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H:)
APPLICATION
OF A SELF-TUNING
REGULATOR
TO
A SOLAR POWER
PLANT
F.
R. Rubio*,
E.
F.
Camacho* and R. Ca mona**
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~bs ac~.
This
pape
p esen s
an
applica i
on
o
a
sel - uning
egula o
o
he
dis ibu ed
colle
c
o
ield
o
a s o
la
powe
plan
.
The
dis ibu ed
collec o
ield
consis s
o
a
se ies
o
pa abolic
mi o s
ha
e le
c
sola
adia i
on
on
a
pipe
whe e
o
il
ge s
hea ed
while
ci
c
ula ing.
The
p
u p
o
se
o
he
egula o
i s
o
main ain
he
o
il
o
u le
empe a u e
as
nea
as
possible
o a
desi ed
le el.
This
is
a
cco
mpli
s
hed
by
a ying
h
e
l
ow o
h
e
luid
h
o
ugh
h
e
ield.
The
ield
exhibi
s a
a iable
delay
ime
ha
depends
on
he
co
n ol
a iable
(
low
) .
The
an
s
e
un
c
i
on o
he
p
oc
ess
a ies
wi h
a
c o
s
su
c h a s
i adian
c e
le
el
,
mi
o
s
e lec an
c e
and
o
il
inle
empe a
u e.
The
sel
-
u
ning
egula
o u s e s
an
iden i
i e
wi h
a
a ia
ble
o
g
e
ing
ac
o
and
an
adap i e
PI
c
on
o
lle
.
The
pape
also
des
c
ibes
he
heu i
s
i
c
us
e d
o
make
he
e
gula o
wo
k
a n
he
expe iences
o
b ain
e d
a
h
e
SSPS
so
la
plan
o
Alme ia
(Spain
).
~e
y
w
o
ds
.
Adap i e
co
n
o
l;
Digi al
co
n ol;
Sel -adjus ing
sys ems.
INTRODUCTION
A l o o wo
k
s
showing
he
ad an ages
o
adap i e
co
n olle s
(As om
1983,
Landau
1974
)
ha e
appea ed
in
he
Li e a u e
since
sel - uning
egula
o
s
we e
i s
in
o
du
c
ed
by
As
om
and
Wi enma k
( 1
973)
. M
os
o
hese
wo k
s
a e
heo e ical
and
in
spi e
o
he
a
c
ha
adap i e
c o
n
o l
has
sh
own
ad an ages
when
applied
o a
a ie y
o
p
oc
esses
( Bo
i
s s on 1
97
6,
Bu c
hh
o
l
1979,
K
al
l
s om
197
9 ,
Na end a
198
0 .
Dum
o
n
198
2 ,
Rubi
o
1982,
e c.)
i
is
no
ye
widely
a
cc
ep ed
a
indus ial
le el.
Thi
s
pape
p esen
s
an
applica i
on o
an
adap i e
egula
o
o
c o
n
o l
he
o
u le
empe a u e
o
he
ACUREX
dis ibu ed
co
llec o
ield
o
he
SSPS
plan
o
Tabe nas.
The
obje
c
i e
o
he
con ol
sys em
in
he
dis ibu ed
c o
llec
o
ield
is
o
main ain
he
ou le
oil
empe a u e
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
o
he
ime
o
day
mi o s
e lec i i y
and
inle
oil
empe a u e.
The
dis ibu ed
collec o s
ields
is
a
nonlinea
sys em
which
can
be
app oxima ed
by
a
linea
sys em
when
conside ing
small
dis u bances.
In
he
design
o
any
egula o
he
ope a ing
poin
o
he
plan
mus
be
bo n
in
mind.
Howe e
in
a
sola
ene gy
plan
he
ope a ing
poin
a ies
acco ding
o
he
ime
o
day
o
dis u bances
caused
by
clouds,
and
2
6l
c
on
o
l;
Ene gy
con
o
l;
Po
we
he e
o
e i i s n o po s s
ibl
e o
design
a
ixed
e
g
ula
o
ull
y g
ua an
e
ed
o
wo
k.
Bec
au
s e
o
his
sel
-
unin
g
egula
o
seem
s o
be
a g
oo
d
solu
i o n o
his
p
o
blem.
T
he
p
la
n
o
be
con
o
lled
i s
de
s c
ibed
in
s e
c io
n 2 o
hi
s
a
i c
le
.
Se
c
i
on 3
gi es
a
de
sc
ip i
on o
he
c o
n
o l
alg
o
i hm
used,
se
c
i
on
4
co
mm
e
n s
up
on
he
esul s
ob
a
i
ne
d
and
s e c
i
on S
is
ded
ic
a
e d
o
he
con
c
lus
i o
ns.
A DESC
RIPTI
ON OF THE P
LANT
The
s
ys em
o
whi
c h
h
e
sel - uning
co
n
o l
e e ed
o
in
hi
s
a i
c
le
has
been
applied
is
ha
o med
by
he
dis
ibu ed
co
llec
o s
ield
(ACUREX ) o
he
so
l a
en
e
gy
plan
o
Tabe nas.
The
dis ib
u
ed
c
olle
c
o s
ield
consis s
mainly
o a
pipe
line
h ough
which
o
il
is
l
o
wing
and
on o
which
he
s
uns
a
y s
a e
con
c
en a ed
by
means
o
pa ab
o
lic
mi
o
s
in
o
de
o
hea
h
e o
il.
I
co
nsis s
o
480
modules
a anged
in
wen y
lines
which
o m
en
pa allel
l
oo
ps
as
shown
in
ig.
1.
The
ield
is
also
p
o
ided
a
sun
seeking
mechanism
which
causes
he
mi o s
o
e
o
l e
a ound
an
axis
pa allel
o
ha
o
he
pipe
line.
On
pa
s
sing
h
o
ugh
he
ield
he
o
il
is
hea ed
and
hen
in oduced
in o
a
s o age
ank
o
be
used
o
he
gene a ion
o
elec ical
ene gy
.
The
cold
inle
oil
o
262
F.
R.
Rubio, E. F.
Camacho
and
R.
Ca mona
COLLECTOR
FIELDS
STORAGE
SYSTEM
POWER
CONVERSION
SYSTEM
ACUREX
FI
ELD
FI LD
PuMPS
BuFFER
T
AlJKS
FCV
I
I
I
I
I
I
I
STEAM
TuRBINE
C
DO:"
ING
TowER
""'--:::J---"
I
I
FIG.
SIMPLIFIED
DCS
PROCESS
FLOW
DIAGRAM
he
ield
is
ex ac ed
om
he
bo om
o
he
s o age
ank.
The
sys em
is
p o ided
wi h
a
h ee
way
al e
which
allows
he
oil
o
be
ecycled
in
he
ield
un il
he
i s
ou le
empe a u e
is
adequa e
o
en e
in:o
:he
s o age
ank.
A
mo e
de ailed
desc Ip Ion
o
he
ield
can
be
ound
in
(Kal
1982).
The
empe a u e
in
he
ield
can
be
gi en
by
he
ollowing
equa ions:
whe e
he
subindex
m
e e s
o
he
me al
and
o
he
luid
and:
oil
densi y
ield
capaci y
ans e sal
a ea
ou le
empe a u e
i adiance
op ical
e iciency
o e all
he mal
loss
coe icien
mi o s
wid h
coe icien
ansmission
o
me al
luid
ex e io
diame e
o
he
pipe
line
inne
diame e
o
he
pipe
line
oil
low
a e
These
equa ions
a e
only
applicable
o
he
ac i e
zones
o
he
ield.
Tha
is,
hose
pa s
o
he
pipe
line
whe e
sola
adia ions
a e
collec ed.
Pa s
o
he
ield,
passi e
zones,
exis s
whe e
i
is
no
possible
o
collec
sola
ene gy
due
o
geome ical
condi ions
as
is
he
case
o
he
join s
be ween
he
modules.
These
zones
cons i u e
a
conside able
pa
o
he
ield
and
hey
a e
cha ac e ized
by
ha ing
nil
i adiance
and
di e en
loss
cons an s.
The
abo e
equa ions
we e
used
o
simUla e
he
sys em
in
a
compu e
di iding
one
o
he
loops
in o
a
100
pieces
and
using
a
model
o
concen a ed
pa ame e s
o
each
piece.
The
model
was
con as ed
agains
he
eal
da a
ob ained
om
he
ield.
The
pa ame e
o
he
model
we e
adjus ed
so
ha
i
ep oduced
he
beha iou
o
he
sys em
(Camacho
1977).
The
ou le
empe a u e
o
he
six h
loop
is
used
o
con ol
he
ield
as
i
ac s
as
he
pilo
loop,
in
his
way
he
o al
ou le
empe a u e
is
main ained
wi hin
an
accep able
ange.
THE
CONTROL
ALGORITHM
Because
o
he
a iabili y
o
cha ac e is ics
as
has
been
men ioned
an
adap i e
con ol
has
been
chosen.
he
plan s
p e iously
algo i hm
The
adap i e
con ol
s uc u e
used
co esponds
o
ha
o
a
sel - uning
egula o
(STR)
( ig.
2),
which,
in
b ie ,
consis s
in
calcula ing
he
pa ame e s
o
he
egula o
supposing
ha
he
ields
pa ame e s
a e
hose
gi en
by
means
o
an
iden i ica ion
algo i hm.
In
his
case
ecu si e
leas
squa e
a
iden i ica ion
algo i hm
has
been
used.
In
each
sampling
pe iod
he
sel - uning
egula o
consis s
o
he
ollowing
s eps:
1)
An
es ima ion
o
he
pa ame e s
o
a
linea
model
by
measu ing
he
inle
and
ou le
alues
o
he
p ocess.
2)
The
adjus men
o
he
pa ame e s
o
he
egula o .
3)
The
calcula ion
o
he
con ol
signal.
4)
The
supe ision
o
he
co ec
wo king
o
he
con ol.
Applica ion
o
a
Sel - uning
Regula o
263
The
egula o
is
composed
o
wo
pa s,
( ig.3),
a
P.I.
in
he
eedback
loop
and
a
eed o wa d
egula o
calcula ed
using
he
a ailable
in o ma ion
on
he
ield.
We
p esume
ha
he
sys em
can
be
modelled
as
a
s able
p ocess,
in a ian
in
ime
and
ha
can
be
linealized
wi h
jus
one
inpu
and
one
ou pu ,
so
ha
i
can
be
desc ibed
by
he
ollowing
linea
di e ence
equa ion:
y(k)
+ a 1
y(k-l)
+
.•..
+
an
y(k-n)
=
bl
u(k-d-l)
+ b Z
u(k-d-Z)
+ bn
u(k-d-n)
+ (k)
and
also
by
he
ec o ial
o m:
y(k)
=
xT(k)
p +
(k)
whe e
(-y(k-l),-y(k-Z)
..
-y(k-n)
u(k-d-l),u(k-d-Z)
..
u(k-d-n»
pT
=
(a
1 '
aZ
'
u(k)
y(l<.)
U(k)
and
U(k)
Uoo
Y(k)
-
Y e
Y(k)
a e
he
inpu
and
ou pu
alues
o
he
sys em
a
he
ins an
k,
Uoo
is
he
a e age
alue
o
he
inpu
signal,
Yoo
is
he
alue
o
he
e e ence
and
(k)
is
a
noise
independen
and
The
z
ans e
be
w i en
as:
y(z)
whe e,
A(z-l)
1 + a1
B(z-l)
b1
The
i s
signal
s a is ically
s a iona y
o
ze o
mean.
unc ion
o
his
sys em
can
z-d
u(z)
+
-1
+ aZ
-2
z z
-1
+ bZ
-2
z z
quo ien
--------
(z)
A(z-l)
+ + a
-n
n z
+ +
bn
z-n
B(z-I)/A(z-l)
ep esen s
hI
model
o
he
ield,
and
he
second
l/A(z-)
ep esen s
he
model
o
he
dis u bances.
Feed o wa d
Con ol.
In
a
concen a ed
ep esen a ion
o
he
plan
he
in e nal
ene gy
a ia ion
o
he
ield
can
be
gi en
by:
C
dT
d
N o
Fig.
2
Sel - uning
egula o
FIElD
Fig.
3
Basic
con ol
layou .
In
he
pe manen
egime
we
ha e
ha :
p Cp (
T
-
Ti
)
This
las
equa ion
can
be
app oxima ed
as:
whe e,
Re e ence
empe a u e.
Inle
empe a u e.
Re lec ance.
I adiance.
This
equa ion
gi es
he
low
as
a
unc ion
o
he
e e ence
empe a u e,
inle
empe a u e,
and
he
i adiance.
The
cons an s
Kl
and
KZ'
ha e
been
de e mined
expe imen ally,
ha ing
he
alues
o
K1
=
0.93
and
KZ
=
155
(Ca mona,
1983).
Feedback
con ol
Using
a
closed
loop
egula o
is
necessa y
o
compensa e
o
any
e o
which
may
be
p oduced
in
he
low
calcula ion
by
he
eed o wa d
con olle .
Gi en
ha
his
low
is
a
good
es ima ion
o
he
pe manen
egime
low,
he
alue
o
he
con ol
signal
becomes
sa u ed
a
+
ZO%
o
he
open
loop
alue,
wi h
his,
g ea e
s abili y
is
ob ained
in
he
ansien s,
as
he
egula ion
band
is
educed.
The
plan
unde
conside a ion
p esen s
a
long
delay
(be ween
2
and
8
minu es)
ha
a ies
wi h
he
inle
low.
Fo
his
ype
o
sys em
whe e
he
delay
is
much
g ea e
han
he
o de
o
he
sys em,
he
con olle
desc ibed
below
can
be
used
(Ise mann,
1981).
Supposing
ha
he
plan
is
modelled
using
he
equa ion
y(k)
= b
u(k-d),
whe e
d
is
he
delay
in
sampling
pe iods
and
b
he
sys em
gain,
he
minimum
se ling
ime
con olle
can
be
exp essed
by:
u
(k)
u(k-d)
+
elk)
/ b
(1)
I
ins ead
o
di ec ly
using
his
con olle
we
app oxima e
a
P.I.
egula o
so
ha
i
has
he
same
beha iou ,
we
ob ain:
u(k)
=
u(k-I)
+
qo
elk)
+
qi
e(k-l)
whe e
/ ( 2 b
(2
)
qo
(d
Z)
/ d
264
F. R.
Rubio
,
E.
F.
Cam<lcho
and
R.
Cannona
I
can
be
shown
ha
his
egula o
is
less
sensi i e
o
he
e o
in
he
accu acy
o
he
delay
(Ise mann,
1981),
and
he e o e
i
is
mo e
ad isable
o
use
i
a he
han
he
con olle
(1),
gi en
he
cha ac e is ics
o
he
p ocess.
The e o e
a
P.I.
has
been
used
in
he
eedback
loop.
I
should
also
be
emembe ed
ha
when
an
e o
occu s
in
he
de e mina ion
o
he
delay
i
is
be e
o
conside
i
as
g ea e
han
he
es ima ed,
in
o de
o
ensu e
he
s abili y.
The
pa ame e s
iden i ie
is
a
e y
impo an
pa
o
he
sel - uning
con olle s.
I
should
be
ecu si e,
as
i
mus
wo k
in
eal
ime
wi h
he
p ocess
and
he e o e
i
will
a
g ea ly
in luence
he
minimum
sampling
ime
we
can
ob ain
o
he
con ol
sys em.
In
he
same
way,
he
s abili y
o
he
sys em
depends
la gely
on
he
es ima o
con e gence.
The e
a e
a ious
ypes
o
iden i ie s
which
a e
deal
wi h
in
he
ela i e
li e a u e.
Gene ally,
he
mos
used
me hods
is
he
ecu si e
leas
squa es
a e,
because
o
i s
simplici y
and
i s
good
con e gence
cha a
c
e is ics.
The
algo i hm
is
pe o med
by
he
ollowing
s eps:
1.
§elec
he
ini ial
alues
o
P(k)
and
p(k).
2.
Read
he
new
alues
o
y(k+1)
and
u(k+1).
3.
Calcula e
he
a
p io i
e o :
e(k+1)
=
y(k+1)
-
XT(k+1
) P (k )
4.
Calcula e
exp ession:
L(k+l)
L(k+1)
gi en
P(k)
X(k+1)
by
c(k)
+ XT
(k+1)
P(k)
X(k+1)
he
5.
Calcula e
he
new
pa ame e
es ima ed
gi en
by:
P(k+1)
=
P(k)
+
L(k+1)
e(k+1)
6.
Ac ualize
he
co a iance
ma ix.
P(k)
P(k+1)
(I
-
L(k+1)
XT
(k+1)
c(k)
7.
Calcula e
he
new
o ge ing
ac o
c(k+1).
c(k+1)
1-(1-X
T
(k+1)
L(k+1»
So
I
c(k+1)
< c
min
Then
c(k+1)
=
cmin
8.
Ac ualize
he
measu emen s
ec o
X(k+2).
9.
Make
k =
k+1
and
e u n
o
s ep
2.
Sampling
an~
delay
ime
The
sampling
ime
used
has
been
se
o
en
seconds.
This
ime
is
easonable
in
espec
o
he
ime
cons an
o
he
sys em,
being
in
he
ange:
T95
:
Time
slgnal.
aken
T m :
Sampling
ime.
o
each
95%
o
he
The
pa ame e
(d)
in
he
model
unde
conside a ion
is
an
in ege
which
ep esen s
he
delay
o
he
sys em.
In
his
p ocess
i
is
a iable
wi h
he
low,
and
can
be
calcula ed
as
a
unc ion
o
he
physical
dimensions
o
he
plan
and
o
he
low,
esul ing
ha :
80
+
187.5
"
5.3
d
----------
-
--------
+
1.5
" T m
The
p e i
o
us
alues
o
he
con ol
signal
a e
s o ed
in
a
ec o ,
in
which
hey
shi .
Because
he
delay
is
a iable
he
i s
idea
was
o
shi
he
in o ma ion
wi hin
his
ec o
a
a
cons an
a e
and
o
ake
as
he
ou pu
he
componen
o
his
ec o
co esponding
o
he
delay.
This
me h
od
causes
p oblems
in
he
iden i ie .
To
a oid
his
p oblem
a
la ge
ec
o
in
which
he
inpu
en e
in
one
end,
and
g o
ou
o
he
o he
a ying
hei
shi ing
a e
ac
c
o ding
o
he
delay
was
used.
This
me hod
ep oduces
wha
eally
happens
in
he
sys em
because
an
elemen
o
luid
is
displaced
al
o
ng
he
ube
a
a
speed
whi
c h
a ies
acco ding
o
he
low
a
a
gi
en
me
men o
In
his
way
sa is ac
o
y
beha iou
o
he
iden i ie
has
been
ac
hie ed.
Gi en
he
ac
ha
he
plan
is
a
no
nlinea
sys em
and
ha
i
is
con inu
o
usly
being
iden i ied
as
a
linea
sys em,
he
pa ame e
o
he
linea
model
a y
wi h
ime.
In
o de
o
educe
he
memo y
o
he
iden i ie
we
use
a
a iable
o
ge ing
ac
o ( c )
(Fo escou
1981),
as
has
been
des
c
ibed
p e iously.
No ice
ha
o
c 1 we
ha e
he
leas
squa es
iden i ie
wi h
in ini e
memo y
and
he
ma ix
P(k)
dec eases
mono
o
nously
so
he
es ima o
gain
can
ea
c h
ze o.
As
he
s y
s em
mu
s o
llow
he
pa ame e
a ia i
o
ns
a
o ge ing
ac o
(c
< 1 )
mus
be
u
se
d.
On
he
o he
hand
i
he
wo king
poin
does
no
change,
he
p oduc
P ( k )
X(k
)
can
be
ze o
and
he e o e
P (
k+1
) =
P(k
)/c.
I
c <
1,
P ( k )
can
g ow
g ea ly,
making
he
iden i ie
e y
sensi i e
o
any
c
hange.
To
a oid
his
a
a iable
o
ge ing
ac o
is
used.
This
ac
o
is
made
o
equal
1
i
he
ace
o
P ( k )
is
g
ea e
han
a
ce ain
alue.
A
he
same
ime,
he
ace
o
P ( k )
is
no
allowed
o
go
below
a
p e ixed
alue
by
adding
a
ma ix
R
o
P(k+l).
Supe ision.
A
basic
equi emen
o
he
adap i e
con ol
algo i hm
o
be
s able
is
ha
he
es ima ed
pa ame e s
con e ge
on
ce ain
alues.
Ce ain
condi ions
a e
necessa y
in
o de
o
and
hese
dis u bances
gua an ee
his
con e gence,
depend
on
he
ype
o
and
whe he
he
inpu
is
pe sis en ly
exci ing.
A
g ea
imp o emen
in
he
beha iou
o
he
closed
loop
sys em
can
be
achie ed
in
many
cases
by
using
a
le el
o
supe ision
which
can
check
hings
such
as:
-
The
es ima ed
pa ame e s.
Applica ion
o
a
Sel - uning
Regula o
265
The
con ol
a iable.
The
e olu ion
o
he
iden i ie .
In
he
conc e e
case
o
plan
he
ollowing
s eps
he
sola
ene gy
a e
aken:
a)
Wi h
ega ds
o
he
plan
iden i ica ion
we
know
ha
he
sys em
gain
is
nega i e
and
in e io
o
a
ce ain
alue.
Because
o
his
he
iden i ied
gain
is
il e ed
be o e
being
conside ed
alid,
in
o de
o
a oid
a
mis aken
iden i ica ion.
This
can
be
p oduced
in
cases
whe e
he
i adiance
dec eases
suddenly.
The
iden i ie
wo ks
using
he
a ia ions
in
he
empe a u e
and
low
wi h
espec
o
he
alues
o
he
pe manen
egime.
These
alues
a e
gi en
by
he
e e ence
empe a u e
and
by
he
low
calcula ed
by
he
eed
o wa d
con olle .
b)
The
ace
o
he
co a iance
ma ix
o
he
iden i ie
is
con inuously
checked,
aking
he
s eps
conside ed
p e iously
c)
The
con ol
a iable
is
sa u a ed
a
+
20%
o
he
alue
o
he
low
calcula ed
by
he
eed o wa d
con olle .
Fu he mo e
a
cau ions
con ol
is
used
in
he
beginning
modi ying
he
exp ession
(2)
as
ollows:
qo
= 1 / ( 2 * b +
ace(P(k»
* b )
RESULTS.
Be o e
applying
he
egula o
o
he
p ocess
a
se ies
o
es s
we e
ca ied
ou
by
simula ion
in
o de
o
alida e
and
p oo
i s
use ullness.
These
es
we e
aimed
a
analysing
he
beha iou
o
he
egula o
when
aced
wi h
changes
in
e e ence
and
all
ypes
o
dis u bances.
Di e en
wo king
poin s
ha e
been
conside ed
and
he
sys em
has
been
subjec ed
o
small
changes
o
e e ence
and
small
dis u bances
as
well
as
sudden
dis u bances.
A
model
o
dis ibu ed
pa ame e s
has
been
used
o
simula e
he
p ocess,
which
has
been
alida ed
and
iden i ied
wi h
eal
da a
om
he
sola
ene gy
plan .
Fig.
4
shows
he
beha iou
o
he
egula o
when
aced
wi h
a
slow
a ia ion
o
he
i adiance,
keeping
he
empe a u e
e e ence
a
280
deg ees.
Fig.
5
shows
he
sys em
eac ion
o
e e ence
changes
o
be ween
280
and
290
deg ees
beha ing
well
a e
he
i s
e e ence
change,
which
belongs
o
he
i s
phase
o
adap ion.
300
QC
27oUOL-----------se--c-.------~-----------8--000
Figu e
4.
I adiance
changes
300
270~----------~~----------------~
o
sec.
8000
Figu e
5.
Se
p
ain
changes
300
sec.
8000
Fi
g
u e
6
Regula o s
comp.
250~----------~--~~---------------
o
sec.
3900
Figu e
7.
Se
poin
changes
Cloud
pe u ba ion
Fig.
6
shows
he
beha iou
o
he
sel
uning
egula o
and
o
a
ixed
egula o
when
he
i adiance
change
suddenly
and
andomly.
I
has
been
p o ed
ha
he
mean
squa e
e o
o
he
ou pu
in
he
case
o
he
sel
uning
egula o
is
hal
ha
o
he
co esponding
one
o
he
ixed
egula o .
Fig.
7
o
10
co espond
o
es s
done
in
he
SSPS
plan
o
Alme la.
Fig.
7
shows
he
ou le
oil
empe a u e
when
he
e e ence
is
changed
om
290
o
280
deg ees,
a
slow
a ia ion
in
he
i adiance
and
sha p
change
in
his
due
o
a
small
cloud
passing,
can
be
seen.
Fig.
8
co esponds
o
he
s a ing-up
phase
o
he
p ocess
and
egula o .
The
e e ence
empe a u e
was
se
a
280
deg ees.
The
e olu ion
o
he
iden i ied
pa ame e
b
can
be
seen
in
his
igu e.
No ice
ha
he
ou le
oil
empe a u e
has
a
small
o e shoo .

266 F.
R.
Rubio, E.
F.
Camacho
and
R C .
a mon
a
T. (·
e)
V(
lI
s)
:
:
-1
-2
-3
S a ing-up
p
hase
10
8
~
o
Fig.-~l~O-~S~::~~~~--~~~~L-I
?
e
pOin
changes
Applicalion
o
a Sel -LUning RegulaLO 267
Fig.
9
shows
he
esponse
o
he
plan
when
he
oil
inside
he
pipe
line
has
been
cool
down
by
ge ing
he
mi o s
ou
o
ocus.
I
can
be
seen
ha
he
ou le
oil
empe a u e
eaches
he
se
poin
(280
deg ees)
sa is ac o ily.
The
esponse
o
he
sys em
when
he
se
poin
is
changed
om
280
o
290
deg ees
and
he
i adiance
is
dec easing
slowly
can
be
seen
in
ig.
10.
CONCLUSIONS
An
adap i e
egula o
o
con ol
he
ield
o
collec o s
in
a
sola
ene gy
plan
is
p esen ed
in
his
pape .
This
egula o
has
been
success ully
ied
ou
unde
a ious
wo king
condi ions
in
he
ACUREX
ield
o
he
sola
ene gy
plan
SSPS
o
Alme ia.
In
he
same
way
o he
ypes
o
sel - uning
egula o s
a e
being
es ed,
one
o
which
being
he
design
o
a
egula o
using
he
pole
assignmen
me hod.
REFERENCIAS
As om,
K.J.
and
Wi enma k,
P.D.
(1973),
On
Sel - uning
Regula o s,
Au o~~~ica
Vol
9
pp
185-199.
As om,
K.J.
(1983),
Theo y
and
Applica ions
o
Adap i e
Con ol:
A
Su ey,
.Au. om_
a
i
ca
Vol
19-5
pp
471-486.
Bo isson,
U.
and
Syding,
R.
(1976),
Sel - uning
Con ol
o
an
O e
C ushe ,
Au oma ica
Vol
!~
pp
1-7.
Buchhol ,
F.
and
Sel - uning
Kummel,
Con ol
M.
(1979),
o
a
PH-Neu aliza ion
P ocess,
Au oma ica
Vol
!~
pp
665-671.
Camacho,
E.F.
(1977),
Iden i icacion
de
Sis emas
no
Lineales,
AJus e
y
Es imacion
de
pa Ame os,
~
_
~
_
~
doc o al.
ETSII
Uni .
de
Se illa.
Ca mona,
R.
y
Ma in,
J.
(1983),
Digi al
DCS
Con ols:
The
SSPS
Expe ience,
Fi s
Te m
_
___
.
Wo l<s
_
l}
_
o~.
Tabe nas
-
(Aiiiie ia)
-
~
-
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Dumon ,
G.A.
(1982),
Sel - unins
Con ol
o
a
Chip
Re ine
Mo o
Load,
Au oma ic~
Vol
18-3
pp
307-314.
Ise mann,
R.
(1981),
Q.iLl, al
Sys ems,
Sp inge -Ve lag
Heidelbe g
New
Yo k.
Con ol
Be lin
Kalls om,C.G.
e
a1.
(1979),
Adap i e
Au opi
lo s
o
Tanke s,
Au
oma
_
,,-.!
<e
_'!_
Vol
15
pp
241-254.
Kal ,
A.
e
al.
Collec o
Sys em
Repo ,
IEA-SSPS
(1982),
D
...!
.
l ib~
.!
,~c1
Plan
Cons uc ion
~~e~a ing
Agen
iFVLR,
Cologne,
FRG.
Landau,
1.D.
(1974),
A
Su ey
o
Model
Re e ence
Adap i e
Techniques
-
Theo y
and
Applica ions,
Au oma ica
Vol
lQ
pp
353-379.
Na end a,
K.S.
and
Monopoli,
R.V.
(1980),
Applica ions
o
Adal" i
_e
Con~ ol,
Academic
i -ess.
Rubio,
F.R.
e
al.
(1982),
S udies
o
he
Aplica ion
and
Adap i e
Con olle
o
Hid o u bine
Gene a o s,
P oc.
o
he
IFAC
So wa e
o
Compu e
Con ol
-
(5OCOCO),
Mad id.
- .