APPLICATION OF SIMPLE CASCADE GPC WITH
ROBUST BEHAVIOUR TO ASUGAR REFINERY
C. Bo dons and E.F. Camacho
Dp o. Ingenie a de Sis emas y Au oma ica, Uni . o Se il le, Spain. Camino de los
Descub imien os sn, 41092 Se il la, Spain.
Phone: +34-95-4487348 Fax: +34-95-4487340 E-mail:bo dons,edua do@ca uja.us.es
Keywo ds
: P edic i eCon ol, P o cess Con ol, Ro-
bus Con ol.
Abs ac
This pap e p esen s he applica ion o a Gene alized P e-
dic i e Con olle 
gpc
 o sludge densi y con ol in a
suga ac o y. The lo op is con olled by a cascade s a egy,
whe e b o h he mas e and he sla econ olle s a e p edic-
i e ones. The con ol law is ex emely simple o compu e
and he uning is s aigh o wa d since a me ho d o im-
plemen
gpc
p e iously de eloped by he au ho s which
is e y simple o implemen and une has b een used. The
con olle s a e embedded in he exis ing con ol sys em,
needing he same compu a ional equi emen s as
pid
ou-
ines. The o iginal
gpc
algo i hm is imp o ed by he use
o he so-called T p olynomial, which inc eases he s abil-
i y obus ness by l e ing he p edic ions in o de o cop e
wi h mo del unce ain ies and die en p ocess dynamics
caused bychanges in he p o cess op e a ing p oin s.
1In o duc ion
This pap e shows an applica ion o a
gpc
o a p o cess in
a suga ac o y.The implemen a ion was ca ied ou by
he au ho s in collab o a ion wi h he  m
p ocisa
.The
suga ene y is lo ca ed in Pe~nael Valladolid, Spain
and b elongs o
Eb oAg icolas
. The con ol s a egy uns
in a
o si
In eg al Cub e Con ol Sys em, whe e he
gpc
has b een included as a lib a y ou ine which can b e inco -
p o a ed in acon ol sys em as easily as he buil -in
pid
ou ine.
Mo del Based P edic i eCon ol 
mbpc
o
mpc
is in-
c easingly gaining accep ance and has b een used in qui e
anumb e o applica ions ac oss he wo ld wi h sp ec acu-
la esul s,  s in he ene y and p e o chemicals sec o
and nowadays also in many o he elds in indus y. The e
a e many applica ions o p edic i econ ol success ully in
use a he p esen ime 10, no only in he p o cess in-
dus y bu also applica ions o he con ol o a di e si y
o p o cesses 8, 11, 12.
Mpc
is pa icula ly a ac-
i e o s a wi h only a limi ed knowledge o con ol, b e-
cause he concep s a e e y in ui i e, and i can b e used
o con ol a g ea a ie yo p ocesses, om hose wi h
ela i ely simple dynamics o o he mo e complex ones.
The e m Mo del P edic i e Con ol do es no designa e a
sp ecic con ol s a egy bu a e y ample ange o con-
ol me ho ds whichmake an explici use o a mo del o he
p o cess o ob ain he con ol signal by minimizing a cos
unc ion.
The
gpc
me ho d p op osed by Cla ke
e al.
5 is a
easonable ep esen a i e o his amily o me hods and
has b ecome one o he mos p opula
mpc
me ho ds, b eing
success ully implemen ed in many indus ial applica ions
3. As is well known, he basic idea o
gpc
is o cal-
cula e a sequence o u u e con ol signals in suchaway
ha i minimizes a mul is age cos unc ion dened o e
a p edic ion ho izon. The index o b e op imized is he ex-
p ec a ion o a quad a ic unc ion measu ing he dis ance
be ween he p edic ed sys em ou pu and some p edic ed
e e ence sequence o e he ho izon plus a quad a ic unc-
ion measu ing he con ol eo .
A Gene alized P edic i eCon olle esul s in a linea
con ol law which is easy o implemen once he con olle
pa ame e s a e known. The de i a ion o he
gpc
pa am-
e e s equi es, howe e , some ma hema ical complexi ies,
which a e dicul o sol e in some indus ial con olle s.
The indus ial applica ion o
gpc
in small con ol sys ems
in indus y has some dicul ies ha mus be o e come.
Apa om needing low compu a ional equi emen s, i
mus b e accep ed by he plan op e a o s. Fi s , he un-
ing p o cedu e mus b e simple enough, so ha a
gpc
can
b e uned as easily as a
pid
, and second, he con olle mus
b e obus , ha is, i mus b eha ewell in he p esence o
he ine i able mo delling e o s.
The applica ion shown he e combines he p owe o p e-
dic i e con ol wi h he simplici y and ease o use o he
adi ional con olle s commonly ound in indus y. The
simplici yisachie ed by using a me ho d de elop ed by he
au ho s which can b e used wi h mos p o cesses in indus y
1. Due o his simplici yin he compu a ional equi e-
men s, wo
gpc
algo i hms can be used as cascade con-
olle s. In o de o imp o e he obus ness o he closed
&VSPQFBO$POUSPM$POGFSFODF&$$
"VHVTUo4FQUFNCFS,BSMTSVIF(FSNBOZ
*4#/ 
lo op sys em, he
T
p olynomial has b een added o he o -
mula ion.
The pap e is o ganised as ollows: Sec ion 2 desc ib es
he applica ion: he sludge densi ycon ol in a suga ac-
o y. The adap a ion o he s anda d
gpc
algo i hm o a
wide class o indus ial p o cesses in o de o educe calcu-
la ions and imp o e obus ness is p esen ed in sec ion 3
sec ion 4 is dedica ed o he ob en ion o he plan mo del,
sec ion 5 shows some op e a ing esul s and nally he con-
clusions o he wo k a e p esen ed in sec ion 6.
2 P o cess Desc ip ion
The ac o y p o duces suga om suga -b ee by means o
a se ies o p o cesses such as p ecipi a ion, c is aliza ion,
e c. The ac o y handles a la ge quan i yo wa e  wa e
is mainly necessa y o p o ducing s eam in he b oile s,
o he diusion p o cess and o washing he suga -b ee .
The wa e is no ac ually consumed so al hough used in
a ious p o cesses i is eco e able. The ob jec i eis ha
he ac o y should b e comple ely sel -sucien wi h ega d
o wa e consump ion.
One o he p o cesses which consumes mos wa e is
washing he b ee . Because i is a o o plan
g owing b e-
low g ound i always a i es a he ac o y co e ed in soil.
Thus he  s p o cess necessa y o he bee is o wash
i . The aw ma e ial is washed using clean wa e o elim-
ina e any emaining soil which logically mus no en e
in o he suga p o ducing p o cess. This op e a ion esul s
in la ge amoun s o di y wa e sludge b eing p o duced
whichmus b e ecycled.
The eco e y o clean wa e om his sludge is achie ed
by using he p o cess shown in gu e 1. A sepa a ing ank
is used whe e sedimen a ion by g a i y akes place, he
wa e s ays on he su ace and he sludge sinks o he
b o om. This sepa a ing ank is an op en con aine wi h a
diame e o 40 me e s and an a e age dep h o 5 me e s.
I is  ed wi h a blade which e ol es a 0.05 pm and
which ejec s he hicke emains in o a 35 m
3
homogenize
cylinde om which i is pump ed in o he cen i uge which
e ol ing a g ea sp eed sepa a es he wa e om he soil
by cen i uga ion. The wa e hus ob ained e u ns o
he sepa a ing ank om whe e he usable wa e is again
d awn ou .
The cen i uge wo ks co ec ly o sludge ows o be-
ween 14 and 22 m
3
h and a densi y which should be
be ween 1100 and 1200 gl. This densi y is he basic a i-
able o b e con olled as i mus emain wi hin his ange
o ensu e he co ec wo king o all he ins alla ion. This
densi y dep ends up on he wa e ecycled om he cen-
i uge o he sepa a ing ank and he e o e on he sludge
ow ha ci cula es om he cylinde o he cen i uge.
I is dicul o mo del he ela ionship b e ween he eci -
cula ion o
w and he densi y, b ecause a ious ac o s come
in o play and he e is no clea ela ionship b e ween said
a iables. Howe e , i do es seem clea ha an inc ease
Soil
Flow con ol
Bu e
FT
Decan e
DT
cleaning p ocess
Wa e om he
Cen i uge
Sludge
Densi y
Figu e 1: Wa e Reco e y P o cess in a Suga Rene y
in he ow causes mo e wa e o b e eci cula ed and hus
he densi y o he sludge o be dec eased a dec ease o
densi y has he opp osi e eec . An exhaus i e mo delling
is a he complica ed so a s o de sys em wi h delay
will b e used o y o app oxima e he esp onse.
An added p oblem is ha he ow measu emen s a e
no e y eliable due o he pa icles in susp ension. Fu -
he mo e he e a e con inuous blo ckages in he con ol
al e which cause b usque al e a ions in he ow. On he
o he hand, b ecause o he mo emen o he blades in he
sepa a ing ank which s i he mud ha will b e pump ed
owa ds he cen i uge, he densi y measu emen s a e no
uni o m b ecause hey keep alling like
lumps
o soil e e y-
ime he blade passes o e he d ain.
3 P ecompu ed GPC
This pap e uses a o mula ion o Gene alized P edic i e
Con ol 
gpc
 de elop ed by he au ho s, easy o imple-
men and une, ha is alid o he ma jo i y o indus ial
p o cesses 1, 2. The me ho d makes use o he ac ha
a gene alized p edic i e con olle esul s in a con ol law
ha can be desc ib ed wi h ew pa ame e s. The con olle
is alid o a wide class o p o cesses in indus y and a se
o simple unc ions ela ing he con olle pa ame e s o
he p o cess pa ame e s has b een ob ained. Wi h his se
o unc ions ei he a xed o a sel uning
gpc
can b e im-
plemen ed in a s aigh o wa d manne .
Mos p o cesses in indus y a e high o de sys ems ha
a e no sui able o con ol pu p oses, bu in gene al i is
p ossible o app oxima e he b eha iou o such high o de
p o cesses wi h a simplied mo del consis ing o a  s o -
de p o cess combined wi h a dead ime elemen 7. This
yp e o sys em is hen desc ib ed by he ollowing ans e
unc ion:
G

s
=
K
1+
s
e
,
s

d
1
whe e
K
is he p o cess s a ic gain,

is he ime cons an
o p ocess lag, and

d
is he dead ime o delay. This

mo del is widely used in indus y o desc ib e he dynamics
o many p o cesses, as shown by he p opula i y o he eac-
ion cu e me ho d and he op en lo op Ziegle -Nichols
pid
uning ules. Ob iously b e e app oxima ions could be
ob ained by using highe o de mo dels, bu his would e-
qui e iden ica ion packages which a e no no mally a ail-
able in indus y.
When he dead ime

d
is an in ege mul iple o he
sampling ime
T


d
=
dT
, he co esp onding disc e e
ans e unc ion o equa ion 1 has he o m:
G

z
,
1
=
bz
,
1
1
,
az
,
1
z
,
d
2
whe e disc e e pa ame e s
a
,
b
and
d
can easily be de-
i ed om he con inuous pa ame e s by disc e iza ion o
he con inuous ans e unc ion, esul ing in he ollowing
exp essions:
a
=
e
,
T

b
=
K
1
,
a

d
=

d
T
The e o e he
ca ima
mo del used o he p edic ion is:
A

z
,
1

y

=
B

z
,
1

u

,
1 +
C

z
,
1

4



whe e
C
is he noise p olynomial. I i is chosen equal o
one, he mo del esul s:
1 +
az
,
1

y

=
bz
,
1
u

,
d
+
1
4



The p edic ions along he ho izon om
+
d
+1 o
+
d
+
N
can be calcula ed by means o he ollowing
equa ion:
^
y

+
d
+
j
j
 = 1 +
a
^
y

+
d
+
j
,
1
j

,
a
^
y

+
d
+
j
,
2
j
+
b
4
u

+
j
,
1 3
In 1 he
gpc
algo i hm is de i ed o his kind o p o-
cesses, leading o he con ol s a egy shown in gu e 2.
The plan pa ame e s a e used o compu e he con olle
co ecien s 
l
y
1
,
l
y
2
,
l
1
 as desc ib ed in 1. These co-
ecien s a e p ecalcula ed as a unc ion o he sys em
pole 
a
and he con ol weigh ing ac o 

wi h ho i-
zons
N
1
=
d
+1,
N
2
=
d
+
N
,
N
u
=
N
,
N
= 15. No ice
ha he dep endence o hese co ecien s on pa ame e
b
can b e a oided i he con olle is designed conside ing he
plan oha e a uni a y s a ic gain. The alues ^
y

+
d
j
,
^
y

+
d
,
1
j
 a e ob ained by he use o he p edic ion
which basically consis s o a mo del o he plan whichis
p o jec ed owa ds he u u e wi h he alues o pas inpu s
and ou pu s and only equi es s aigh o wa d compu a-
ion. The con ol signal is di ided by he p ocess s a ic
gain in o de o ge a sys em wi h a uni a y s a ic gain
since he con olle co ecien s ha e b een calcula ed con-
side ing he sys em o ha e uni a y gain. The con ol law
is gi en by:
4
u

=
l
y
1
^
y

+
d
j
+
l
y
2
^
y

+
d
,
1
j
+
l
1


The con ol algo i hm educes o:
1 - a z
-1
b z
-1
-d
z
l
l
+
+
+
+
y
y
P edic o
z
-1
Δu
z
-1
Δu
k-1
k+d
k+d-1
k
y1
y2
k
u
k
y
k
l
1
Figu e 2: Con ol Scheme
1. Compu e
k
ji
as unc ions o he con ol
weigh ing ac o

.
2. Make
l
yi
=
k
1
i
+
k
2
i
^
a
k
3
i
,
^
a
o
i
=1

2and
l
1
=
,
l
y
1
,
l
y
2
3. Compu e ^
y

+
d
j
and ^
y

+
d
,
1
j
 using
equa ion 3 ecu si ely.
4. Compu e con ol signal
u

 wi h:
4
u

=
l
y
1
^
y

+
d
j
+
l
y
2
^
y

+
d
,
1
j
+
l
1


5. Di ide he con ol signal by he s a ic gain.
6. Go o s ep 2.
I can be seen ha he algo i hm is eally simple and can
b e easily included in any comme cial con ol sys em wi h-
ou complex calcula ion equi emen s. This algo i hm
has b een success ully es ed in some exp e imen al plan s.
Howe e , i has also been shown 2 ha al hough i is
a he obus o gain and ime cons an unce ain ies, i
has small obus ness o dead ime unce ain ies, ha a e
commonly ound in eal plan s. Tha is why he algo i hm
mus b e mo died o conside his ci cums ances, since he
p o cess o b e con olled p esen ha kind o unce ain y
as will b e seen la e .
The s abili y obus ness o
gpc
can b e imp o ed wi h
he use o an obse e polynomial, he so-called
T

z
,
1

p olynomial. In 4 a e o mula ion o he s anda d
gpc
algo i hm including his p olynomial can b e ound. In o -
de o do his, he
ca ima
mo del is exp essed in he o m:
A

z
,
1

y

=
B

z
,
1

u

,
1 +
T

z
,
1

4



Up o now he
T

z
,
1
 has b een conside ed equal o 1, de-
sc ibing he mos common dis u bances o as he colou -
ing p olynomial
C

z
,
1
. This p olynomial is e y dicul
o ob ain and in many cases i is conside ed as a design
pa ame e . In consequence he p edic ions will no b e op-
imal bu highe obus ness in he ace o unce ain ies
can b e achie ed, in a simila in e p e a ion as ha used

GPC2GPC1
P ocessPipes
-
-
Se poin
Densi y Flow
Se poin
Flow
Densi y
Figu e 3: Cascade con olle s
byLjung 9. This p olynomial can b e conside ed as a p e-
l e as well as an obse e . The eec i e use o obse e s
is known o play an essen ial ole in he obus ealiza ion
o p edic i econ olle s see 4 o he eec o p el e -
ing on obus ness and 14 o guidelines o he selec ion
o
T
.
The T p olynomial can b e easily added o he p op osed
o mula ion, compu ing he p edic ion wi h he alues o
inpu s and ou pu s l e ed by
T

z
,
1
. Then, he p edic o
wo ks wi h
y

=
y


T

z
,
1

and
u

=
u


T

z
,
1

. The ac ual
p edic ion o he con ol law is compu ed as ^
y

+
d
=
T

z
,
1
^
y

+
d
.
The co ec choice o he
T
p olynomial is a p oblem ha
has no comple ely b een sol ed, al hough i s eec on he
obus ness o he closed loop sys em has b een analysed in
se e al pap e s 6, 4, 13, 15. In his applica ion,
T
is made equal o
A

z
,
1
1
,
z
,
1
, b eing

a alue close
o he sys em p ole, as sugges ed in 15.
4Mo del A ainmen
As has b een explained, i is p ossible o con ol he densi y
wi h he eci cula ion ow. As his ow sue s equen
dis u bances due o he p esence o discon inui ies in he
uid comp osi ion, i is necessa y o keep i con olled wi h
ano he egula o . The con ol s a egy is, he e o e, go-
ing o b e a cascade con ol, he densi ycon ol ac ing on
he emo e se p oin o he local con olle o he o
w o he
cen i uge sla econ olle , see gu e 3. This lo cal con-
ol can b e ca ied ou using ei he a
pi
con olle o a
gpc
indis inc i ely. The dynamics o his lo op a simple ow
lo op do es no jus i y i sel he use o a
gpc
ins ead o a
pi
,
bu as he
gpc
ou ine is al eady ins alled in he con ol
sys em and he compu a ion ime is simila in b o h cases,
hisloopwas also used as a es b ed o he con olle . Be-
sides, he uning o he
gpc
is done au oma ically e e y
ime he sys em pole is up da ed.
A ea men o he densi y me e signal is needed o
a ain he mo del. P io l e ing is necessa y o elimina e
he noises and he eec o he blade s okes in he sepa-
a ing ank, in o de o b e able o wo k wi h an
eec i e
alue indica i e o he e olu ion o he ac ual densi y.
Following an ini ial analysis i is obse ed ha he cha -
ac e is ic ime o he sys em esp onse is in he o de o
hou s. In o de o ob ain a mo del, a s ep is p o oked a
he inpu , whichis heow se poin , om 18 o 16 m
3
h.
I is p ossible o ob ain om he da a a dead ime o 2.6
hou s, a ime cons an o 1 hou and a gain o -25
g=l
m
3
=h
.
5 Op e a ing Resul s
The con ol was s a ed up using l e ing wi h he T-
p olynomial. This p olynomial is made equal o
A

z
,
1
1
,
z
,
1
, wi h

= 0
:
9. The con ol eo

was chosen
equal o 0.1. The lo cal owcon olle had p e iously b een
adjus ed by he s ep esp onse p o cedu e ob aining
K
=
2
:
5,

=4s and

d
=10
s
no ice he clea die ence in
he dynamics b e ween he ou e and inne lo ops.
Fo op e a i e easons i was necessa y o limi he ow
se p oin be ween 14 and 22 m
3
h, al hough i was no p os-
sible o use a p edic i e s a egy wi h cons ain s b ecause
o compu a ional limi a ions.
Wi h he nominal mo del chosen o he densi yloopand
wi h a sampling ime o 12 minu es, he disc e e pa ame-
e s o he p o cess mo del a e gi en b
y:
a
=0
:
8187
b
=
,
0
:
4531
d
=13
The con olle co ecien s can b e compu ed see 1 cal-
cula ing
k
ji


 and hen
l
y
1
,
l
y
2
and
l
1
as unc ions o he
sys em p ole in he o m:
l
yi
=
k
1
i
+
k
2
i
a
k
3
i
,
a
i
=1

2
l
=
,
l
y
1
,
l
y
2
k
11
=
,
exp0
:
3598
,
0
:
9127

+0
:
3165

2

k
21
=
,
exp0
:
0875
,
1
:
2309

+0
:
5086

2

k
31
= 1
:
05
k
12
= exp
,
1
:
7383
,
0
:
40403


k
22
=exp
,
0
:
32157
,
0
:
81926

+0
:
3109

2

k
32
= 1
:
045
As he sys em p ole is in 0
:
8187, i a alue o

equal o
0.1 is chosen, he con olle co ecien s a e
l
y
1
=
,
4
:
7454
l
y
2
=2
:
5930
l
1
=2
:
1524
A simila p o cedu e is used o he ob en ion o he
as
owcon olle , wi h alues:
l
y
1
=
,
3
:
2448
l
y
2
=2
:
1294
l
1
=1
:
1154
The con ol sys em op e a ion is shown in he ollowing
diag ams. No e he ime scale, whe e he slowness in he
densi ye olu ion can b e seen, wo hou s b eing necessa y
in o de o ca y ou a change in he se p oin see gu e 4.
No ice ha he ou pu shows an oscilla o y signal added
o he mean alue. These oscilla ions a e densi ychanges
due o he eec o he blades which s i he mud in he
decan e , so he densi y measu emen s show his esp onse
b ecause hey keep alling like lumps o soil e e y ime he
blade passes o e he d ain.

0 20 40 60 80 100 120 140 160 180 200
Time (minu es)
1090
1095
1100
1105
1110
1115
1120
1125
1130
Densi y (g/l)
Figu e 4: Se p oin change
0 50 100 150 200 250 300 350 400 450 500
Time (minu es)
1050
1060
1070
1080
1090
1100
1110
Densi y (g/l)
Figu e 5: Dis u bance ejec ion in he densi yloop
No e he imp o ance o in o ducing he T-p olynomial,
gi en ha he dead ime ob ained exp e imen ally is no
e y p ecise and ha also o he es s showed ha i s alue
a ied subs an ially om one si ua ion o ano he . As is
known,
gpc
is no e y obus when aced wi h dead ime
mo delling e o s and he T-p olynomial should b e used in
o de o inc ease he obus ness.
The con ol ob jec i e is o main ain he app op ia e
condi ions o he cen i uge o wo k co ec ly. This e-
qui es o main ain he densi y a a cons an alue. The
main densi y lo op ob jec i e is o ejec dis u bances. Fig-
u e 5 show he beha iou o he con olle du ing eigh
hou s keeping he densi y a he igh alue o 1090 gl.
The b eha iou o he inne lo op  he owcon ol lo op
is d as ically die en om he densi yloop. The dynam-
ics a e as e , wi h apid changes in he o
w alue. Figu e
6shows he b eha iou o his loop when aced o se poin
changes p o oked by he mas e con olle . I can b e seen
ha he signal is e y noisy due o he dicul y o measu -
ing a he e ogeneous ow in a zone wi h la ge ib a ions
due o he p oximi y o he cen i uge, bu i s means
alue ollows he e e ence. No ice ha he ou e lo op is
op en du ing his es in o de o show he beha iou o
he inne lo op.
The con olle in e ace allows he p o cess pa ame e s
o b e changed on line. The mo dels a e uned by he op e -
0 20406080100
Time (minu es)
5.0
7.0
9.0
11.0
13.0
15.0
17.0
19.0
21.0
23.0
25.0
Flow (m3/h)
Figu e 6: Se p oin ollowing in he owloop
a o as so on as a disc epancy b e ween he ac ual and he
p edic ed ou pu s  ha app ea on he sc een is de ec ed.
I should b e emphasised ha his con olle wo ked sa -
is ac o ily and wi hou in e up ion un il he end o he
yea 's campaign, b eing handled wi hou dicul yby he
plan op e a o s. The esul s ob ained using his con olle
in e ms o e o a iance imp o ed he ones ob ained in
he las yea 's campaign, when he p ocess was con olled
by an op e a o , since hey did no da e o une a
pid
b ecause o he long dead ime.
6Conclusions
An applica ion o a Cascade Gene alized P edic i e Con-
olle 
gpc
 o he sludge densi y con ol in a suga ac-
o y has b een p esen ed. The con ol lawwas ex emely
simple o compu e and he uning was s aigh o wa d b e-
cause a me ho d o compu e
gpc
p e iously de elop ed by
he au ho s whichis e y simple o implemen and une
was used. The o iginal
gpc
algo i hm was imp o ed by
he use o he T p olynomial o inc eases he s abili
y o-
bus ness, since mo del unce ain ies app ea ed when wo k-
ing a die en op e a ing p oin s. The con olle has b een
success ully wo king in he ac o y, showing ago o d be-
ha iou .
The applica ion shown he e combines he p owe o p e-
dic i e con ol wi h he simplici y and ease o use o he
adi ional con olle s commonly ound in indus y, show-
ing howa
gpc
can b e easily used in clasical con ol s uc-
u es like cascade con ol in he same wayas
pid
s.
7 Acknowledgmen s
The au ho s would like o acknowledge Juan He mida
om
p ocisa
by his in e es and supp o in he de elop-
men o he con olle and he people om Eb o Ag icolas
by he acili ies o es ing he con olle in he plan . The
nancial supp o o
cicy
by p o jec s TAP 96-884 y TAP
95-370 is g a e ully app ecia ed.


Re e ences
1 C. Bo dons and E.F. Camacho. Gene alized P edic-
i eCon olle o a Wide Class o Indus ial P o cess.
IEEE T ansac ion on Con ol Sys ems Technology
,
63:372387, 1998.
2 E.F. Camacho and C. Bo dons.
Model P edic i e
Con ol in he P ocess Indus y
. Sp inge -Ve lag,
1995.
3 D. W. Cla ke. Applica ion o Gene alized P edic i e
Con ol o Indus ial P o cesses.
IEEE Con ol Sys-
ems Magazine
, 122:4955, 1988.
4 D.W. Cla keand C. Moh adi. P op e ies o Gene al-
ized P edic i eCon ol.
Au oma ica
, 256:859875,
1989.
5 D.W. Cla ke, C. Moh adi, and P.S. Tus. Gene al-
ized P edic i eCon ol - Pa I. The Basic Algo i hm.
Au oma ica
, 232:137148, 1987.
6 D.W. Cla ke, C. Moh adi, and P.S. Tus. Gene -
alized P edic i eCon ol - Pa II. Ex ensions and
In e p e a ions.
Au oma ica
, 232:149160, 1987.
7 P.B. Deshpande and R.H. Ash.
Elemen s o Com-
pu e P ocess Con ol
. ISA, 1981.
8 D.A. Linke s and M. Mah on .
Ad ances in Model-
BasedP edic i e Con ol
, chap e Gene alized P e-
dic i e Con ol in Clinical Anaes hesia. Ox o d Uni-
e si y P ess, 1994.
9 L. Ljung.
Sys em Iden ica ion. Theo y o he use
.
P en ice-Hall, 1987.
10 S.J. Qin and T.A. Badgwell. "An O e iew o Indus-
ial Mo del P edic i eCon ol Technology" in Chem-
ical P o cess Con ol: Assessmen and New Di ec ions
o Resea ch. In
AIChE Symposium Se ies 316, 93.
Je ey C. Kan o , Ca los E. Ga cia and B iceCa -
nahan Eds. 232-256
, 1997.
11 J. Richale . Indus ial Applica ions o Mo del Based
P edic i e Con ol.
Au oma ica
, 295:12511274,
1993.
12 J. Richale , A. Raul , J.L. Tes ud, and J. Papon.
Mo del P edic i e Heu is ic Con ol: Applica ion o
Indus ial P o cesses.
Au oma ica
, 142:413428,
1978.
13 B.D. Robinson and D.W. Cla ke. Robus ness eec s
o a p el e in Gene alized P edic i e Con ol.
P o-
ceedings IEE, Pa D
, 138:28, 1991.
14 T.W. Yoon and D.W. Cla ke.
Ad ances in Model-
Based P edic i e Con ol
, chap e Towa ds Robus
Adap i
e P edic i eCon ol, pages 402414. Ox o d
Uni e si y P ess, 1994.
15 T.W. Yoon and D.W. Cla ke. Obse e Design in
Receding-Ho izon Con ol.
In e na ional Jou nal o
Con ol
, 2:151171, 1995.
