening, sola adia ion, field inle empe a u e, which
is he accumula o s ou pu empe a u e (Tac)aswellas
model pa ame e s a,band d.
Figu e 4 p esen s he esul o he expe imen ca ied ou
o show e e ence acking capabili ies. The expe imen akes
o e h ee hou s, and co esponds o a clea day (see sola
adia ion).
The e exis s a slow a ia ion in he sola adia ion and inle
empe a u e Tac du ing all day which gi es ise o changes in
p ocess dynamics. In his case he delay emains unchanged
(d=5), bu he o he pa ame e s (aand b), a e modified by
he con olle in o de o ob ain a good closed loop beha iou .
One o he mos appealing ea u es o his me hod, as is
i capabili y o s a ing o con ol wi hou p io knowledge
o he plan , is shown in he nex expe imen .
Figu e 5 shows he e olu ion o he plan a he beginning
o he day. Du ing he s a -up phase, he con ol s a egy is
1359

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
80
85
90
95
T o(ºC)
Expe imen al esul s I
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
35
40
45
50
VM1(%)
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
800
950
1100
Radia ion (W/m
2
)
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
60
70
80
Tac (ºC)
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
−0.8
−0.7
−0.6
pa ame e a
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
−0.1
−0.08
−0.06
−0.04
pa ame e b
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
4
4.5
5
5.5
6
Samples ime (Ts=40s)
pa ame e d
Fig. 4. Expe imen al esul s I
able o d i e he plan owa ds he desi ed ope a ing egime
and ack he se poin , e en wi h changes in adia ion. In
his case he pa ame e s cons ain s a e: amax =−0.6,
amin =−1,bmax =1,bmin =−0.9,dmax =10,dmin =1.
No ice ha some o hese cons ain s a e ac i e du ing he
expe imen , showing ha a cons ained MPC is sol ed on
line.
The esul s ob ained in bo h expe imen s a e good in spi e
o he a ying condi ions, showing ha he p oposed me hod
is a good candida e o con ol his kind o plan s.
VI. CONCLUSIONS
The pape has shown he applica ion o a p edic i e
con olle wi h simul aneous iden ifica ion o a sola plan .
The con ol s a egy allows he s a -up o he plan wi hou
a edious iden ifica ion p ocedu e and has shown good pe -
o mance in changing ope a ing condi ions. The use o a
sub-op imal solu ion o he MINLP p oblem allows i s use
in eal ime wi h low compu a ional equi emen s. While
he applicabili y o he me hod has been illus a ed, u u e
in es iga ion is needed ela ing he op imiza ion p ocedu e
and s abili y issues.
2000 2500 3000 3500 4000 4500 5000 5500 6000
60
80
100
T o(ºC)
Expe imen al esul s II
2000 2500 3000 3500 4000 4500 5000 5500 6000
0
20
40
VM1(%)
2000 2500 3000 3500 4000 4500 5000 5500 6000
400
700
1000
Radia ion(W/m
2
)
2000 2500 3000 3500 4000 4500 5000 5500 6000
48
49
50
51
Tac(ºC)
2000 2500 3000 3500 4000 4500 5000 5500 6000
−0.9
−0.8
−0.7
−0.6
−0.5
pa ame e a
2000 2500 3000 3500 4000 4500 5000 5500 6000
−1
−0.75
−0.5
−0.25
0
pa ame e b
2000 2500 3000 3500 4000 4500 5000 5500 6000
2
3
4
5
6
Samples ime (Ts=40s)
pa ame e d
Fig. 5. Expe imen al esul s II
REFERENCES
[1] E. Camacho and C. Bo dons, 2nd Edi ion. Model P edic i e Con ol.
London: Sp inge Ve lag, 2004.
[2] C. Cu le and B. Ramake , “Dynamic Ma ix Con ol- A Compu e
Con ol Algo i hm,” in Au oma ic Con ol Con e ence, San F ancisco,
1980.
[3] D. Ram´
ı ez and E. Camacho, “Cha ac e iza ion o Min-Max MPC wi h
Global Unce ain ies,” in P oc. Ame ican Con ol Con e ence, ACC,
2002.
[4] E. Mosca, Op imal, P edic i e and Adap i e Con ol. P en ice Hall,
1995.
[5] E. Camacho, M. Be enguel, and F. Rubio, Ad anced Con ol o Sola
Powe Plan s. Sp inge -Ve lag, London, 1997.
[6] K. As ¨
om and B. Wi enma k, Adap i e Con ol. Addison-Wesley,
1989.
[7] M. Shouche, H. Genceli, and M. Nikolaou, “E ec o On-line Op i-
miza ion Techniques on Model P edic i e Con ol and Iden ifica ion
(MPCI),” Au oma ica, ol. 23/2, pp. 137–160, 2002.
[8] G. Goodwin and K. Sin, Adap i e fil e ing: p edic ion and Con ol.
P en ice Hall, 1984.
[9] A. N´
u˜
nez-Reyes, J. No mey-Rico, C. Bo dons, and E. Camacho, “A
Smi h P edic i e based MPC in a Sola Ai Condi ioning Plan ,”
Jou nal o P ocess Con ol, ol. 15/1, pp. 1–10, 2005.
[10] N. Fila o and H. Unbehauen, Adap i e Dual Con ol. Be lin:
Sp inge -Ve lag, 2004.
[11] D. Cla ke, C. Moh adi, and P.S.Tu s, “Gene alized P edic i e Con ol.
Pa I. The Basic Algo i hm,” Au oma ica, ol. 23, no. 2, pp. 137–148,
1987.
[12] P. Deshpande and R. Ash, Elemen s o Compu e P ocess Con ol.
ISA, 1981.
[13] B. Ande son, “Adap a i e Sys ems, Lack o Pe sis en Exci a ion and
Bu s ing Phenomenon,” Au oma ica, ol. 21, pp. 247–258, 1985.
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