PREDICTIVE CONTROL OF AN OLIVE OIL MILL WITH
MULTI-OBJECTIVE PRIORITIZATION
C.B. Sche e -Du a
,A. N´u˜
nez-Reyes
,C. Bo dons
Dep . Au omac¸˜
ao e Sis emas, Uni . Fede al de San a Ca a ina
CP: 476, CEP: 88040-900, Flo ian´
opolis-SC, B azil
[email p o ec ed]
Dep . Ing. Sis emas y Au om´
a ica, Uni . de Se illa
Camino de los Descub imien os s/n, 41092, Se illa, Spain
ampa o, bo dons
@ca uja.us.es
Abs ac : This pape p esen s a mul i-objec i e con olle applied o an oli e oil mill. The
p ac ical expe ience using a Gene alized P edic i e Con olle (GPC) in he eal plan showed
he necessi y o including objec i es, wi h di e en p io i ies, in he p ocess con ol. The
analysis demons a es ha GPC wi h p io i iza ion objec i es can con ol he p ocess and
ulfill he specified ope a ional condi ions. The esul s a e illus a ed wi h some simula ions
ha compa e he adi ional GPC o he mul i-objec i e one.
Keywo ds: Mul iobjec i e op imiza ions, Op imiza ion p oblems, P io i y, P ocess con ol,
P edic i e con ol.
1. INTRODUCTION
Nowadays, a con ol sys em mus be able o ope a e
he p ocess in such a way ha mul iple and chang-
ing ope a ional c i e ia (economical, sa e y, en i on-
men al o quali y) can be ulfilled in he p esence o
changes in p ocess cha ac e is ics. Model P edic i e
Con ol (MPC) is he mos popula ad anced con ol
echnique in indus y (Camacho and Bo dons, 1999),
due o i s abili y o mee his challenge and he in u-
i i e con ol p oblem o mula ion.
Mos MPC s a egies a e based on op imizing a single
objec i e cos unc ion, which is usually quad a ic,
in o de o de e mine he u u e sequence o con ol
mo es ha makes he p ocess beha e bes . Howe e ,
in many con ol p oblems he beha iou o he p ocess
canno be measu ed by a single objec i e unc ion bu ,
mos o he ime, he e a e di e en , and some imes
conflic ing, con ol objec i es. The easons o mul i-
ple con ol objec i es a e a ied:
½
Suppo ed by CAPES-BRASIL, con ac BEX0704/00-8 and
FEDER, con ac 1FD97-0836
P ocesses ha e o be ope a ed di e en ly when
hey a e a di e en ope a ing s ages. Fo exam-
ple a he s a up phase o he p ocess, a min-
imum s a -up ime may be desi ed, while once
he p ocess has eached he ope a ing egime,
a minimum a iance o he con olled a iables
may be he p ima y con ol objec i e.
E en i he p ocess is wo king a a pa icula op-
e a ing s age, he con ol objec i e may depend
on he alue o he a iables. Fo ins ance he
con ol objec i e, when he p ocess is wo king a
he nominal ope a ing poin , may be o minimize
he weigh ed sum o he squa e e o s o he con-
olled a iables wi h espec o hei p esc ibed
alues. Bu i he alue o one o he a iables
is oo high, because o a sudden pe u ba ion
o example, he main con ol objec i e may be
o educe he alue o his a iable as soon as
possible.
Fu he mo e, in many cases, he con ol objec i e is
no o op imize he sum o he squa ed e o s, bu o
keep some a iables wi hin specified bounds. No ice
ha his si ua ion is di e en o he cons ained MPC,
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15 h T iennial Wo ld Cong ess, Ba celona, Spain
85
as he objec i e is o keep he a iable he e, al hough
excu sions o he a iable ou side his egion, hough
no desi able, a e pe mi ed. In cons ained MPC he
a iables should be kep wi hin he p esc ibed egion
because o physical limi a ions, plan sa e y o o he
conside a ions. Cons ain s which canno be iola ed
a e e e ed as ha d cons ain s, while hose which
can a e known as so cons ain s. These ypes o
objec i es can be exp essed by penalizing he amoun
by which he o ending a iable iola es he limi .
Some imes all con ol objec i es can be summa ized
in a single objec i e unc ion. Conside , o exam-
ple, a p ocess wi h a se ies o con ol objec i es
½
¾
. Some o he con ol objec i es may
be o keep some o he con olled a iables as close
o hei e e ences as possible, while o he con ol
objec i es may be ela ed o keeping some o he a i-
ables wi hin specified egions. Conside all objec i es
o ha e been ans o med in o minimizing a quad a ic
unc ion
, subjec o a se o linea cons ain s on
he decision a iables
. The u u e con ol
sequence can be de e mined by minimizing he ol-
lowing objec i e unc ion:
Â
¬
Â
subjec o
; o
.
The impo ance o each o he objec i es can be modu-
la ed by app op ia e se ing o all
. This is, howe e ,
a non i ial ma e in gene al as i is e y di ficul o
de e mine he se o weigh s which will ep esen he
ela i e impo ance o he con ol objec i es. Fu he -
mo e, p ac ical con ol objec i es a e some ime qual-
i a i e, making he ask o de e mining he weigh s
e en mo e di ficul .
In some cases, he ela i e impo ance o he con ol
objec i es can be es ablished by p io i iza ion. Tha
is, he objec i es o g ea e p io i y, o example ob-
jec i es ela ed o secu i y, mus be accomplished be-
o e o he objec i es o less p io i y a e conside ed.
Objec i es can be p io i ized by gi ing much highe
alues o he co esponding weigh s. Howe e his is a
di ficul ask which is usually done by a ial and e o
me hod.
In (Tyle and Mo a i, 1999) a way o in oducing mul-
iple p io i ized objec i es in o he MPC amewo k
using p oposi ional logic is gi en. These ideas we e
ex ended in (Bempo ad and Mo a i, 1999) using he
new mixed logic dynamic (MLD) amewo k, which
allows one o ep esen sys ems which can be de-
sc ibed by in e dependen physical laws, logical ules
and ope a ing cons ain s.
This wo k applies hese ideas o an oli e oil mill. This
is a mul i a iable plan which se e al objec i es o be
ulfilled, which a e also logic-dependen . The p ocess
has ex a deg ees o eedom, which allows di e en
con ol s a egies. The p ac ical expe ience in he eal
plan demons a ed ha he p ocess can be con olled
by a cons ained GPC, limi ing he manipula ed a i-
ables. Howe e , he possibili y o including objec i es,
wi h di e en p io i ies, in he p ocess con ol, could
imp o e he indus ial pe o mance.
The pape is o ganized as ollows. In sec ion 2 a
desc ip ion o he p ocess is p esen ed. The model
iden ifica ion is desc ibed in sec ion 3. Mul i-objec i e
op imiza ion is p esen ed in sec ion 4, showing he
con olle used in his amewo k, based on p io i ized
objec i es. The con ol s a egy applied o he model
a e desc ibed in sec ion 5, including he con ol p io -
i ies. Sec ion 6 is dedica ed o p esen ing some simu-
la ion esul s and finally he conclusions a e p esen ed
in sec ion 7.
2. PROCESS DESCRIPTION
The au oma ic con ol o he ex ac ion o oil ou o
oli es is s ill an open field, since many ins alla ions
a e usually ope a ed in manual mode. As oli e oil
mills a e becoming bigge he chances o au oma ion
a e inc easing, he e o e i is impo an o acqui e he
necessa y knowledge o he p ocess beha iou in o de
o design he app op ia e con ol s a egies.
The p ocess is composed o se e al ope a ions: e-
cep ion o aw ma e ial (oli es), washing, p epa a ion,
ex ac ion, and s o age o he p oduced oil (Ci an os,
1999). Figu e 1 shows he mos impo an phases o
he p ocess.
Fig. 1. Oli e oil mill - p ocess desc ip ion
The p epa a ion phase consis s o wo subp ocesses.
The fi s one is oli e c ushing by an special mill,
whose objec i e is o des oy he oli e cells whe e
oil is s o ed. The second one aims a homogenizing
he pas e by e ol ing i while i s empe a u e is kep
cons an a a specified alue (a ound
C). This is
pe o med in a machine called he momixe ,which
homogenizes he h ee phases o he pas e (oil, wa e
and by-p oduc (alpeo ujo)) while exchanges ene gy
wi h su ounding pipes o ho wa e . This is done
in o de o acili a e oil ex ac ion in he ollowing
86
p ocess: mechanical sepa a ion, o ex ac ion, in he
decan e .
Homogeniza ion is eally impo an in he whole p o-
cess, because bad ope a ion condi ions in he he -
momixe can d ama ically educe he quali y and
quan i y o he final p oduc . The pas e is hea ed in
o de o acili a e mixing since he pas e u ns mo e
fluen when empe a u e ises. Howe e , he e exis s
an uppe empe a u e limi behind which oli e oil
loses quali y (fla ou , ag ance, e c.) due o he ox-
ida ion p ocess and he loss o ola ile componen s.
The e o e, keeping low alues o empe a u e will
be a high-p io i y objec i e. Expe iences o modeling
and p edic i e con ol o his phase a e desc ibed in
(Bo dons and Cueli, 2001).
The nex s age is based on he sepa a ion o he p od-
uc phases by means o a cen i uge. This is a con inu-
ous p ocess which sepa a es he di e en componen s
ha cons i u e he pas e by means o cen i ugal o ce.
This sepa a ion is made in he ho izon al cen i uge o
decan e . The e a e wo ypes o decan e : he h ee
phases decan e , and he wo phases one. The fi s one
sepa a es wo liquid componen s (oil and was e wa e )
om a solid phase (solid by-p oduc ). The second one,
ha is he mos used and he one ha exis s in he plan
ha is con olled in his wo k, sepa a es oli e oil om
by-p oduc .
In o de o pe o m a good sepa a ion, he pas e ha
en e s he decan e mus be accommoda ed. I s flow
mus be con olled o a se poin ha depends on op-
e a ing condi ions and some wa e mus be added de-
pending on he p ope ies o he aw ma e ial.
Finally, he las s age o he sys em consis s o he
s o age and he conse a ion o he ob ained oil.
Se e al a iables ake pa in oli e oil ex ac ion p o-
cess. The final p oduc quali y and he indus ial yield
a e influenced by di e en p ocess a iables. Nex , he
mos impo an a iables will be desc ibed:
¯
Tempe a u e in he he momixe . The hea ing o
he pas e has o be cons an and g adual since
ab up changes a ec nega i ely he quali y o
he final p oduc . Two main di ficul ies appea :
he fi s one is he exis ence o la ge delays due
o he he mal na u e o he p ocess and he
second one is caused by he on-o mechanism
o eeding he pas e.
¯
Residence ime. Ano he impo an ac o be
conside ed is he mixing ime ( esidence ime)
inside he he momixe . A sho ime d i es o
incomple e mixing and a long one can gi e ise
o emulsions, which in e e e wi h he ex ac ion
p ocess.
¯
Pas e consis ency. The pas e consis ency gi es
in o ma ion abou he pas e fluidi y deg ee, which
is associa ed o he oli e mois u e. This alue has
a g ea influence in he wa e ha mus be added
be o e he pas e en e s he decan e .
¯
Pas e flow o decan e . The pas e flow o de-
can e and he wa e /mass p opo ion de e mine
he maximum indus ial yield. The mass flow is
adjus able acco ding o he oli e ype.
¯
Wa e flow o decan e . This also de e mines he
ex ac ion e ec i eness. The amoun o wa e
ha is in oduced in he decan e mus be con-
s an ; ha is, he sum o he ege a ion wa e o
he oli e plus he added wa e mus be cons an .
As is well known, he aw ma e ial does no con-
ain a homogeneous mois u e, which o ces he
wa e flow o be con inually adjus ed in o de o
ob ain he maximum oil in he decan e .
In he majo i y o oli e oil mills, he p ocess is con-
olled manually, since he e a e many ac o s ha
a ec p oduc ion. The e a e many objec i es o be ul-
filled and he ope a o mus use his expe ience o ha e
he p ocess unde con ol. This si ua ion jus ifies he
use o a mul i a iable p edic i e con olle ha is able
o manipula e se e al ac ua o in o de o ob ain he
desi ed pe o mance. The con ol s a egies applied o
his plan a e desc ibed in sec ion 5.
3. MODEL IDENTIFICATION
Mos p ocesses in indus y when conside ing small
changes a ound an ope a ing poin can be desc ibed
by a linea model o , no mally, e y high o de . These
models would be di ficul o use o con ol pu pose
bu , o una ely, i is possible o app oxima e he be-
ha iou o such high o de p ocesses by a sys em
wi h one ime cons an and a dead- ime (Camacho and
Bo dons, 1999). The e o e, he chosen ma hema ical
s uc u e o he iden ifica ion o he sys em is based
in he sys ems dynamics o fi s o de wi h delay.
The da a used o he a iables iden ifica ion, ha e
been ob ained expe imen ally om a eal oli e oil
mill. These eal da a ha e been ea ed (fil e ed,
sampled, no malized) sui ably o each a accep able
model.
The inpu a iables and he measu able dis u bances
ha e been exci ed wi h di e en s eps, in o de o
iden i y he eal sys em. The pa ame e s o he sys-
em model a e de e mined by ecu si e leas squa es
es ima ion and he eac ion cu e me hod.
The p ocess ma ix ac ion desc ip ion can be seen
in equa ion (1), whe e he con olled a iable
is he
oil flow, he manipula ed a iables
½
,
¾
and
¿
a e,
espec i ely, he empe a u e in he he momixe , he
pas e flow o decan e and he wa e flow o decan e ,
and he measu able dis u bances
½
and
¾
a e ela ed
o he oli e ype. These measu able dis u bances ha e
a g ea influence in he pe o mance, because hey
ep esen he oli e ea u es o he he momixe .These
measu emen s ha e e ec on he decision making in
he plan con ol.
½
¾
¿
½
¾
(1)
87
To exempli y he iden ifica ion o he sys em model,
figu e 2 shows how was ob ained he model o he
oil flow in unc ion o he empe a u e in he he -
momixe . The da a alues a e no malized. The fi s
g aphic shows he empe a u e applied o he sys em
(and o he model). In he second g aphic he simula ed
ou pu (dashed line) is compa ed o he eal one (solid
line). In he ollowing g aphic, he model e o signal
can be obse ed.
020 40 60 80 100 120 140 160 180 200
−30
−20
−10
0
10
model e o
samples (S =90s)
020 40 60 80 100 120 140 160 180 200
−5
0
5
10
empe a u e
020 40 60 80 100 120 140 160 180 200
−50
0
50
oil low
Model Valida ion
Fig. 2. Modeling o he oil flow espec o he empe -
a u e in he he momixe
To ge mo e in o ma ion abou he plan model iden i-
fica ion, see (N´u˜nez-Reyes e al., 2001) and (Bo dons
and Cueli, 2001).
4. MULTI-OBJECTIVE OPTIMIZATION
One o he s eng hs o MPC is i s abili y o inco po a e
cons ain s in he con ol o mula ion. F equen ly a
dis u bance d i es he sys em in o a egion whe e he
MPC p oblem is in easible and hence no con ol ac ion
can be compu ed. Feasibili y can be eco e ed by so -
ening he cons ain s using slack a iables. In many
applica ions, he con ol objec i es and cons ain s can
be assigned a hie a chy o le els o p io i y. O en, a
dis u bance o a aul occu s, esul ing in some con-
s ain s o objec i es being iola ed. Inadequa e han-
dling o his si ua ion migh esul in componen o
e en sys em-wide ailu es (Ke igan e al., 2000). In
(Tyle and Mo a i, 1999), i is p esen ed a me hod o
handling mul i-objec i e p io i iza ions o model p e-
dic i e con ol, combining p oposi ional logic using
in ege a iables wi h quan i a i e models.
The me hod p esen ed in (Tyle and Mo a i, 1999)
consis s o desc ibing he quali a i e in o ma ion in
e ms o p oposi ional logic and, using in ege a i-
ables, ansla e he p oposi ions in o linea cons ain s.
Fo con ol p oblems, he quali a i e knowledge may
be inco po a ed wi hin he model p edic i e con ol
amewo k by appending he p io i iza ion cons ain s
o he con ol calcula ion p oblem.
This me hod conside a p ocess wi h a se ies o
p io i ized con ol objec i es
. Suppose ha objec-
i e
has a highe p io i y han objec i e
·½
and
ha he objec i es can be exp essed as:
.
The main idea consis s o in oducing in ege a iables
which ake he alue one when he co esponding
con ol objec i e is me and ze o o he wise. Objec i es
a e exp essed as:
(2)
whe e
is a conse a i e uppe bound on
.I
objec i e
is sa isfied,
and he e o mula ed
objec i e coincides wi h he o iginal con ol objec i e.
By in oducing
, he objec i e (cons ain ) is always
sa isfied e en when he co esponding con ol objec-
i e
is no me (
½
).
The p io i iza ion o objec i es can be es ablished by
imposing he ollowing cons ain s:
o
(3)
To imp o e he deg ee o he cons ain sa is ac ion
o objec i es ha canno be sa isfied, he se o con-
s ain s (2) can be modified. In o de o come as close
as possible o sa is ying a ailed objec i e
, a slack
a iable
sa is ying he ollowing se o cons ain s is
in oduced:
(4)
and he objec i e unc ion o be minimized, subjec o
(2), (3), (4), is:
(5)
whe e
is a penal y unc ion o he slack a iable
(posi i e and s ic ly inc easing) and
is an uppe
bound on
. The op imiza ion algo i hm will y o
maximize he numbe o sa isfied objec i es (
)
be o e a emp ing o educe
. The op imiza ion
me hod will op imize he deg ee o sa is ac ion o he
fi s objec i e ha ailed only a e all mo e p io i ized
objec i es ha e been sa isfied. No ice ha
does
no imply ha objec i e
is no sa isfied, i only
indica es ha he co esponding cons ain has been
elaxed.
5. CONTROL STRATEGY
The con ol s a egy ha has being used o con ol
he oli e oil mill can be seen as wo con ol le els,
as a cascade s uc u e. A mul i a iable cons ained
GPC was implemen ed o ack he oil flow o a desi -
able e e ence, modi ying he manipula ed a iables
ha a e he e e ence signals o an inne loop which
ope a e wi h classical mono a iables con olle s PID.
88
The indus ial implemen a ion o he GPC ha e shown
he impo ance o including economical and con ol
objec i es in he oil p oduc ion sys em (N´u˜nez-Reyes
e al., 2001).
The mul i-objec i e algo i hm implemen ed o he
oli e oil mill p esen s ou con ol (and economical)
objec i es. The con ol p io i ies a e ela ed o he op-
e a o en ies in he plan . These en ies a e called
Ý
o he se poin and
Ù
o he desi able manipula ed
a iables. The pe o mance c i e ia selec ed in o de
o dec easing impo ance a e gi en as ollow:
(1) keep he he momixe empe a u e as nea as
possible o he op imum alue o gua an ee he
bes oil cha ac e is ics:
Ù
½
Ù
½
ÓÔ
¯
Ù
½
(6)
(2) maximize he ex ac ed oil:
Ý
Ý
ÓÔ
¯
Ý
(7)
(3) keep he pas e flow as close as possible o he
ope a o e e ence ( educe he necessa y flow):
Ù
¾
Ù
¾
ÓÔ
¯
Ù
¾
(8)
(4) educe he wa e flow necessa y in he p oduc-
ion:
Ù
¿
Ù
¿
ÓÔ
¯
Ù
¿
(9)
whe e
(
½
¾
¿
) a e e y small posi i e
scala s, ep esen ing he maximum ole ance admissi-
ble o a end he objec i es.
The fi s objec i e is he mos impo an one, since he
a ia ion o
½
can change he final p oduc cha ac e -
is ics. The second objec i e is he adjus men o he
ou pu a iable o be con olled o i s se poin . The
hi d and he las objec i es a e ela ed o he ene gy
sa ings in he p oduc ion. Each one o hese objec-
i es is associa e o a dis inc
,
, wi h
di e en p io i iza ion weigh s. The design o weigh s
is an a bi a y p ocedu e, guided by he heu is ic.
In o de o apply his p ocedu e o MPC, o each ime
in he p edic ion ho izon, he p io i iza ion p oblem is
ecalcula ed. The op imum alues ob ained om he
objec i es p io i iza ion a e used as desi able goal o a
GPC con olle . The cos unc ion implemen ed in GPC
consis s o a weigh ed sum o squa es o he indi idual
objec i es, exp essed as
Â
Ý
Ý
ÓÔ
¾
ÓÔ
¾
(10)
6. SIMULATION RESULTS
To illus a e he applica ion o his app oach, conside
he oli e oil mill desc ibed in sec ion 2. The con-
olle uses h ee manipula ed a iables, he momixe
empe a u e, pas e flow and wa e flow, o adjus he
con ol a iable, oil flow. The con ol p io i ies a e
implemen ed as desc ibed in sec ion 5.
The mul i-objec i e app oach was compa ed o a adi-
ional cons ained GPC using a cos unc ion consis ing
o a weigh ed sum o squa es o he manipula ed a i-
ables. The desi able ope a ional condi ions (
Ý
,
Ù
)
a e used as op imal e e ence o he mul i-objec i e
con olle .
To pe o mance he plan simula ions, model unce -
ain ies a e conside ed (model dead- ime di e s o
he p ocess delay in
) wi hou changing he uning
o he con olle s. The closed loop beha io o GPC
and he mul i-objec i e con olle a e showed in he
figu es 3 and 4. In all cases, he solid lines co espond
o he GPC and he dashed lines o he mul i-objec i e
con olle . Fo he simula ion, a
s ep e e ence
has been applied a
, ano he
s ep e e ence
a
and a
s ep dis u bance has been applied
a he inpu o he plan a
.
0 100 200 300 400 500 600 700
0
50
100
inpu 1 (%)
0 100 200 300 400 500 600 700
20
50
80
inpu 2 (%)
0 100 200 300 400 500 600 700
0
50
100
inpu 3 (%)
ime (samples)
Fig. 3. Manipula ed a iables
0 100 200 300 400 500 600 700
0
20
40
60
80
100
ou pu (%)
ime (samples)
Fig. 4. Con olled a iable
I is impo an o no e ha he esponses a e simila
and bo h con olle s a e well adjus ed, ha ing a good
acking esponse. The mul i-objec i e GPC p esen s
e en a as e esponse. Bu he special app oach p o-
ided by his con olle is he gua an ee ha objec i es
a e ulfilled. No ice ha all he objec i es a e sa isfied
un il he second e e ence changes. A his poin , he
89
con olle can sa is y h ee o he objec i es, acco ding
o he p io i ies, so he wa e flow do no each he
op imum. When he dis u bance is included, he he -
momixe empe a u e is he only a iable ha is sa is-
fied, con olled in he desi ed alue (
). The e o e,
his app oach is capable o p io i izing cons ain s as
well as al e ing he con ol objec i e depending upon
he posi ions o con ol inpu s. As can be obse ed,
he adi ional GPC can con ol he sys em, bu he
manipula ed a iables a e dis inc om he desi ed
alues
.
The applica ion o he mul i-objec i e GPC con olle
in he eal plan can be jus ified by:
¯
The con olle p o ides a as e esponse;
¯
The manipula ed a iables o en ge he op imum
alues;
¯
The main objec i e is always eached;
¯
As he wa e flow and he pas e flow a e mini-
mized, he ene gy is sa ed.
The only incon enien on ha app oach is he ab up
esponse, ela ed o he ac ha no dynamic is in-
cluded in he p io i iza ion algo i hm. When a dy-
namic in he con olle was in oduced, he p oblem
became compu a ionally in ac able, as commen ed in
(Tyle and Mo a i, 1999).
I was also implemen ed a mul i-objec i e weigh ed
GPC, wi h no p io i iza ion, using he same cos unc-
ion (10), ob aining simila esul s. By con as , he
only design pa ame e s needed o he p io i iza ion
GPC algo i hm a e bounds on he a iables o in e -
es . In weigh ed GPC, he weigh s adjus men mus
be chosen by ial and e o , h ough nume ical sim-
ula ions, o ia o he ad hoc app oaches in o de ha
mo e objec i es be sa isfied. This p ocedu e depends
on heu is ic, and usually akes much mo e ime han
he p io i iza ion algo i hm implemen a ion.
7. CONCLUSIONS
This a icle has in es iga ed he possibili ies o apply-
ing a mul i-objec i e GPC con olle in an oli e oil
mill. Using he p oposi ional logic, by including in e-
ge a iables ep esen ing he objec i es sa is ac ion,
i is possible o combine logic based con ol decisions
wi hin he MPC amewo k. By implemen ing such
s a egy, he con olle pe o mance can be imp o ed.
The simula ion esul s o he oil plan show ha he
manipula ed a iables ulfill he objec i es acco ding
o he p io i ies.
8. REFERENCES
Bempo ad, A. and M. Mo a i (1999). Con ol o sys-
ems in eg a ing logic, dynamics and cons ain s.
Au oma ica 35, 407–427.
Bo dons, C. and J.R. Cueli (2001). Modeling and p e-
dic i e con ol o an oli e oil mill. In: Eu opean
Con ol Con e ence.Po o.
Camacho, E.F. and C. Bo dons (1999). Model P edic-
i e Con ol. Sp inge Ve lag.
Ci an os, L. (1999). Ob enci´
on del Acei e de Oli a
Vi gen (in spanish).Ed.Ag ´ıcola Espa˜nola, S.A.
Ke igan, E.C., A. Bempo ad, D. Mignone, M. Mo a i
and J.M. Maciejowski (2000). Mul i-objec i e
p io i isa ion and econfigu a ion o he con ol
o cons ained hyb id sys ems. In: P oceedings o
he Ame ican Con ol Con e ence.
N´u˜nez-Reyes, A., J.R. Cueli and C. Bo dons (2001).
Modelado y con ol de una almaza a de ex-
acci´on de acei e de oli a (in spanish). In: P o-
ceedings JA’01. Ba celona.
Tyle , M. L. and M. Mo a i (1999). P oposi ional logic
in con ol and moni o ing p oblems. Au oma ica
35, 565–582.
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