scieee Science in your language
[en] (orig)

Dependencia entre los parámetros de un sistema y de un modelo borroso del tipo Takagi-Sugeno

Abstract

En este trabajo se presenta una discusión sobre las propiedades de los parámetros de un Sistemas de Inferencia Borrosa del tipo Tagani-Sugeno (TS FIS por sus siglas en inglés) usado como modelo de un sistema. Dicha discusión exteinde trabajos anteriores donde se presentó al detalle TS FIS y se analizaron tres propiedades del mismo: la Zona de Validez del Modelo (MVZ) la posibilidad de obtener los parámetros del modelo por emdio de una linealización de un modelo matemático y la posibilidad de acoplamiento (o fusión) entre dos modelos borrosos. Aquí se hace una corta revisión de tales tópicos. Luego se analiza la diferencia entre adaptación de parámetros y ajustes de parámetros en los modleos. Finalmente se describe la dependencia entre los parámetros del sistema y los parámetros del modelo y se presenta un ejemplo para ilustrar las propiedades de los parámetros discutidas.

Read accessible full text

Dependencia entre los parámetros de un sistema y de un modelo borroso del tipo Takagi-Sugeno

Author: Peña, Miguel; Piñón, Sandra; Camacho, Eduardo F.
Publisher: CEA - Comité Español de Automática
Year: 2002
Source: https://idus.us.es/bitstreams/7fccf4de-5a17-452c-821d-ba527acb74df/download
'(3(1'(1&,$(175(/263$5È0(7526'(81
6,67(0$<'(8102'(/2%255262'(/7,32
7$.$*,68*(12
0LJXHO3HxD6DQGUD3LxyQ (GXDUGR)&DPDFKR
'SWRGH6LVWHPDV $XWRPiWLFD(VFXHOD6XSHULRUGH,QJHQLHURV8QLYHUVLGDGGH6HYLOOD
&DPLQRGHORV'HVFXEULPLHQWRVVQ6HYLOOD(VSDxD
PLJXHOS#FDUWXMDXVHV
5HVXPHQ
(Q HVWH WUDEDMR VH SUHVHQWD XQD GLVFXVLyQ VREUH ODV
SURSLHGDGHV GH ORV SDUiPHWURV GH XQ 6LVWHPDV GH
,QIHUHQFLD%RUURVDGHO7LSR7DNDJL6XJHQR76),6
SRUVXVVLJODVHQLQJOpVXVDGRFRPRPRGHORGHXQ
VLVWHPD'LFKDGLVFXVLyQH[WLHQGHWUDEDMRVDQWHULRUHV
GRQGH VH SUHVHQWy HQ GHWDOOH HO 76 ),6  VH
DQDOL]DURQ WUHV SURSLHGDGHV GHO PLVPR OD =RQD GH
9DOLGH]GHO0RGHOR09=ODSRVLELOLGDGGHREWHQHU
ORV SDUiPHWURV GHO PRGHOR SRU PHGLR GH XQD
OLQHDOL]DFLyQ GH XQ PRGHOR PDWHPiWLFR  OD
SRVLELOLGDG GH DFRSODPLHQWR R IXVLyQ HQWUH GRV
PRGHORVERUURVRV$TX VHKDFHXQDFRUWDUHYLVLyQGH
WDOHV WySLFRV /XHJR VH DQDOL]D OD GLIHUHQFLD HQWUH
DGDSWDFLyQGHSDUiPHWURV DMXVWHGHSDUiPHWURVHQ
ORV PRGHORV)LQDOPHQWHVHGHVFULEHODGHSHQGHQFLD
HQWUHORVSDUiPHWURVGHOVLVWHPD ORVSDUiPHWURVGHO
PRGHOR  VH SUHVHQWD XQ HMHPSOR SDUD LOXVWUDU ODV
SURSLHGDGHVGHORVSDUiPHWURVGLVFXWLGDV
 ,1752'8&&,Ï1
(O FRQFHSWR GH LGHQWLILFDFLyQ LPSOLFD HO XVR GH
PpWRGRV SDUD HVWDEOHFHU PRGHORV GH SURFHVRV
PDWHPiWLFRV R VLPEyOLFRV FRQ OD LQIRUPDFLyQ GHO
SURFHVR FRQWHQLGD HQ XQ FRQMXQWR GH GDWRV GH
HQWUDGDVDOLGD$TX VHKDDGRSWDGRFRPRPRGHORXQ
6LVWHPDGH,QIHUHQFLD%RUURVR),6GHOWLSR7DNDJL
6XJHQR 76 ),6 HVWDEOHFLGR HQ >@ (Q >@ VH
SUHVHQWDXQDGLVFXVLyQGHWDOODGDVREUHXQDSURSXHVWD
GHLGHQWLILFDFLyQFRQHVWHWLSRGHPRGHORV$GHPiV
HQ>@VHGHVDUUROODURQODVSURSLHGDGHVGHODV=RQDV
GH 9DOLGDFLyQ GHO 0RGHOR 09= OD SURSLHGDG GH
REWHQFLyQ GH XQ PRGHOR ERUURVR PHGLDQWH OD
OLQHDOL]DFLyQGHOPRGHORPDWHPiWLFR SRU~OWLPROD
SURSLHGDG GH HO DFRSODPLHQWR R IXVLyQ HQWUH GRV
PRGHORV ERUURVRV (Q >@ VH UHVXPH HVWD
DSUR[LPDFLyQ
(Q HO SUHVHQWH WUDEDMR VH GHVDUUROODQ GRV
FRQWULEXFLRQHV3ULPHURVHDQDOL]DODGLIHUHQFLDHQWUH
DGDSWDFLyQ GH SDUiPHWURV  DMXVWH GH SDUiPHWURV
6HJXQGR VH GHVFULEH OD GHSHQGHQFLD HQWUH HO
SDUiPHWURGHOVLVWHPD ORVSDUiPHWURVGHOPRGHOR
(OWUDEDMRHVWiRUJDQL]DGRFRPRVLJXH(QODVHFFLyQ
VHGDXQDGHVFULSFLyQGHOPRGHORERUURVRXWLOL]DGR
(QODVHFFLyQVHGHVFULEHQODVSURSLHGDGHVGHORV
PRGHORV 76 ),6 3ULPHUDPHQWH VH KDQ UHYLVDGR
SURSLHGDGHV D HVWXGLDGDV DQWHULRUPHQWH  VH
GHVDUUROODQ QXHYDV SURSLHGDGHV )LQDOPHQWH VH GDQ
DOJXQDVFRQFOXVLRQHVHQODVHFFLyQ
 02'(/2%25526287,/,=$'2
(QHVWHWUDEDMRVHKDXWLOL]DGRXQPRGHORERUURVRGHO
WLSR7DNDJL6XJHQR76),6SHURPRGLILFDGRFRQHO
REMHWR GH XWLOL]DU HQ HO DQWHFHGHQWH FRQMXQWRV
ERUURVRV PXOWLGLPHQVLRQDOHV (VWD SURSXHVWD VH
SUHVHQWy HQ >@ (VWH 76 ),6 SXHGH UHSUHVHQWDU R
PRGHODUXQDFODVHGHVLVWHPDVQROLQHDOHVHVWiWLFRV
GLQiPLFRV (Q GLFKR PRGHOR ODV UHJODV VRQ GH OD
IRUPD




[
[
%
[








HQWRQFHV
H

L
L
L
L
I
V
6L
5
GRQGH
>
@
0
[
[


[
VRQODV0HQWUDGDVGHOPRGHOR


[%

L
HV XQ FRQMXQWR ERUURVR GH GLPHQVLyQ 0H

L
HVODVDOLGDSDUDFDGDUHJODGHILQLGDSRUPHGLR
GHODIXQFLyQIL[(QJHQHUDOVHHOLJHXQDIXQFLyQ
OLQHDODI QGHODVHQWUDGDVGHODIRUPD
0
L
0
L
L
L
[
D
[
D
D
I



















[
GRQGH

L
M
D
VRQ HVFDODUHV /D VDOLGD GHO PRGHOR VH
REWLHQHPHGLDQWHXQSURPHGLRSHVDGRGHODVVDOLGDV
LQGLYLGXDOHV GH ODV UHJODV

L
 6RQ XWLOL]DGDV
IXQFLRQHV GH QRUPDOL]DFLyQ VREUH ODV HQWUDGDV
VDOLGDV 3RUWDQWR OD QXHYD IRUPXODFLyQ SDUD HO76
),6FRQQRUPDOL]DFLyQVREUHODVHQWUDGDV VDOLGDHV


HQWRQFHV


HV
6L

5
Q
L
L
Q
Q
L
Q
L
[
[
[
I
%

FRQ
Q
7
L
L
Q0
L
0
Q
L
L
Q
L
D
[
D
[
D
D
I
[
D
[


























GRQGH
>
@
7
L
0
L
L
D
D








D

/D VDOLGD GHO PRGHOR QRUPDOL]DGR
Q
 VH FDOFXOD
FRPRXQSURPHGLRSHVDGRGHODFRQWULEXFLyQGHFDGD
UHJOD




Q
/
L
L
L
Q
Q
/
L
L
Q
Z
Z
[
[
¦
¦









(VWDHFXDFLyQJHQHUDOPHQWHVHH[SUHVDFRPR




¦
/
L
Q0
L
0
Q
L
L
Q
L
Q
[
D
[
D
D


















[
M

FRQ






¦
¦
/
L
Q
L
/
L
Q
L
Q
L
Z
Z








[
[
[
M
GRQGH/HVHOQ~PHURGHUHJODV 
Z
L
HVHOJUDGRGH
YHUGDGYDORUGHSHUWHQHQFLDGHODLpVLPD UHJOD(O
YDORUGHSHUWHQHQFLDVHREWLHQHFRPRXQDIXQFLyQGH
GLVWDQFLDGHODIRUPD
¦
/
M
M
L
L
G
G
Z









SDUD[QzYL ZL   SDUD [Q  YL (Q HVWD
H[SUHVLyQ










L
Q
7
L
Q
L
G
Y
[
Y
[


HVHOFXDGUDGR
GHODGLVWDQFLDGHVGH HOGDWR
[
Q
KDVWDHOFHQWUR

L
Y

/RV YHFWRUHV

L
Y
VRQ HOHPHQWRV UHSUHVHQWDWLYRV GH
FDGD UHJOD /RV UHVXOWDGRV REWHQLGRV PXHVWUDQ XQD
IRUPD HVIpULFD HQ HO HVSDFLR PGLPHQVLRQDO GH ODV
YDULDEOHV GH HQWUDGD 'HELGR D  VH FXPSOH OD
FRQGLFLyQ
Z
L
L
/
¦


SRUWDQWRGH
Z
L
M
(VWD
IXQFLyQ GH SHUWHQHQFLD OOHYD D FDER XQD SDUWLFLyQ
ERUURVDGHOHVSDFLRGHHQWUDGD>@
/D HQWUDGD  OD VDOLGD QRUPDOL]DGDV [QH Q VH
REWLHQHQFRPR
[
[
[
Q
Q
J
J






/DV IXQFLRQHV GH QRUPDOL]DFLyQ VH XWLOL]DQ FRQ HO
REMHWRGHIDFLOLWDU HOSURFHGLPLHQWRSDUD GHWHUPLQDU
OD HVWUXFWXUD GHO PRGHOR  SDUD PHMRUDU VX
GHVHPSHxR (VWDV IXQFLRQHV GH QRUPDOL]DFLyQ WUDHQ
FRQVLJRXQD FRUUHFFLyQ GHHVFDODV  XQD FRUUHFFLyQ
HVWDG VWLFDHQORVGDWRV1yWHVHTXHODQRUPDOL]DFLyQ
GHODVDOLGDGHEHWHQHULQYHUVD
 3523,('$'(6'(/02'(/2
%255262
 5(9,6,Ï1 '( /$6 3523,('$'(6 '(
/2602'(/2676),6
(Q HVWD VHFFLyQ VH SUHVHQWDQ DOJXQDV GH ODV
SURSLHGDGHV TXH D VH KDE DQ GDGR HQ >@
3ULPHUDPHQWHVHFRQVLGHUDOD]RQDGHYDOLGH]SDUDHO
PRGHOR 76 ),6 /XHJR VH DQDOL]D OD FDSDFLGDG GH
OLQHDOL]DFLyQGHOPRGHOR ILQDOPHQWHVHLQWURGXFHOD
SURSLHGDG GH DFRSOH R IXVLyQ GHO PRGHOR FRQ
UHVSHFWRDOGDWRGLVSRQLEOH
 =RQDGH9DOLGH]GHO0RGHOR
/DSULPHUDSURSLHGDGH[SORUDOD=RQDGH9DOLGH]GHO
0RGHOR 09= SDUD XQ PRGHOR 76 ),6 (VWD
SURSLHGDG GD XQD IXHUWH FDUDFWHUL]DFLyQ GHO PRGHOR
SDUDGHWHUPLQDUODYDOLGH]GHVXVDOLGDFRQUHVSHFWRD
XQYHFWRUGHHQWUDGDSDUWLFXODU3RU WDQWRFXDOTXLHU
GDWR GH HQWUDGD DO PRGHOR 76 ),6 SURGXFLUi XQD
VDOLGDYiOLGDVLHVWHHVWiGHQWURGHOD09=
&XDOTXLHUPRGHORQROLQHDOLGHQWLILFDGRSRUPHGLRGH
ORV GDWRV GH HQWUDGD VDOLGD KHUHGD WRGDV ODV
OLPLWDFLRQHV TXHFRQWLHQH HO FRQMXQWR GH GDWRV3RU
WDQWRODYDOLGH]GHOPRGHORHVWiUHVWULQJLGDDOD]RQD
GHWHUPLQDGD SRU VHxDOHV XWLOL]DGDV SDUD SURGXFLU HO
FRQMXQWRGHGDWRV>@
&RQVLGHUDQGR HO PRGHOR 76 ),6 HVWDEOHFLGR HQ ODV
HFXDFLRQHV  D OD  HO FRQMXQWR ERUURVR GHO
DQWHFHGHQWH HV XQD IXQFLyQ GH OD GLVWDQFLD HQWUH HO
GDWR HOFHQWURGHOJUXSR'HELGRDHVWRQRVHWLHQH
XQDLQIRUPDFLyQH[SO FLWDHQWUHHOGDWR OD09=/D
)LJPXHVWUDXQDDOWHUQDWLYDSDUDGHWHUPLQDUVLXQ
GDWRGHHQWUDGDHVWiGHQWURGHOD 09=(OHMHPSOR
SRU VLPSOLFLGDG HVWi HQ GRV GLPHQVLRQHV SHUR VH
SXHGHH[WHQGHUDPiV
3HTXHxRV F UFXORV UHSUHVHQWDQ ORV GDWRV GH HQWUDGD
XWLOL]DGRV SDUD OD LGHQWLILFDFLyQ /D ILJXUD WDPELpQ
PXHVWUDXQDDOWHUQDWLYDUHVWULFWLYDSDUDGHWHUPLQDUOD
09=(QHVWHPpWRGRVHUHDOL]DXQDSDUWLFLyQGXUD
HQ OD HQWUDGD FRQVLGHUDQGR HO PLVPR Q~PHUR GH
JUXSRV  ORV PLVPRV YDORUHV GH ORV FHQWURV GHO
PRGHOR8QGDWRSHUWHQHFHUiDXQJUXSRVLHOJUDGR
GHSHUWHQHQFLDHVHOPi[LPRHQWUHWRGRVORVJUXSRV
(VWR LQGLFD TXH HO GDWR SHUWHQHFH DO JUXSR FX R
FHQWURHVWiPiVFHUFDGHOPLVPR6HGHWHUPLQDFRPR
YDORU GH FRWD SDUD FDGD JUXSR OD GLVWDQFLD Pi[LPD
GHVGHHOFHQWURKDVWDHOGDWRGHOJUXSRPiVDOHMDGR











L
N
L
Q
1
N
L
PD[
L
Y
[
Y

G

GRQGH
N
L
Q


[
HVHONHVLPRGDWRGHOJUXSRLL /


L
1
HO Q~PHUR GH GDWRV GHO JUXSR L (V SRVLEOH
HVWDEOHFHUXQLQFUHPHQWRGHODFRWDSDUDLQFUHPHQWDU
OD JHQHUDOLGDG GHO PRGHOR SHUR PDQWHQLHQGR XQ
YDORU GHFRWDTXHUHIOHMHODULTXH]DGHOFRQMXQWRGH
GDWRV(O SURFHGLPLHQWRSDUDDQDOL]DU VL XQ GDWR GH
HQWUDGDHVWiGHQWURGHOD09=HV
L&DOFXODUODGLVWDQFLD HQWUHHOGDWR FDGDFHQWURGHO
PRGHOR76),6
LL(QFRQWUDUHOFHQWURDOFXDOFRUUHVSRQGHODP QLPD
GLVWDQFLD GHHVWDPDQHUDGHWHUPLQDUHOJUXSRDOFXDO
FRUUHVSRQGHHVWDP QLPDGLVWDQFLD
LLL6LHVWDP QLPDGLVWDQFLDHVPHQRUTXHODFRWDGHO
JUXSRHQWRQFHVHOGDWRGHHQWUDGDHVWiGHQWURGHOD
09=
 02'(/2%2552620(',$17(
/,1($/,=$&,Ï1
'HELGR D OD IRUPD OLQHDO GH OD IXQFLyQ GHO
FRQVHFXHQWHHO76),6SUHVHQWDXQDFDUDFWHU VWLFDGH
OLQHDOL]DFLyQ TXH SXHGH DSURYHFKDUVH SDUD OD
FRQVWUXFFLyQ GH PRGHORV $ SDUWLU GH XQ PRGHOR
PDWHPiWLFR GHO SURFHVR SRU PHGLR GH VX
OLQHDOL]DFLyQSXHGHREWHQHUVHXQPRGHOR76),6/D
VLJXLHQWH SURSRVLFLyQ VXVWHQWD OD HTXLYDOHQFLD HQWUH
ODOLQHDOL]DFLyQGHOPRGHORPDWHPiWLFR GHOPRGHOR
76),6'HHVWDIRUPDHVSRVLEOHXWLOL]DUHOPRGHOR
PDWHPiWLFR OLQHDOL]DGR SDUD REWHQHU ORV SDUiPHWURV
GHO76),6/DSURSRVLFLyQVXSRQHTXHODIXQFLyQGH
SHUWHQHQFLD XWLOL]DGD HVWi GDGD SRU   TXH




P
Q
Y
Y
z
 SDUD WRGR
Q
P
z
HV GHFLU QR H[LVWHQ
FHQWURVUHSHWLGRVHQODEDVHGHUHJODV
3URSRVLFLyQ  /LQHDOL]DFLyQ GH XQD IXQFLyQ
FRQWLQXDHQHOFHQWURGHODEDVHGHUHJODVERUURVDV
'DGDXQDIXQFLyQFRQWLQXD
I
Q
Q
 


[
[
HOPRGHOR76),6GHODIRUPD






¦

/
M
M
Q
7
M
M
Q
I
D
Z








[
D
[
FRQ OD IXQFLyQ GH SHUWHQHQFLD   FRQVLGHUDQGR




P
Q
Y
Y
z
SDUD
PQ
/













O
Q
Q
Q
O
Y
[
[
[
D
w
w












O
O
7
O
O
D
Y
Y
D



(QWRQFHVSXHGHYHULILFDUVHTXH
D


Q
I
Q
OLP
OLP
L
Q
L
Q
[
[
Y
[
Y
[






o
o

/
D
L

E
Q
Q
I
Q
Q
OLP
OLP
L
Q
L
Q
[
[
[
[
Y
[
Y
[








w
w
w
w
o
o

D/
L

Q
/D SURSRVLFLyQ DQWHULRU PXHVWUD TXH OD IXQFLyQ
PDWHPiWLFD ODIXQFLyQJHQHUDGDSRUHOPRGHOR76
),6 WLHQHQ HO PLVPR YDORU GH VDOLGD  ODV PLVPDV
GHULYDGDVHQHOFHQWURGHOJUXSR8QDLQWHUSUHWDFLyQ
GHHVWRVXJLHUHTXHHOPRGHOR76 ),6  HO SURFHVR
WLHQHQ OD PLVPD OLQHDOL]DFLyQ HQ ORV FHQWURV GH ORV
JUXSRVERUURVRV(VWRVJUXSRVVHJHQHUDQ FXDQGRHO
PRGHOR76),6GLYLGHHOHVSDFLRGHHQWUDGD$V OD
OLQHDOL]DFLyQ GHO PRGHOR PDWHPiWLFR HQ ORV FHQWURV
GHOPRGHOR76),6GDQORVSDUiPHWURVGHOPRGHOR76
),6XWLOL]DQGR 
 $&23/$0,(1722)86,Ï1'(
02'(/2676),6
(VWD SURSLHGDG SHUPLWH TXH GRV PRGHORV 76 ),6
LGHQWLILFDGRV FRQ GRV FRQMXQWRV GH GDWRV GLIHUHQWHV
GH XQ PLVPR VLVWHPD SXHGDQ VHU DFRSODGRV R
IXVLRQDGRV HQ XQ ~QLFR PRGHOR 76 ),6 (VWD
SURSLHGDGHVLQWHUHVDQWHFXDQGRHOVLVWHPDSURFHVR
TXH VH HVWi LGHQWLILFDQGR SRVHHQ GRV R PiV ]RQDV
GRQGHVXFRPSRUWDPLHQWRGLQiPLFRHVPX GLIHUHQWH
8Q PRGHOR 76 ),6 REWHQLGR FRQ XQ FRQMXQWR GH
GDWRV~QLFRJHQHUDOPHQWHLQWHUSRODODVGRVGLQiPLFDV
GHO SURFHVR SURGXFLHQGR XQD UHVSXHVWD EDVWDQWH
GLVWLQWDGHODUHVSXHVWDGLQiPLFDGHOVLVWHPDUHDO6LQ
HPEDUJRVHSXHGHQREWHQHUPRGHORVLQGHSHQGLHQWHV
SDUD FDGD ]RQD FRQ EXHQ FRPSRUWDPLHQWR /D
VLJXLHQWHSURSRVLFLyQVXJLHUHTXHVHSXHGHQDFRSODU
R IXVLRQDU ORV PRGHORV TXH VH KDQ REWHQLGR FRQ
GLVWLQWRVFRQMXQWRVGHGDWRVGDQGROXJDUDXQPRGHOR
~QLFRTXHFRQWHPSODHOFRPSRUWDPLHQWRGHFDGD]RQD
HQSDUWLFXODU
3URSRVLFLyQ $FRSODPLHQWRRIXVLyQGHPRGHORV
76),6 'DGRVGRVPRGHORVERUURVRV








¦

/$
M
M
Q
7
M
/$
M
$
Q
I$
D
Z











[
D
Y
Y
[



¦
¸
¸
¹
·
¨
¨
©
§

















/$
N
N
M
/$
M
$
G
G
Z
Y
Y









¦





/%
/$
/$
M
M
Q
7
M
/%
/$
/$
M
%
Q
I%
D
Z















[
D
Y
Y
[



¦




¸
¸
¹
·
¨
¨
©
§
/%
/$
/$
N
N
M
/%
/$
/$
M
%
G
G
Z















Y
Y

GRQGH




N
M
Y
Y
z
SDUD
MN
/$
/%






DVXPLHQGRTXHORVGRVPRGHORV76),6YHULILFDQ























[
[

)LJ  09= WHQLHQGR HQ FXDQWD OD QRUPD
DFRWDGD
HQWRQFHVHVSRVLEOHREWHQHUHOPRGHORERUURVR
DFRSODGRRIXVLRQDGR






¦


/%
/$
M
M
Q
7
M
M
$%
Q
I$%
D
Z








[
D
[


¦


¸
¸
¹
·
¨
¨
©
§
/%
/$
N
N
M
/%
/$
M
$%
G
G
Z















Y
Y

TXHVDWLVIDFHODVLJXLHQWHFRQGLFLyQ
D








Q
Q
I$%
OLP
OLP
L
Q
L
Q
[
[
Y
[
Y
[
o
o

L
WR
/$
/%


E
Q
Q
Q
Q
I$%
OLP
OLP
L
Q
L
Q
[
[
[
[
Y
[
Y
[








w
w
w
w
o
o

L
WR
/$
/%


Q
(VWDSURSRVLFLyQPXHVWUDTXHVLGRVPRGHORV76),6
VRQ YHUVLRQHV OLQHDOL]DGDV GHO PRGHOR PDWHPiWLFR
REWHQLGRVHQ]RQDVSDUWLFXODUHVHQWRQFHVHOPRGHOR
76 ),6 DFRSODGR R IXVLRQDGR REWHQLGR FRQ
/$
/%

WDPELpQ HV XQD YHUVLyQ OLQHDOL]DGD GHO
PRGHOR PDWHPiWLFR (VWR VXJLHUH XQD KHUUDPLHQWD
SDUD OD LGHQWLILFDFLyQ D TXH HV SRVLEOH LGHQWLILFDU
GRVRPiV PRGHORV76),6HQ]RQDVGLIHUHQWHVFRQ
GLQiPLFDV GLIHUHQWHV  DFRSODU R IXVLRQDU HQ XQ
PRGHOR76),6~QLFR(VWHPRGHOR76),6~QLFRHV
XQPRGHORJHQHUDOGHOSURFHVRSHURTXHHVGLIHUHQWH
GH XQ PRGHOR 76 ),6 LGHQWLILFDGR FRQ XQ~QLFR
FRQMXQWRGHGDWRVIRUPDGRSRUODVXPDGHORVGDWRV
XVDGRVSDUDREWHQHUORVGRVPRGHORVORFDOHV
6L HO SURFHVR GH LGHQWLILFDFLyQ VH KD UHDOL]DGR HQ
IRUPD FRUUHFWD HQ ODV ]RQDV GRQGH VH KDQ REWHQLGR
ORV PRGHORV ORFDOHV HQWRQFHV VH VDWLVIDUiQ ODV
VLJXLHQWHVFRQGLFLRQHV
I1
Q
Q




[
[
|



w
w
w
w
I1
Q
Q
Q
Q
[
[
[
[
|



SDUD  FDGD XQR GH ORV PRGHORV ORFDOHV &RPR HO
PRGHOR VHUi YiOLGR SDUD OD ]RQD GH YDOLGH]  ORV
FHQWURVVHHQFXHQWUDQ GHQWURGHOD]RQDGHYDOLGH]
ODVHFXDFLRQHV WDPELpQVHUiQYiOLGDSDUD
ORV FHQWURV GH ORV PRGHORV $O DFRSODU ORV GRV
PRGHORVODVHFV VHJXLUiQPDQWHQLpQGRVH
SDUDORVFHQWURVGHOPRGHORDFRSODGRRIXVLRQDGR
 $'$37$&,Ï1 2 6,1721Ë$ '(
3$5È0(7526
(Q HVWD VHFFLyQ VH DQDOL]D OD GLIHUHQFLD HQWUH
DGDSWDFLyQ GH SDUiPHWURV  VLQWRQ D GH SDUiPHWURV
(VWH DQiOLVLV HV XQD H[WHQVLyQ GH ODV SURSLHGDGHV
HVWXGLDGDVSUHYLDPHQWH
&XDQGR VH UHDOL]D XQ SURFHVR GH LGHQWLILFDFLyQ FRQ
XQ PRGHOR WLSR FDMD QHJUD FRQ OD FDSDFLGDG GH
DSUR[LPDU IXQFLRQHV FRQ HO JUDGR GH SUHFLVLyQ
QHFHVDULD VREUH XQ VLVWHPD QR OLQHDO HQ HVWDGR GH
IXQFLRQDPLHQWRVHGHEHQGLIHUHQFLDUHOFRQFHSWRGH
DMXVWHGHSDUiPHWURV HOFRQFHSWRGHDGDSWDFLyQ
GH SDUiPHWURV 6H VXSRQH TXH XQ VLVWHPD HQ
IXQFLRQDPLHQWRHVWiVLHQGRLGHQWLILFDGRHQO QHDSRU
XQ PRGHOR WLSR FDMD QHJUD 3DUD FODULGDG HQ OD
H[SOLFDFLyQ VH VXSRQH WDPELpQ TXH HO DOJRULWPR GH
LGHQWLILFDFLyQ DMXVWD ORV SDUiPHWURV GHO PRGHOR
SHULyGLFDPHQWHGH DFXHUGR D XQ ORWH R FRQMXQWR GH
GDWRVGHHQWUDGDVDOLGD$QWHXQ FRQMXQWR QXHYRGH
GDWRVSXHGHQRFXUULUGLVWLQWDVDOWHUQDWLYDV
TXHDOJXQRVGHORVSDUiPHWURVGHOVLVWHPDI VLFR
KD DQ FDPELDGR 'H HVWR VXUJH XQ HUURU HQWUH OD
VDOLGDGHOVLVWHPD GHOPRGHOR
TXHHOVLVWHPDKD DFDPELDGROD]RQDGHWUDEDMR
(VWR WDPELpQ SURYRFD XQ HUURU HQWUH OD VDOLGD GHO
VLVWHPD GHOPRGHOR(VWRVHGHEHDTXHHOPRGHOR
QRVHWLHQHLQIRUPDFLyQGHOVLVWHPDHQHVD]RQD
$QWH OD SULPHUD DOWHUQDWLYD VH GHEH UHDOL]DU XQD
DGDSWDFLyQ GH ORV SDUiPHWURV GHO PRGHOR SDUD
FRQWHPSODUORVFDPELRVHQORVSDUiPHWURVI VLFRVGHO
VLVWHPD(VWHDMXVWH VHGHEHUHDOL]DUSDUDUHGXFLUHO
QGLFH GH HUURU $ HVWH FRQFHSWR VH OR SXHGH
LQWHUSUHWDUFRPRDGDSWDFLyQGHORVSDUiPHWURV
(QODVHJXQGDDOWHUQDWLYDHODMXVWHGHORVSDUiPHWURV
SXHGH VHU SHUMXGLFLDO SRUTXH VH FDPELD HO
FRPSRUWDPLHQWRJHQHUDO GHO PRGHORFXDQGROR TXH
RFXUUH HV TXH KD VXUJLGR XQD QXHYD ]RQD GH
RSHUDFLyQ GHO VLVWHPD (Q  HVWDV FLUFXQVWDQFLDV VH
GHEH UHDOL]DU XQD H[WHQVLyQ GHO PRGHOR D OD ]RQD
QXHYDGHWUDEDMR
3DUD SRGHU OOHYDU D FDER HVWRV FRQFHSWRV HV
LPSRUWDQWH OD SURSLHGDG GH DFRSODPLHQWR  OD
SURSLHGDGGHODGHWHUPLQDFLyQGHOD]RQDGHYDOLGH]
GHO PRGHOR /R TXH VH GHEH KDFHU HV DQDOL]DU VL HO
QXHYR FRQMXQWR GH GDWRV SHUWHQHFH D OD ]RQD GH
YDOLGH]GHOPRGHOR6LHVWHSHUWHQHFHDGLFKD]RQDVH
GHEH DSOLFDU XQ DOJRULWPR SDUD HO DMXVWH GH ORV
SDUiPHWURV GHO PRGHOR D TXH VH HVWDU D DQWH XQ
SUREOHPDGHDGDSWDFLyQGHORVSDUiPHWURV3RUOR
FRQWUDULRVLHOQXHYRFRQMXQWRGHGDWRVQRSHUWHQHFH
DOD]RQDGHYDOLGH]GHOPRGHORVHGHEHREWHQHUXQ
PRGHORORFDO FRQ HVWH FRQMXQWR GH GDWRV  D WUDYpV
GHODFRSODPLHQWRGHORVPRGHORVREWHQHUXQPRGHOR
JOREDO
 '(3(1'(1&,$ 3$5$0e75,&$ (175(
(/6,67(0$<(/02'(/2
(Q HVWD VHFFLyQ VH DQDOL]D HO FRQFHSWR GH
GHSHQGHQFLDHQWUHORVSDUiPHWURVGHOVLVWHPDUHDO
ORV SDUiPHWURV GHO PRGHOR LGHQWLILFDGR FXDQGR VH
XWLOL]D HO PRGHOR 76 ),6 SURSXHVWR R HQ IRUPD
JHQHUDOXQDSUR[LPDGRUXQLYHUVDOGHIXQFLRQHV
6HVXSRQHTXHDOJXQRVSDUiPHWURVGHOVLVWHPDI VLFR
FDPELDQ FRQ HO WLHPSR  TXH ORV SDUiPHWURV GHO
PRGHORVHHVWiQLGHQWLILFDQGRHQIRUPDSHULyGLFD(Q
HVWDVFLUFXQVWDQFLDVVLHOPRGHORXWLOL]DGRVHEDVDHQ
ORV SULQFLSLRV I VLFRV TXH ULJHQ DO SURFHVR PRGHOR
WLSR FDMD EODQFD HO FDPELR HQ XQSDUiPHWUR GHO
VLVWHPD I VLFR SURGXFLUi GHVSXpV GHO SURFHVR GH
LGHQWLILFDFLyQ HO FDPELR HQ XQ SDUiPHWUR HQ HO
PRGHOR 3RU RWUR ODGR FXDQGR HO VLVWHPD HVWi
PRGHODGRSRUXQPpWRGRJHQpULFRFRPRSXHGHVHUXQ
DSUR[LPDGRU XQLYHUVDO GH IXQFLRQHV PRGHORV WLSRV
FDMD QHJUD HO FDPELR HQ XQ SDUiPHWUR GHO VLVWHPD
I VLFR SXHGH SURGXFLU HO FDPELR HQ XQR YDULRV R
WRGRV ORV SDUiPHWURV GHO PRGHOR (Q JHQHUDO XQ
FDPELR HQ XQ SDUiPHWUR GHO VLVWHPD SURGXFH XQ
FDPELRHQPXFKRVSDUiPHWURVGHOPRGHOR
&RPR OD FRPSOHMLGDG GHO SUREOHPD GH FiOFXOR HV
PHQRUFXDQGRHVPHQRUODFDQWLGDGGHSDUiPHWURVD
DMXVWDU HV FRQYHQLHQWH TXH DQWH FDPELRV HQ ORV
SDUiPHWURVGHOVLVWHPDFDPELHQODPHQRUFDQWLGDGGH
SDUiPHWURVGHOPRGHOR/RLGHDOVHU DTXHXQFDPELR
HQHOSDUiPHWURGHOVLVWHPDSURGX]FDXQFDPELRHQHO
SDUiPHWURGHOPRGHOR
(ODQiOLVLVGHODGHSHQGHQFLDHQWUHORVSDUiPHWURVGHO
VLVWHPD I VLFR  ORV SDUiPHWURV GHO PRGHOR SXHGHQ
EULQGDU XQD PHMRU LQWHUSUHWDFLyQ GHO VLVWHPD HQ
FRQMXQWR
'DGR XQ VLVWHPD I VLFR GHILQLGR HQ HQWUDGDVDOLGD
FX R FRPSRUWDPLHQWR GHSHQGH GH VXV SDUiPHWURV
I VLFRV TXH VH SXHGH PRGHODU HQ IXQFLyQ GH VXV
SDUiPHWURVI VLFRFRPR






S
[
S
[
Q
Q
I
GRQGH
S
HVHOYHFWRUGHSDUiPHWURVFRQVLJQLILFDGR
I VLFR HVODVDOLGDGHOVLVWHPD [QHVHOYHFWRUGH
HQWUDGDV 'LFKR VLVWHPD VH PRGHOD D WUDYpV GH XQ
PpWRGRGHLGHQWLILFDFLyQFRQ XQPRGHORERUURVRGH
ODIRUPD






¦

/
M
M
Q
7
M
M
I
Q
I
D
Z









[
D
S
[
GRQGH
I
S
HVHOYHFWRUFRQORVSDUiPHWURVGHOPRGHOR
ERUURVR(OREMHWRHVDQDOL]DUHOFRPSRUWDPLHQWRGH
ORV SDUiPHWURV GHO PRGHOR
I
S
HQ IXQFLyQ GHO
FRPSRUWDPLHQWRGHORVSDUiPHWURVGHOVLVWHPD
S

8QD IRUPD GH HYDOXDU HVWH FRPSRUWDPLHQWR HV
HYDOXDQGRODGHULYDGDGHORVSDUiPHWURVGHOPRGHOR
UHVSHFWR GH ORV SDUiPHWURV GHO VLVWHPD R VHD
HYDOXDQGR
S
S
w
w

I
 'LFKR FRPSRUWDPLHQWR HV
DQDOL]DGR SDUD XQ PRGHOR ERUURVR REWHQLGR SRU
OLQHDOL]DFLyQHQORVFHQWURVGHORVFRQMXQWRVERUURVRV
GHODQWHFHGHQWHSURSRVLFLyQ
'HELGR D TXH VH FRQVLGHUD TXH HO FHQWUR GH ORV
FRQMXQWRV ERUURVRV GHO DQWHFHGHQWH

L
Y
HV ILMR ORV
SDUiPHWURVGHOFRQVHFXHQWHFRQVWLWX HQHOYHFWRUGH
SDUiPHWURVDDMXVWDU3RUORWDQWR
>
@















/
/
I
D
D
D
D
S

'HELGRDTXHHOPRGHORERUURVRVHVXSRQHTXHVHKD
REWHQLGR SRU OLQHDOL]DFLyQ HQ ORV FHQWURV VHJ~Q OD
SURSRVLFLyQUHVXOWD







O
Q
Q
Q
O
Y
[
[
S
[
D
w
w















O
Q
O
Q
Q
Q
7
O
Q
O
D
Y
[
Y
[
[
S
[
Y
S
[

w
w

/D GHULYDGD GH ORV SDUiPHWURV GHO PRGHOR
I
S
UHVSHFWRGHORVSDUiPHWURVGHOVLVWHPD
S
UHVXOWD








O
Q
Q
Q
O
Y
[
S
[
S
[
S
D
w
w
w
w
w

















O
Q
O
Q
Q
Q
7
O
Q
O
D
Y
[
Y
[
S
[
S
[
Y
S
S
[
S
w

w
w
w
w
w
w

/DVHFXDFLRQHV PXHVWUDQFXDOHVHOHIHFWR
TXH VH SURGXFH HQ ORV SDUiPHWURV GHO FRQVHFXHQWH
FXDQGR H[LVWH XQ FDPELR HQ ORV SDUiPHWURV GHO
VLVWHPD 3DUD DFODUDU HVWH FRQFHSWR VH SUHVHQWD XQ
HMHPSORVHQFLOOR
(MHPSOR
(O VLJXLHQWH VLVWHPD SXHGH LOXVWUDU HO FRQFHSWR
DQWHULRU
'DGRXQVLVWHPDFRQXQDHQWUDGD XQDVDOLGDGHOD
IRUPD













[
[
N
[
[
N
N
[




S

GRQGH
[
HV OD HQWUDGD
HV OD VDOLGD
>
@
7
N
N
N
N







S
HVHOYHFWRUGHORVSDUiPHWURVGHO
VLVWHPD
(QHVWHHMHPSOR









N
[
[
N
[
[


w
w
S
3RUODHYDOXDFLyQUHVSHFWRGHOSDUiPHWUR

N





w
w
N
[
S







w
w
w
N
[
[
S

SRUODVXVWLWXFLyQGHHQ 




N
D
O
w
w






N
D
O
w
w

6LVHHYDO~DFRQUHVSHFWRDOSDUiPHWUR

N





[
[
N
[

w
w
S







w
w
w
N
[
[
S

VXVWLWX HQGRHQ 




N
D
O
w
w













[
Y
[
[
N
D
O
Y
[
O
O



w
w

(QIRUPDVLPLODUSDUD

N









[
[
N
[

w
w
S










[
[
N
[
[

w
w
w
S

VXVWLWX HQGRHQ 















[
Y
[
[
N
D
O
Y
[
O
O


w
w























O
Y
[
O
Y
[
O
Y
[
[
[
Y
[
[
N
D
O
O




w
w
)LQDOPHQWHHYDOXDQGRSDUD

[










N
[
[
N
[
[



w
w
S








N
[
[
[

w
w
w
S

3RUODVXVWLWXFLyQGHHQ 









N
N
[
D
O
Y
[
O


w
w






















N
[
N
N
Y
N
[
[
N
[
D
O
O
Y
[
O
Y
[
O





w
w
3DUDDQDOL]DUORVUHVXOWDGRVGHHVWHHMHPSORVHKDFH
XQD DQDORJ D FRQ OD DSUR[LPDFLyQ ORFDO SRU XQ
SROLQRPLR GH 7D ORU GH VHJXQGR RUGHQ (VWD
DSUR[LPDFLyQVHREWLHQHFRPR




















[
[
G[
[
G
[
[
G[
[
G
[
[
[
[
[
[




|

GRQGHGHVSXpVGHFRQWUDVWDUFRQVHSXHGHQ
FRQWUDVWDUORVSDUiPHWURV




[
N





[
[
G[
[
G
N







[
[
G[
[
G
N
$QDOL]DQGRHVWRVUHVXOWDGRVSDUDXQFRPSRUWDPLHQWR
ORFDOVHSXHGHLQIHULUORVLJXLHQWH
 (O FDPELR HQ XQ SDUiPHWUR GHO VLVWHPD TXH
FDPELH HQ XQD FRQVWDQWH OD HFXDFLyQ GHO VLVWHPD
FDPELR GHO RIIVHW HQ HVWH FDVR


[
 HV GHFLU

N
SURGXFLUiTXHORVSDUiPHWURVGHOPRGHOR

O
D
QR FDPELHQ ORV SDUiPHWURV


O
D
FDPELHQ HQ OD
PLVPDSURSRUFLyQTXHHOSDUiPHWURTXHFDPELRHQ
HO VLVWHPD (Q OD )LJ  VH REVHUYD HO
FRPSRUWDPLHQWR GH OD IXQFLyQ   GH ORV
SDUiPHWURV SDUD GLIHUHQWHV YDORUHV GH

N
 (Q OD
SDUWH VXSHULRU L]TXLHUGD VH REVHUYD OD IXQFLyQ
O QHD GH SXQWRV  VX DSUR[LPDFLyQ O QHD
FRQWLQXDSDUDGLVWLQWRVYDORUHVGH

N
(QODSDUWH
VXSHULRUGHUHFKDVHPXHVWUDQ ORV GLVWLQWRVYDORUHV
GHORVSDUiPHWURV(QSDUWHLQIHULRUVHREVHUYDORV
YDORUHV TXH WRPDQ ORV SDUiPHWURV

O
D



O
D
HQ
IXQFLyQGHORVYDORUHVGHORVFHQWURV
O
Y
SDUDORV
GLIHUHQWHVYDORUHVGH

N

(O FDPELR HQ XQ SDUiPHWUR GHO VLVWHPD TXH
PRGLILTXHODSHQGLHQWHGHODHFXDFLyQGHOVLVWHPD
FDPELR GH OD GHULYDGD SULPHUD
G[
[
G 
 HV GHFLU

N
SURGXFLUiTXHORVSDUiPHWURVGHOPRGHOR

O
D
FDPELHQHQODPLVPDSURSRUFLyQTXHHOSDUiPHWUR
TXHFDPELyHQHOVLVWHPD/RVSDUiPHWURV


O
D
VH
PRGLILFDQ HQ XQD IXQFLyQ FRQVWDQWH TXH GHSHQGH
GH

[
 (Q OD )LJ  VH REVHUYD OD LQIOXHQFLD GHO
FDPELRGH

N
HQHOYDORUHVGHORVSDUiPHWURV

O
D



O
D

 (O FDPELR HQ XQ SDUiPHWUR GHO VLVWHPD TXH
PRGLILFD OD FXUYDWXUD FRQFDYLGDG R FRQYH[LGDG
GHODHFXDFLyQGHOVLVWHPDFDPELRGHODGHULYDGD
VHJXQGD




G[
[
G
 HV GHFLU

N
 SURGXFLUi XQ
FDPELR HQ IRUPD OLQHDO HQ ORV SDUiPHWURV GHO
PRGHOR

O
D
 UHVSHFWRD OD SRVLFLyQ GH ORV FHQWUR
O
Y
DO TXH FRUUHVSRQGH HO SDUiPHWUR /RV
FDPELRV HQ ORV SDUiPHWURV


O
D
VHUiQ IXQFLyQ
FXDGUiWLFDUHVSHFWRDODSRVLFLyQGHORVFHQWUR
O
Y

(QOD)LJVHREVHUYDODLQIOXHQFLDGHOFDPELRGH

N
HQORVYDORUHVGHORVSDUiPHWURV

O
D



O
D

 8Q FDPELR HQ XQ SDUiPHWUR GHO VLVWHPD TXH
SURGX]FD XQ GHVSOD]DPLHQWR HQ
[
 HV GHFLU XQ
FDPELRHQ

[
GHODHFXDFLyQGHOVLVWHPDSURGXFH
XQ FDPELR HQ ORV SDUiPHWURV

O
D
IXQFLyQ GH OD
FXUYDWXUD GH OD IXQFLyQ GH OD GHULYDGD VHJXQGD




G[
[
G
HVGHFLU

N
(OFDPELRHQORVSDUiPHWURV


O
D
VHUiIXQFLyQOLQHDOGHOFDPELRHQ

[
GHORV
SDUiPHWURV

N
FXUYDWXUD 

N
SHQGLHQWH(QOD
)LJVHREVHUYDODLQIOXHQFLDGHOFDPELRGH

[
HQ
ORVYDORUHVGHORVSDUiPHWURV

O
D



O
D

 &21&/86,21(6
(Q HVWH DUW FXOR VH DQDOL]DURQ GLVWLQWDV SURSLHGDGHV
GH XQ PRGHOR ERUURVR GHO WLSR 7DNDJL6XJHQR $
PRGR GH LQWURGXFFLyQ VH UHSDVDURQ SURSLHGDGHV
SUHYLDPHQWHHVWXGLDGDV(QWUHpVWDVVHUHVXPLHURQOD
]RQD GH YDOLGH] GHO PRGHOR OD FDSDFLGDG GH
OLQHDOL]DFLyQHQORVFHQWURVGHORVFRQMXQWRVERUURVRV
 OD FDSDFLGDG GH DFRSODPLHQWR R IXVLyQ  GH ORV
PRGHORVERUURVRV
$ FRQWLQXDFLyQ VH DQDOL]y HO FRPSRUWDPLHQWR GHO
PRGHORDQWHODSUHVHQFLDGHGDWRVQXHYRV FXDQWRVH
HVWiQ DMXVWDQGR ORV SDUiPHWURV HQ O QHD 6H
GLIHUHQFLDURQ ORV FRQFHSWRV GH DGDSWDFLyQ GH
SDUiPHWURV HO FXDO RFXUUH FRQ XQ FDPELR HQ ORV
SDUiPHWURV I VLFRV GHO VLVWHPD FRQ HO GH DMXVWH GH
SDUiPHWURVHOFXDORFXUUHSRUXQFDPELRHQOD]RQD
GHWUDEDMRGHOPRGHOR






[

&DPELRHQ
N
R
[

N


R[
N


N


[










Y
O
D







Y
O
D
)LJ&DPELRHQ

O
D



O
D
FRPRFRQVHFXHQFLDGH
XQFDPELRHQN






[
&DPELRHQ
N

R
[

N


N


R[
N


[










Y
O
D







Y
O
D
)LJ&DPELRVHQ

O
D



O
D
FRPRFRQVHFXHQFLDGH
XQFDPELRHQN
(QHVWHWUDEDMRWDPELpQ VHDQDOL]DFXDOHVHO HIHFWR
TXHVHSURGXFHHQORVSDUiPHWURVGHOPRGHORFXDQGR
VHSURGXFHXQFDPELRHQORVSDUiPHWURVGHOVLVWHPD
6HREVHUYDTXHGHELGRDODHVWUXFWXUDHOHJLGDHQHO
PRGHOR ERUURVR VH SXHGHQ GHWHUPLQDU SDUWH GHO
FRPSRUWDPLHQWR GH ORV SDUiPHWURV GHO VLVWHPD
REVHUYDQGRHOFRPSRUWDPLHQWRGHORVSDUiPHWURVGHO
PRGHOR
 5()(5(1&,$6
>@ %H]GHN - &  3DWWHUQ 5HFRJQLWLRQ ZKLW
)X]]  2EMHFWLYH )XQFWLRQ $OJRULWKPV 6HFRQG
3ULQWLQJ3OHQXP3UHVV1HZ<RUN
>@ /DXNRQHQ ( DQG 3DVVLQR .  7UDLQLQJ
IX]]  V VWHPV WR SHUIRUP HVWLPDWLRQ DQG
LGHQWLILFDWLRQ(QJ$SSOLF$UWLI,QWHOO9RO1R
SS
>@3HxD0&DUHOOL5DQGGL6FLDVFLR)D
6 VWHPV ,GHQWLILFDWLRQ XVLQJ D 7 SH RI 7DNDJL
6XJHQR )X]]  0RGHO 6,&,&$  %XHQRV
$LUHV$UJHQWLQD
>@3HxD0ÈOYDUH]+&DUHOOL5DQGGL6FLDVFLR
)E 9DOLGLW /LQHDUL]DWLRQ DQG&RXSOLQJ
3URSHUWLHV RI D 7DNDJL6XJHQR )X]]  0RGHO ,;
&RQJUHVR/DWLQRDPHULFDQRGH&RQWURO$XWRPiWLFR
&RORPELD
>@ 3HxD 0  &RQWURO %DVDGR HQ 0RGHORV
%RUURVR 7HVLV GH GRFWRUDGR ,QVWLWXWR GH
$XWRPiWLFD )DF GH ,QJHQLHU D 816- ,6%1
()86DQ-XDQ$UJHQWLQD
>@ 7DNDJL 7 DQG 6XJHQR 0  )X]]
,GHQWLILFDWLRQ RI V VWHPV DQG LWV DSSOLFDWLRQ WR
PRGHOLQJ DQ FRQWURO ,((( 7UDQVDFWLRQV RQ
6 VWHPV0DQDQG& EHUQHWLFV9RO1R3DJ







[
&DPELRHQ
N

R
[

N


N


N


R[
[










Y
O
D







Y
O
D
)LJ&DPELRHQ

O
D



O
D
FRPRFRQVHFXHQFLDGHO
FDPELRHQN











[
&DPELRHQ
[

R
[

N


N


N


[


R[










Y
O
D









Y
O
D
)LJ  &DPELRV HQ

O
D



O
D
FRPR FRQVHFXHQFLD
GHOFDPELRHQ[