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

'(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[