5.2 Jimmy Steering Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . 81 ...... [29] J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis. State-space solutions to.
Y
5REXVW /DWHUDO &RQWURO RI +LJKZD\ 9HKLFOHV 5D\PRQG + %\UQH
%6(( 8QLYHUVLW\ RI 9LUJLQLD
06(( 8QLYHUVLW\ RI &RORUDGR %RXOGHU
3K' 8QLYHUVLW\ RI 1HZ 0H[LFR
$EVWUDFW
7KLV GLVVHUWDWLRQ H[SORUHV UREXVW FRQWURO WRSLFV UHODWHG WR WKH DXWRPDWLF ODWHUDO FRQWURO
RI KLJKZD\ YHKLFOHV 7KH PDLQ WRSLF LV WKH DSSOLFDWLRQ RI UREXVW FRQWURO WR WKH ODWHUDO FRQWURO
SUREOHP ZKHUH WKH PRGHO XQFHUWDLQW\ LV FKDUDFWHUL]HG DV DGGLWLYH XQVWUXFWXUHG SHUWXUED
WLRQV LQ WKH IUHTXHQF\GRPDLQ 7KLV DSSURDFK UHOLHV RQ LQWHUSRODWLRQ WKHRU\ WR FRQVWUXFW WKH
VWDELOL]LQJ FRQWUROOHU 1HZ LQWHUSRODWLRQ WHFKQLTXHV DUH SUHVHQWHG ZKLFK DOORZ LQWHUSRODWLRQ
RQ WKH
MZ
D[LV DQG ZLWK SRLQWV WKDW KDYH PXOWLSOLFLW\ 7HVW UHVXOWV FRPSDULQJ WKH UREXVW
FRQWUROOHU DQG D 3,' FRQWUROOHU DUH SUHVHQWHG 7ZR RWKHU UREXVW FRQWURO DSSURDFKHV VLPXO
WDQHRXV VWDELOL]DWLRQ RI D IDPLO\ RI SODQWV DQG D PXOWLREMHFWLYH GHVLJQ DUH DOVR GLVFXVVHG LQ
WKH FRQWH[W RI WKH ODWHUDO FRQWURO SUREOHP
&RQWHQWV $FNQRZOHGJHPHQWV
LLL
$EVWUDFW
Y
7DEOH RI &RQWHQWV
YLLL
/LVW RI )LJXUHV
[
/LVW RI 7DEOHV
[L
,QWURGXFWLRQ
/DWHUDO &RQWURO RI +LJKZD\ 9HKLFOHV
5REXVW &RQWURO
&RQWULEXWLRQV RI WKH 7KHVLV
7KHVLV 2XWOLQH
5HYLHZ RI /DWHUDO 9HKLFOH &RQWURO 5HVHDUFK
(DUO\ 5HVHDUFK
0RGHUQ &RQWURO 7KHRU\
6XPPDU\ DQG &RQFOXVLRQV
5REXVW &RQWURO
YL
&217(176
YLL
7KH 5REXVW 6WDELOLW\ &RQGLWLRQ
,QWHUSRODWLRQ 7KHRU\
,QWHUSRODWLRQ 3RLQWV RQ WKH
,QWHUSRODWLRQ 3RLQWV ZLWK 0XOWLSOLFLW\
6XPPDU\ DQG &RQFOXVLRQ
MZ
$[LV
7KH /DWHUDO &RQWURO 3UREOHP
9HKLFOH 0RGHOLQJ DQG 8QFHUWDLQW\
&RQWUROOHU 'HVLJQ
6XPPDU\ DQG &RQFOXVLRQV
6\VWHP ,PSOHPHQWDWLRQ DQG ([SHULPHQWDO 5HVXOWV
7HVWEHG 6\VWHP 2YHUYLHZ
$OJRULWKP ,PSOHPHQWDWLRQ
'LVFXVVLRQ RI 7HVW 5HVXOWV
6XPPDU\ DQG &RQFOXVLRQV
6LPXOWDQHRXV 6WDELOL]DWLRQ 6HQVLWLYLW\ 0LQLPL]DWLRQ
6LPXOWDQHRXV 6WDELOL]DWLRQ
6HQVLWLYLW\ 0LQLPL]DWLRQ
6XPPDU\ DQG &RQFOXVLRQV
6XPPDU\ DQG &RQFOXVLRQV
6XPPDU\
5HFRPPHQGDWLRQV IRU )XWXUH 5HVHDUFK
&217(176
YLLL
$ +DUGZDUH 'RFXPHQWDWLRQ
% 0$7/$% 3URJUDPV
& 9HKLFOH 6RIWZDUH
/LVW RI )LJXUHV
6LPSOLnHG %LF\FOH 0RGHO IRU WKH &DU
1RQOLQHDU *DLQ &XUYH
&ORVHG/RRS 6\VWHP
*HQHUDO FORVHGORRS V\VWHP
)HQ\YHV $UUD\
)HQ\YHV $UUD\ IRU ([DPSOH
)HQ\YHV $UUD\ IRU ([DPSOH
$QDO\WLF 5HJLRQ
)HQ\YHV $UUD\ IRU ([DPSOH
0RGLnHG )HQ\YHV $UUD\
)HQ\YHV $UUD\ IRU ([DPSOH
)HQ\YHV $UUD\ IRU ([DPSOH
6LPXODWLRQ RI 3ODQW 8QFHUWDLQW\
0RGLnHG )HQ\YHV $UUD\ IRU &DU 3UREOHP
6WHS 5HVSRQVH RI &ORVHG/RRS 6\VWHP ZLWK WKH 1RPLQDO 3ODQW
'
L[
/,67 2) ),*85(6
[
/DQH &KDQJH 7UD MHFWRU\
/DQH &KDQJH 5HVSRQVH )DPLO\ RI 3ODQWV
7HVW 9HKLFOH 5HSULQWHG ZLWK 3HUPLVVLRQ IURP *HQHUDO 0RWRUV &RUS
-LPP\ 6WHHULQJ %ORFN 'LDJUDP
$QDORJ %DFNXS 6WHHULQJ %ORFN 'LDJUDP
6WHHULQJ $FWXDWRU &ORVHG/RRS 5HVSRQVH
5REXVW &RQWUROOHU
9[
NPSK
5REXVW &RQWUROOHU
9[
NPSK
5REXVW &RQWUROOHU
9[
NPSK
3,' &RQWUROOHU
9[
NPSK
3,' &RQWUROOHU
9[
NPSK
3,' &RQWUROOHU
9[
NPSK
+XPDQ 'ULYLQJ 6DPSOH
%RGH 3ORW RI 6LPXOWDQHRXVO\ 6WDELOL]LQJ &RQWUROOHU
/DQH &KDQJH 5HVSRQVH IRU )DPLO\ RI 3ODQWV
)HHGEDFN 6\VWHP ZLWK :HLJKWLQJ
$XJPHQWHG 0RGHO
1RPLQDO 3ODQW 6WHS 5HVSRQVH
/DWHUDO &RQWURO 6\VWHP 0RGHO
/LVW RI 7DEOHV
6XPPDU\ RI &RHpFLHQWV LQ %LF\FOH 0RGHO
6XPPDU\ RI &RQWUROOHU 'HVLJQ 5HTXLUHPHQWV DQG 'LpFXOWLHV
6XPPDU\ RI /DWHUDO &RQWURO 7HFKQLTXHV
(VWLPDWHG 3DUDPHWHUV IRU 6 %OD]HU
506 (UURU IRU 3,' DQG 5REXVW &RQWUROOHUV
6XPPDU\ RI &RHpFLHQW &KDQJHV
[L
/,67 2) 7$%/(6
[LL
&KDSWHU ,QWURGXFWLRQ $XWRPDWLF FRQWURO RI KLJKZD\ YHKLFOHV KDV EHHQ RI JUHDW LQWHUHVW VLQFH WKH FRQFHSW ZDV nUVW
LQWURGXFHG E\ *HQHUDO 0RWRUV &RUSRUDWLRQ DW WKH :RUOG V )DLU >@ 0DQ\ DGYDQWDJHV
WR DXWRPDWLF RSHUDWLRQ RI KLJKZD\ YHKLFOHV KDYH EHHQ FODLPHG
7KHVH LQFOXGH LQFUHDVHG
IUHHZD\ WKURXJKSXW LQFUHDVHG KLJKZD\ FDSDFLW\ LQFUHDVHG VDIHW\ DQG UHGXFHG FRQJHVWLRQ
$XWRPDWHG KLJKZD\V ZRXOG DOVR IUHH KXPDQV RI WKH GULYLQJ WDVN 7KH H[SHFWHG EHQHnWV RI
DXWRPDWHG KLJKZD\V DUH GHVFULEHG LQ PRUH GHWDLO LQ > @ 7KLV WKHVLV LJQRUHV PDQ\ RI
WKH ODUJHU QRQWHFKQLFDO LQVWLWXWLRQDO LVVXHV DQG IRFXVHV RQ WKH ODWHUDO FRQWURO RI KLJKZD\
YHKLFOHV 7KH JRDO RI WKH ODWHUDO FRQWURO V\VWHP LV WR NHHS WKH YHKLFOH FHQWHUHG LQ WKH ODQH
,Q DGGLWLRQ WKH ODWHUDO FRQWURO V\VWHP PLJKW EH UHTXLUHG WR SHUIRUP ODQH FKDQJHV RU HYDVLYH
PDQHXYHUV IRU FROOLVLRQ DYRLGDQFH
,Q WKLV LQWURGXFWRU\ FKDSWHU VRPH RI WKH GLpFXOWLHV DVVRFLDWHG ZLWK WKH ODWHUDO FRQWURO
RI KLJKZD\ YHKLFOHV DUH H[DPLQHG
7KHVH GLpFXOWLHV SURYLGH WKH PRWLYDWLRQ IRU DSSO\LQJ
UREXVW FRQWURO WHFKQLTXHV 7KHQ FRQWULEXWLRQV RI WKLV WKHVLV DUH VXPPDUL]HG DQG DQ RXWOLQH
RI WKH GRFXPHQW LV SURYLGHG
&+$37(5 ,1752'8&7,21
/DWHUDO &RQWURO RI +LJKZD\ 9HKLFOHV 7KH JRDO RI WKH ODWHUDO FRQWURO V\VWHP LV WR NHHS WKH YHKLFOH RQ WKH GHVLUHG WUD MHFWRU\
8VXDOO\ WKLV LV FHQWHUHG LQ WKH ODQH EXW PD\ DOVR LQFOXGH ODQH FKDQJHV DQG HYDVLYH FROOLVLRQ
DYRLGDQFH PDQHXYHUV 7KHUHIRUH RQH RI WKH GHVLJQ REMHFWLYHV LV WR PLQLPL]H WKH ODWHUDO SDWK
HUURU EHWZHHQ WKH DFWXDO WUDMHFWRU\ DQG WKH GHVLUHG WUDMHFWRU\
$ WZR GHJUHHRIIUHHGRP
'2) OLQHDUL]HG PRGHO LV W\SLFDOO\ XVHG WR GHVLJQ WKH ODWHUDO FRQWURO V\VWHP 7KLV PRGHO
LV GLVFXVVHG LQ PRUH GHWDLO LQ &KDSWHU
+RZHYHU LW LV LPSRUWDQW WR QRWH WKDW LW LV D
OLQHDUL]HG PRGHO DQG WKDW PDQ\ RI WKH SDUDPHWHUV DUH VXEMHFW WR FKDQJH RU DUH XQNQRZQ
)RU LQVWDQFH WKH YHKLFOH PDVV FKDQJHV DV SDVVHQJHUV DQG FDUJR DUH ORDGHG DQG XQORDGHG
$V WLUH SUHVVXUH DQG URDG FRQGLWLRQV FKDQJH WKH FRUQHULQJ VWLmQHVV RI WKH WLUHV FDQ FKDQJH
GUDPDWLFDOO\ 7KH OLQHDUL]HG PRGHO LV DOVR KLJKO\ GHSHQGHQW RQ WKH YHKLFOH V YHORFLW\ ZKLFK
KDV D ZLGH UDQJH RI SRVVLEOH YDOXHV 7KHUHIRUH DQRWKHU GHVLJQ FULWHULRQ LV WKDW WKH ODWHUDO
FRQWURO V\VWHP PXVW IXQFWLRQ RYHU D ZLGH UDQJH RI SDUDPHWHU FKDQJHV
,Q DGGLWLRQ WR SURYLGLQJ SHUIRUPDQFH RYHU D ZLGH UDQJH RI SDUDPHWHU FKDQJHV WKH ODWHUDO
FRQWURO V\VWHP PXVW DOVR HQVXUH WKDW WKH GULYHU LV FRPIRUWDEOH XQGHU DXWRPDWLF FRQWURO 7KLV
LV XVXDOO\ WUDQVODWHG LQWR PLQLPL]LQJ WKH ODWHUDO DFFHOHUDWLRQ DQG MHUN WKDW LV H[SHULHQFHG
XQGHU DXWRPDWLF FRQWURO )LQDOO\ WKH ODWHUDO FRQWURO V\VWHP PXVW H[KLELW VRPH UREXVWQHVV
WR VHQVRU DFWXDWRU DQG FRQWUROOHU IDXOWV ZKLFK UHVXOWV LQ D JUDFHIXO GHJUDGDWLRQ DV V\VWHPV
PDOIXQFWLRQ 7KH IDFW WKDW WKH YHKLFOH PRGHO LV WLPHYDU\LQJ DQG VXEMHFW WR PDQ\ YDULDWLRQV
DQG XQFHUWDLQWLHV OHQGV LWVHOI WR WKH DSSOLFDWLRQ RI UREXVW FRQWURO WHFKQLTXHV ZKLFK DUH
LQWURGXFHG LQ WKH QH[W VHFWLRQ
&+$37(5 ,1752'8&7,21
5REXVW &RQWURO 5REXVW FRQWURO FDQ EH GHnQHG DV WKH FRQWURO RI XQFHUWDLQ V\VWHPV ZLWK n[HG FRQWUROOHUV >@
*HQHUDOO\ WKH JRDO LV WR GHVLJQ D n[HG FRPSHQVDWRU ZKLFK JXDUDQWHHV VWDELOLW\ DQG KRSHIXOO\
VRPH SHUIRUPDQFH DV WKH SODQW YDULHV 7KH GHVLJQ RI WKH UREXVW FRQWUROOHU LV JRYHUQHG E\
WKH PRGHO RI WKH V\VWHP XQFHUWDLQW\
7KH XQFHUWDLQW\ LV W\SLFDOO\ FODVVLnHG DV VWUXFWXUHG
RU XQVWUXFWXUHG GHSHQGLQJ RQ WKH DPRXQW RI LQIRUPDWLRQ DYDLODEOH
7KH XQFHUWDLQW\ FDQ
EH H[SUHVVHG LQ WKH WLPH GRPDLQ YLD D VWDWHVSDFH PRGHO RU LQ WKH IUHTXHQF\ GRPDLQ ZLWK
D WUDQVIHU IXQFWLRQ PRGHO 7KLV OHDGV WR WKH IROORZLQJ IRXU FRPPRQ FODVVLnFDWLRQV IRU WKH
PRGHOLQJ RI WKH V\VWHP XQFHUWDLQW\
q
WLPHGRPDLQ XQVWUXFWXUHG XQFHUWDLQW\
q
WLPHGRPDLQ VWUXFWXUHG XQFHUWDLQW\
q
IUHTXHQF\GRPDLQ XQVWUXFWXUHG XQFHUWDLQW\
q
IUHTXHQF\GRPDLQ VWUXFWXUHG XQFHUWDLQW\
)UHTXHQF\GRPDLQ XQVWUXFWXUHG XQFHUWDLQW\ FDQ EH IXUWKHU EURNHQ GRZQ LQWR DGGL
WLYH SHUWXUEDWLRQ LQSXWPXOWLSOLFDWLYH SHUWXUEDWLRQ DQG RXWSXWPXOWLSOLFDWLYH SHUWXUED
WLRQ ([DPSOHV RI HDFK DUH VKRZQ LQ ZKHUH
* V
UHSUHVHQWV WKH WUDQVIHU IXQFWLRQ
RI WKH QRPLQDO SODQW
$GGLWLYH SHUWXUEDWLRQ
*V
* V p*V
,QSXW PXOWLSOLFDWLYH SHUWXUEDWLRQ
*V
* V ,
5V
2XWSXW PXOWLSOLFDWLYH SHUWXUEDWLRQ
*V
,
/V * V
&+$37(5 ,1752'8&7,21
7KLV GLVVHUWDWLRQ GHDOV ZLWK WKH DSSOLFDWLRQ RI UREXVW FRQWURO WR WKH ODWHUDO FRQWURO SURE
OHP XVLQJ IUHTXHQF\GRPDLQ DGGLWLYH XQVWUXFWXUHG XQFHUWDLQW\ WR PRGHO WKH XQNQRZQ DQG
WLPHYDU\LQJ SDUDPHWHUV $OWKRXJK WKLV DSSURDFK LV QRW VSHFLnFDOO\ GHVLJQHG WR DFFRPPR
GDWH WLPHYDU\LQJ V\VWHPV WKH DVVXPSWLRQ WKDW WKH YDULDWLRQV ZLOO RFFXU VORZO\ DOORZV WLPH
YDULDWLRQV WR EH LQFOXGHG 5REXVW FRQWURO LV DQ DWWUDFWLYH WHFKQLTXH WR GHDO ZLWK WKH ODWHUDO
FRQWURO SUREOHP IRU VHYHUDO UHDVRQV )LUVW D n[HG FRQWUROOHU FDQ EH XVHG ZKLFK HOLPLQDWHV
WKH QHHG IRU DQ\ JDLQVFKHGXOLQJ RU DGDSWDWLRQ DOJRULWKPV $ UREXVW FRQWUROOHU DOVR WKHR
UHWLFDOO\ JXDUDQWHHV VWDELOLW\ RYHU D ZLGH UDQJH RI SDUDPHWHU FKDQJHV )LQDOO\ EHFDXVH WKH
YHKLFOH PRGHO DQG XQFHUWDLQW\ DUH WUHDWHG LQ WKH IUHTXHQF\ GRPDLQ DFWXDO WHVW GDWD RQ WKH
YHKLFOH UHVSRQVH FDQ EH JDWKHUHG E\ LQMHFWLQJ VLQXVRLGV RI GLmHUHQW IUHTXHQFLHV
7KH RQO\
GUDZEDFN RI WKLV DSSURDFK LV WKDW D VROXWLRQ LV QRW JXDUDQWHHG WR H[LVW EXW WKLV LV GLVFXVVHG
LQ PRUH GHWDLO LQ &KDSWHU 7KH QH[W VHFWLRQ SUHVHQWV WKH FRQWULEXWLRQV RI WKLV WKHVLV
&RQWULEXWLRQV RI WKH 7KHVLV 7KH FRQWULEXWLRQV RI WKLV WKHVLV DUH PDGH LQ WZR DUHDV 7KH nUVW FRQWULEXWLRQ LV LQ UREXVW
FRQWURO RI V\VWHPV ZLWK IUHTXHQF\GRPDLQ XQVWUXFWXUHG DGGLWLYH SHUWXUEDWLRQV 7KH VHFRQG
FRQWULEXWLRQ LV LQ DSSO\LQJ WKLV WKHRU\ WR WKH ODWHUDO FRQWURO RI DXWRPRELOHV DQG FRPSDULQJ
LW WR VHYHUDO RWKHU WHFKQLTXHV 7KLV LQFOXGHV nHOG WHVWLQJ RI WKH UREXVW FRQWURO DOJRULWKP RQ
DQ H[SHULPHQWDO YHKLFOH
5REXVW FRQWURO RI V\VWHPV ZLWK DGGLWLYH XQVWUXFWXUHG SHUWXUEDWLRQV ZDV nUVW SUHVHQWHG
E\ .LPXUD LQ >@
7KLV WKHVLV H[WHQGV WKH UHVXOWV RI .LPXUD E\ DOORZLQJ PXOWLSOLFLW\
RI XQVWDEOH SROHV DV ZHOO DV SROHV RQ WKH
MZ
D[LV
7KHVH H[WHQVLRQV DUH EDVHG RQ QHZ
&+$37(5 ,1752'8&7,21
LQWHUSRODWLRQ WHFKQLTXHV IRU KDQGOLQJ LQWHUSRODWLRQ SRLQWV RQ WKH
PXOWLSOLFLW\ 2QH WHFKQLTXH IRU KDQGOLQJ SROHV RQ WKH
EXW KDQGOLQJ D PXOWLSOLFLW\ RI SROHV RQ WKH
MZ
MZ
MZ
D[LV DQG SRLQWV ZLWK
D[LV ZDV GHYHORSHG E\ /L LQ >@
D[LV ZDV QRW GLVFXVVHG
7KH LQWHUSRODWLRQ
WHFKQLTXHV SUHVHQWHG LQ WKLV WKHVLV DUH DOVR DSSOLFDEOH WR RWKHU W\SHV RI UREXVW FRQWURO WKHRU\
7KH PRWLYDWLRQ IRU H[WHQGLQJ WKH ZRUN RI .LPXUD ZDV WR DOORZ WKH DSSOLFDWLRQ RI WKLV
W\SH RI UREXVW FRQWURO WKHRU\ WR WKH ODWHUDO FRQWURO RI KLJKZD\ YHKLFOHV
7KLV WKHVLV DOVR
SUHVHQWV H[SHULPHQWDO UHVXOWV IURP WKH LPSOHPHQWDWLRQ RI WKH UREXVW FRQWURO DOJRULWKP RQ
D WHVWEHG YHKLFOH
7KH SHUIRUPDQFH RI WKH UREXVW FRQWURO DOJRULWKP LV FRPSDUHG WR D
SURSRUWLRQDOLQWHJUDOGHULYDWLYH 3,' FRQWUROOHU
,Q DGGLWLRQ VHYHUDO RWKHU FRQWURO WHFK
QLTXHV DSSOLFDEOH WR WKH ODWHUDO FRQWURO SUREOHP DUH GLVFXVVHG 7KHVH LQFOXGH VLPXOWDQHRXV
VWDELOL]DWLRQ DV ZHOO DV PLQLPL]LQJ WKH VHQVLWLYLW\ DQG WKH GHULYDWLYH RI WKH FRQWURO VHQVL
WLYLW\ WR LPSURYH GULYHU ULGH FRPIRUW
7KHVLV 2XWOLQH $Q RXWOLQH RI WKH UHPDLQLQJ FKDSWHUV LV DV IROORZV
q
,Q &KDSWHU D PRUH GHWDLOHG UHYLHZ RI SUHYLRXV ODWHUDO FRQWURO UHVHDUFK LV SURYLGHG
q
,Q &KDSWHU 5REXVW FRQWURO WKHRU\ IRU SODQWV ZLWK XQVWUXFWXUHG DGGLWLYH SHUWXU
EDWLRQV LV UHYLHZHG
7KLV LQFOXGHV D GLVFXVVLRQ RI LQWHUSRODWLRQ WKHRU\ ZKLFK LV WKH
EDVLF WRRO XVHG WR DUULYH DW WKH UREXVWO\ VWDELOL]LQJ FRQWUROOHU 7KH OLPLWDWLRQV RI LQ
WHUSRODWLRQ WKHRU\ DUH GLVFXVVHG DQG WHFKQLTXHV ZKLFK RYHUFRPH WKHVH OLPLWDWLRQV DUH
SURSRVHG
&+$37(5 ,1752'8&7,21 q
,Q &KDSWHU WKH UHVXOWV SUHVHQWHG LQ &KDSWHU DUH XVHG WR GHVLJQ D UREXVWO\ VWDEL
OL]LQJ FRPSHQVDWRU IRU WKH ODWHUDO FRQWURO V\VWHP
q
,Q &KDSWHU WKH FRQWURO V\VWHP GHVLJQHG LQ &KDSWHU LV LPSOHPHQWHG RQ D WHVW
YHKLFOH
7KH SHUIRUPDQFH RI WKH UREXVW FRQWUROOHU LV FRPSDUHG WR D SURSRUWLRQDO
LQWHJUDOGHULYDWLYH 3,' FRQWUROOHU GXULQJ nHOG WHVWLQJ
q
,Q &KDSWHU VHYHUDO RWKHU SURPLVLQJ FRQWURO WHFKQLTXHV IRU ODWHUDO FRQWURO DUH GLV
FXVVHG 7KHVH LQFOXGH PLQLPXPSKDVH VLPXOWDQHRXV VWDELOL]DWLRQ DQG PLQLPL]LQJ WKH
FRPSOLPHQWDU\ VHQVLWLYLW\ IXQFWLRQ DQG LWV GHULYDWLYH WR LPSURYH ULGH FRPIRUW
q
,Q &KDSWHU RXU FRQFOXVLRQV DQG UHFRPPHQGDWLRQV IRU IXWXUH ZRUN DUH SUHVHQWHG
q
$SSHQGL[ $ GHVFULEHV WKH WHVWEHG YHKLFOH LQ PRUH GHWDLO
q
$SSHQGL[ % FRQWDLQV 0$7/$% SURJUDPV GHYHORSHG IRU YHKLFOH FRQWURO VLPXODWLRQV
q
$SSHQGL[ & FRQWDLQV YHKLFOH FRQWURO VRIWZDUH XVHG LQ WKH nHOG WHVWLQJ
&KDSWHU 5HYLHZ RI /DWHUDO 9HKLFOH &RQWURO 5HVHDUFK 2QH RI WKH IXQGDPHQWDO JRDOV RI ,76 ,QWHOOLJHQW 7UDQVSRUWDWLRQ 6\VWHPV LV WR GHYHORS
DXWRPDWHG KLJKZD\V ZKHUH YHKLFOHV DUH FDSDEOH RI DXWRPDWLF RSHUDWLRQ 7KH PRVW SRSXODU
FRQFHSW LV SODWRRQV RI YHKLFOHV VHSDUDWHG E\ PHWHU WUDYHOLQJ GRZQ WKH KLJKZD\ LQ D
VSHFLDO ODQH DW QRUPDO KLJKZD\ VSHHGV $XWRPDWLF RSHUDWLRQ RI KLJKZD\ YHKLFOHV LV XVXDOO\
EURNHQ GRZQ LQWR ODWHUDO DQG ORQJLWXGLQDO FRQWURO
$W D KLJKHU OHYHO ODWHUDO DQG ORQJLWX
GLQDO FRQWURO PXVW EH FRRUGLQDWHG WR SHUIRUP PDQHXYHUV OLNH D ODQH FKDQJH
/DWHUDO DQG
ORQJLWXGLQDO G\QDPLFV DUH DOVR UHODWHG ^ ODWHUDO PRGHOV DUH D IXQFWLRQ RI ORQJLWXGLQDO YHORF
LW\ DQG ODWHUDO VWHHULQJ FDXVHV WRUTXH GLVWXUEDQFHV LQ WKH HQJLQH DQG SRZHUWUDLQ +RZHYHU
ODWHUDO DQG ORQJLWXGLQDO FRQWURO DUH XVXDOO\ WUHDWHG VHSDUDWHO\ LQ WKH OLWHUDWXUH HVSHFLDOO\
ZKHQ WKH QHFHVVDU\ ORZOHYHO FRQWURO V\VWHPV DUH DGGUHVVHG :KLOH RWKHU VXUYH\ SDSHUV KDYH
PHQWLRQHG YHKLFOH FRQWURO WRSLFV > @ WKLV FKDSWHU UHYLHZV WKH GLmHUHQW DSSURDFKHV
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
WR ODWHUDO FRQWURO V\VWHP GHVLJQ WDNHQ RYHU WKH ODVW \HDUV 7KH FKDSWHU LV RUJDQL]HG LQ D
URXJKO\ FKURQRORJLFDO RUGHU EXW VRPH GLVFXVVLRQV DUH NHSW WRJHWKHU DQG RXW RI RUGHU ZKHQ
WKH\ DUH SHUIRUPHG E\ WKH VDPH UHVHDUFKHU RU RUJDQL]DWLRQ
(DUO\ 5HVHDUFK 7KH DXWRPDWHG KLJKZD\ V\VWHP FRQFHSW $+6 ZDV nUVW LQWURGXFHG LQ WKH *HQHUDO 0RWRUV
3DYLOLRQ DW WKH :RUOG V )DLU >@
,QLWLDO UHVHDUFK HmRUWV ZHUH FRQGXFWHG E\ 5&$
/DERUDWRULHV LQ WKH V >@ /DWHUDO FRQWURO ZDV DFKLHYHG E\ IROORZLQJ DQ HOHFWULnHG FDEOH
EXULHG LQ WKH FHQWHU RI WKH ODQH 7KH VHQVLQJ V\VWHP FRQVLVWHG RI WZR FRLOV DW WKH IURQW RI WKH
YHKLFOH ZKLFK GHWHFWHG WKH PDJQHWLF nHOG FDXVHG E\ WKH DOWHUQDWLQJ FXUUHQW oRZLQJ WKURXJK
WKH ZLUH
7KH FRQWURO DOJRULWKP XVHG LQ WKH HDUO\ WHVWV LV VXPPDUL]HG E\ ?,Q D G\QDPLF
VLWXDWLRQ ZLWK SURSHUO\ VWDELOL]HG VHUYR FRQWUROV WKH FDU ZLOO SURFHHG GRZQ WKH FDEOH ZLWK
QR ZDYHULQJ >@ $ IRRW VHFWLRQ RI KLJKZD\ QHDU /LQFROQ 1HEUDVND ZDV XVHG IRU D IXOO
VFDOH ZRUNLQJ GHPRQVWUDWLRQ LQ 6HSWHPEHU RI >@ 2WKHU GHPRQVWUDWHG WHFKQRORJLHV
LQFOXGHG ORRS YHKLFOH GHWHFWRUV DQG D UDGLR ZDUQLQJ V\VWHP IRU IROORZLQJ YHKLFOHV FRQWUROOHG
E\ WKH GHWHFWRUV >@
5&$ DQG *HQHUDO 0RWRUV GHPRQVWUDWHG DQ DXWRPDWHG KLJKZD\ V\VWHP DW DQ HOHFWURQLF
WHVW WUDFN GHYHORSHG E\ 5&$ LQ WKH ODWH V >@ 7KH VDPH FRQFHSW RI IROORZLQJ D EXULHG
ZLUH IRU ODWHUDO FRQWURO ZDV DSSOLHG
7KH FRQWURO DOJRULWKP GHYHORSHG ZDV D IXQFWLRQ RI
YHORFLW\ RWKHUZLVH ?WKH FDU FRXOG RSHUDWH VXFFHVVIXOO\ DW RQO\ RQH VSHHG >@
([WHQVLYH UHVHDUFK HmRUWV LQ YHKLFOH FRQWURO ZHUH FRQGXFWHG DW WKH 2KLR 6WDWH 8QLYHUVLW\
268 IURP XQWLO >@
,Q %DUULFN XVHG WKH WUDQVIHU IXQFWLRQ VKRZQ LQ
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
HTXDWLRQ WR PRGHO WKH ODWHUDO G\QDPLFV RI D YHKLFOH >@
(I V
. 9[ V D9[
V
pI V ZKHUH
(I V
ODWHUDO GHYLDWLRQ IURP ODQH FHQWHU RI WKH IURQW FHQWHU RI WKH YHKLFOH
pI V
WKH IURQWZKHHO DQJOH
9[ . 9[
DQG
WKH YHKLFOH IRUZDUG VSHHG
D9[
YHORFLW\ GHSHQGHQW SDUDPHWHUV
$IWHU IXUWKHU WHVWV DW 268 WKLV PRGHO ZDV GHWHUPLQHG WR EH LQDFFXUDWH DQG PRUH VXLWDEOH
PRGHOV ZHUH GHYHORSHG 2QH RI WKH VLPSOHVW PRGHOV IRU WKH ODWHUDO PRWLRQ RI D YHKLFOH LV D
WZR GHJUHHRIIUHHGRP ELF\FOH PRGHO 7KLV LV VKRZQ LQ )LJXUH DQG GHVFULEHG E\ HTXDWLRQV
DQG >@
P9B
\
P9[
B ,] l ]
O
O &mI
b O&mU 9[
&
mI b O &mU 9[
w
l]
l]
&mI &mU
w 9\
9[
b O&mU
O &mI
&mI pI W
O &mI pI W
w 9\
9[
7KH TXDQWLWLHV VKRZQ LQ )LJXUH DQG HTXDWLRQV DQG DUH GHVFULEHG LQ 7DEOH
5HDUUDQJLQJ HTXDWLRQV DQG \LHOGV WKH IROORZLQJ VWDWHVSDFH V\VWHP
[B
ZKHUH
$
D D
%
E X
D
D
$[ %X
E
pI
DQG
[
9\ l]
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
)LJXUH 6LPSOLnHG %LF\FOH 0RGHO IRU WKH &DU
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
3DUDPHWHU 'HVFULSWLRQ P
9HKLFOH PDVV NJ
9[
/RQJLWXGLQDO YHORFLW\ YHKLFOH FRRUGLQDWHV P
9\
/DWHUDO YHORFLW\ YHKLFOH FRRUGLQDWHV P
O O
V
'LVWDQFH IURP IURQW DQG UHDU D[OHV WR FJ P
l]
@
+RZHYHU LQDGHTXDWH VHQVRU WHFKQRORJ\ GLG QRW
DOORZ SUDFWLFDO LPSOHPHQWDWLRQV XQWLO PXFK ODWHU
7KHUHIRUH IUHTXHQF\GRPDLQ DQG FODV
VLFDO FRQWURO WHFKQLTXHV ZKLFK DUH PRUH RULHQWHG WRZDUGV LQSXWRXWSXW WUDQVIHU IXQFWLRQ
DQDO\VLV UHPDLQHG SUHYDOHQW LQ WKH HDUO\ KDUGZDUH LPSOHPHQWDWLRQV 7KLV VHFWLRQ UHYLHZV
WKH DSSOLFDWLRQ RI PRGHUQ FRQWURO WKHRU\ WR ODWHUDO FRQWURO RI KLJKZD\ YHKLFOHV
3DVWHUQDFN LQ GLVFXVVHG WKH REVHUYDELOLW\ DQG FRQWUROODELOLW\ RI WKH OLQHDUL]HG ODWHUDO
G\QDPLFV RI D UXEEHUWLUHG YHKLFOH >@ +H DOVR GLVFXVVHG WKH DSSOLFDWLRQ RI RSWLPDO FRQWURO
WR WKH ODWHUDO FRQWURO SUREOHP ,Q %RQGHUVRQ SURSRVHG XVLQJ RSWLPDO FRQWURO ZLWK D
TXDGUDWLF SHUIRUPDQFH LQGH[ WKDW SHQDOL]HV WKH ODWHUDO GLVSODFHPHQW ODWHUDO DFFHOHUDWLRQ
DQG \DZ DFFHOHUDWLRQ >@
,Q WKH PLG V DQ RSWLPDO FRQWUROOHU ZDV GHYHORSHG DW 268 >@ 7KH RSWLPDO FRQWURO
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
GHVLJQ LQYROYHG FKRRVLQJ D ZHLJKWLQJ PDWUL[ IRU WKH FRVW IXQFWLRQ DQG VROYLQJ WKH DOJHEUDLF
5LFFDWL HTXDWLRQ $5( 7KH YHKLFOH G\QDPLFV DUH GHVFULEHG E\ 7KH VWHHULQJ DFWX
DWRU G\QDPLFV ZHUH DOVR PRGHOHG \LHOGLQJ D WKRUGHU VWDWHVSDFH PRGHO ,Q RUGHU WR WDNH
FDUH RI WKH YHORFLW\ GHSHQGHQFH RI WKH PRGHO WKH $5( ZDV VROYHG DW GLmHUHQW YHORFLWLHV VR
WKDW
.
. 9[
JDLQVFKHGXOLQJ
7KH YHORFLW\ LQFUHPHQW
ZDV PV DQG JDLQV ZHUH FDOFXODWHG DV
9[
9[
XVHG IRU JDLQVFKHGXOLQJ
YDULHG IURP PV WR PV 6LQFH DOO VWDWHV
ZHUH QRW DYDLODEOH D UHGXFHGRUGHU REVHUYHU ZDV GHVLJQHG WR HVWLPDWH WKH VWDWHV 7KH SROHV
RI WKH REVHUYHU ZHUH SODFHG DW WKH URRWV RI V V
7KH GHVLJQ ZDV FDUULHG
RXW IRU D FRQWLQXRXVWLPH V\VWHP DQG WKHQ GLVFUHWL]HG XVLQJ WKH ELOLQHDU WUDQVIRUPDWLRQ IRU
FRPSXWHU LPSOHPHQWDWLRQ
$ VDPSOLQJ SHULRG RI
7
PV ZDV FKRVHQ ZKLFK LV IDVWHU
WKDQ WHQ WLPHV WKH FORVHGORRS EDQGZLGWK WHQ WLPHV FORVHGORRS EDQGZLGWK
z PV
7KH
RSWLPDO FRQWUROOHU ZDV LPSOHPHQWHG RQ DQ ,QWHO PLFURSURFHVVRU DQG VLPXODWHG RQ DQ
DQDORJ FRPSXWHU UHSUHVHQWLQJ WKH YHKLFOH G\QDPLFV
$OWKRXJK DQ RSWLPDO FRQWUROOHU ZDV
LPSOHPHQWHG /LQHDU 4XDGUDWLF 5HJXODWRU /45 GHVLJQ D WUDGLWLRQDO REVHUYHU ZDV XVHG
WR HVWLPDWH WKH VWDWHV ,I D .DOPDQ )LOWHU KDG EHHQ XVHG LQ FRQMXQFWLRQ ZLWK /RRS 7UDQVIHU
5HFRYHU\ /75 VRPH UREXVWQHVV SURSHUWLHV FRXOG KDYH EHHQ DGGHG WR WKH V\VWHP DW n[HG
YHORFLWLHV +RZHYHU QR UREXVWQHVV SURSHUWLHV FDQ EH JXDUDQWHHG IRU WKH RSWLPDO DSSURDFK
WDNHQ
5HVHDUFK RQ $XWRPDWHG *XLGHZD\ 7UDQVLW 9HKLFOHV FRQGXFWHG LQ WKH V ZDV YHU\
PXFK FRQFHUQHG ZLWK WKH ODWHUDO FRQWURO RI UXEEHUWLUHG YHKLFOHV
$XWRPDWHG *XLGHZD\
7UDQVLW $*7 ZDV D FODVV RI SURSRVHG XUEDQ WUDQVSRUWDWLRQ V\VWHPV LQ ZKLFK YHKLFOHV RS
HUDWHG XQGHU DXWRPDWLF ORQJLWXGLQDO DQG ODWHUDO FRQWURO RQ H[FOXVLYH JXLGHZD\V >@ 6HYHUDO
ODWHUDO FRQWURO VWUDWHJLHV ZHUH SUHVHQWHG LQ >@ 7KHVH LQFOXGHG DQ RSWLPDO :LHQHU nOWHU DQ
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
/45 GHVLJQ DQG D VXERSWLPDO UHGXFHGVWDWHIHHGEDFN FRQWUROOHU $ WZR GHJUHHRIIUHHGRP
ELF\FOH PRGHO ZDV XVHG WR GHVLJQ DQG HYDOXDWH WKH GLmHUHQW FRQWURO VWUDWHJLHV 7KH SHUIRU
PDQFH LQGH[ IRU WKH :LHQHU nOWHU FRQVLVWHG RI PHDQVTXDUH DFFHOHUDWLRQ DQG PHDQVTXDUH
WUDFNLQJ HUURU DW D JLYHQ SRLQW RQ WKH YHKLFOH
$ IRXUWKRUGHU FRPSHQVDWRU ZDV GHVLJQHG
ZKLFK FDQFHOV XQZDQWHG YHKLFOH SROHV DQG ]HURV WR \LHOG WKH RSWLPDO GHVLUHG WUDQVIHU IXQF
WLRQ 7KH KLJKRUGHU RI WKH FRPSHQVDWRU DQG SROH]HUR FDQFHOODWLRQ PDGH WKH :LHQHU nOWHU
LPSOHPHQWDWLRQ XQDWWUDFWLYH DW WKH WLPH
$ IXOOVWDWHIHHGEDFN /LQHDU 4XDGUDWLF 5HJXODWRU /45 GHVLJQ ZDV DOVR SUHVHQWHG LQ
>@ ZLWK WKH GHWDLOHG FDOFXODWLRQV DSSHDULQJ LQ >@ $OWKRXJK WKH /45 GHVLJQ DQG :LHQHU
nOWHU DUH YHU\ VLPLODU WKH /45 DSSURDFK GRHV QRW UHO\ RQ SROH]HUR FDQFHOODWLRQV WR \LHOG
WKH GHVLUHG WUDQVIHU IXQFWLRQ +RZHYHU WKH /45 GHVLJQ GRHV UHO\ RQ IXOOVWDWH IHHGEDFN $
.DOPDQ nOWHU ZDV SURSRVHG IRU FDVHV ZKHQ IXOOVWDWH IHHGEDFN ZDV QRW DYDLODEOH %HFDXVH RI
WKH DGGHG FRPSOH[LW\ RI D .DOPDQ nOWHU GHVLJQ D UHGXFHGVWDWH IHHGEDFN FRQWUROOHU ZKLFK
XVHG RQO\ ODWHUDO SRVLWLRQ DQG \DZ DQJOH HUURU ZDV GHVLJQHG WR HYDOXDWH WKH SHUIRUPDQFH RI
D UHODWLYHO\ VLPSOH FRQWUROOHU
7KH UHGXFHGVWDWHIHHGEDFN SURSRVHG LQ >@ FDQ EH LPSOHPHQWHG ZLWK RQH RU WZR VHQVRUV
GHSHQGLQJ RQ WKH VHQVRU ORFDWLRQ ZLWK WKH IROORZLQJ FRQWURO ODZ
pI
ZKHUH
t
b.\ \ b \ b .t t
UHSUHVHQWV WKH \DZ DQJOH DQG \
PXOWLSOLHV WKH SDWK HUURU ZKLOH
.t
b \ LV WKH
ODWHUDO SDWK HUURU
.\
LV WKH JDLQ ZKLFK
LV WKH JDLQ ZKLFK PXOWLSOLHV WKH \DZ DQJOH HUURU
QRWHG LQ >@ LI WKH ODWHUDO HUURU VHQVRU LV ORFDWHG D GLVWDQFH
OA
$V
LQ IURQW RI WKH YHKLFOH FHQWHU
RI PDVV WKH HUURU VHQVHG LV D IXQFWLRQ RI WKH YHKLFOH ODWHUDO SRVLWLRQ HUURU DV PHDVXUHG DW
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+ WKH FHQWHU RI PDVV \
b \
DQG RI WKH \DZ DQJOH
(I
\
t
IRU QRQ]HUR
OA
OA t b \
7DNLQJ DGYDQWDJH RI WKH VLPSOH VWHHULQJ FRQWUROOHU GHVFULEHG E\ ZDV H[DPLQHG
LQ >@ 7KH JDLQ
.F
UHSUHVHQWV WKH RYHUDOO FRQWUROOHU JDLQ ZKLFK PXOWLSOLHV WKH ODWHUDO HUURU
DQG WKH \DZ DQJOH HVWLPDWH
OA t
pI
b.F >\ OA t b \ @
7KH SHUIRUPDQFH RI WKH VLPSOH FRQWUROOHU GHVFULEHG E\ ZDV FRPSDUHG WR WKH SHUIRU
PDQFH RI WKH EDVHOLQH :LHQHU RSWLPDO GHVLJQ 7KH UHVXOWV LQGLFDWHG WKDW WKH SHUIRUPDQFH
RI WKH VLPSOH FRQWUROOHU FORVHO\ PDWFKHG WKH RSWLPXP GHVLJQ DQG WKH ORDGLQJ RI WKH YHKLFOH
GLG QRW VLJQLnFDQWO\ DmHFW SHUIRUPDQFH 0XFK RI WKLV ZDV DWWULEXWHG WR WKH GHVLJQ RI WKH
YHKLFOH _ ZHOOGDPSHG RSHQORRS G\QDPLFV DQG QHDUO\ QHXWUDOVWHHU
7KH HmHFWV RI VWHHULQJ DFWXDWRU G\QDPLFV RQ YHKLFOH SHUIRUPDQFH ZHUH DOVR H[DPLQHG
LQ >@
7KH VWHHULQJ DFWXDWRU G\QDPLFV ZHUH PRGHOHG E\ D nUVWRUGHU ODJ
)RU DOO RI WKH
FRQGLWLRQV VWXGLHG YHKLFOH G\QDPLFV ZHUH XQDmHFWHG E\ DFWXDWRUV ZLWK UHVSRQVHV oDW XS
WR +] :LWK WKH VLPSOH SURSRUWLRQDO FRQWUROOHU VWXGLHG DFWXDWRU WLPHFRQVWDQWV JUHDWHU
WKDQ DERXW VHFRQGV FDXVHG LQVWDELOLW\
2WKHU UHVXOWV GLVFXVVHG LQ >@ LQFOXGH WKH
HmHFWV RI YHKLFOH VSHHG RQ FRQWUROOHU SHUIRUPDQFH DQG RFFXSDQW FRPIRUW 7KH ,62 ,QWHU
QDWLRQDO 2UJDQL]DWLRQ IRU 6WDQGDUGL]DWLRQ SDVVHQJHU FRPIRUW VSHFLnFDWLRQV ZHUH XVHG WR
HYDOXDWH URRWPHDQVTXDUH UPV ODWHUDO DFFHOHUDWLRQ GDWD
7KH SHUIRUPDQFH RI WKH VLP
SOH SURSRUWLRQDO FRQWUROOHU ZDV IRXQG WR GHJUDGH TXLFNO\ ZLWK LQFUHDVLQJ VSHHG ZKLOH WKH
IXOOVWDWHIHHGEDFN FRQWUROOHU ZDV PRUH UREXVW ZLWK UHVSHFW WR YHORFLW\ FKDQJHV 7KLV LV UHD
VRQDEOH EHFDXVH /45 GHVLJQV ZLWK IXOO VWDWH IHHGEDFN KDYH LQKHUHQW UREXVWQHVV SURSHUWLHV
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
F bF
JDLQ PDUJLQ DQG
SKDVH PDUJLQ >@
,Q WKH PLG V 'DLPOHU%HQ] FRQGXFWHG UHVHDUFK RQ DXWRPDWLF ODWHUDO FRQWURO RI
EXVHV > @
6WDWHVSDFH GHVLJQ PHWKRGV ZHUH DSSOLHG
7KH VWDELOLW\ OLPLWDWLRQV RI D
VLPSOH SURSRUWLRQDO FRQWUROOHU ZLWK RXWSXW IHHGEDFN IURQW HUURU IURQW DQG UHDU HUURU ZHUH
GLVFXVVHG %DVHG RQ WKH OLPLWDWLRQV RI SURSRUWLRQDO FRQWURO DQ RSWLPDO /45 DSSURDFK ZDV
VXJJHVWHG $Q DWWHPSW ZDV PDGH WR nQG D n[HG RSWLPDO FRQWUROOHU ZKLFK SHUIRUPHG ZHOO
RYHU D ZLGH UDQJH RI YDU\LQJ SDUDPHWHUV
$ n[HG RSWLPDO FRQWUROOHU ZLWK ORZ SDUDPHWHUV
VHQVLWLYLW\ ZDV QRW IRXQG VR HmRUWV VKLIWHG WR GHVLJQLQJ D SROHSODFHPHQW FRQWUROOHU
$Q
REVHUYHU ZDV GHVLJQHG WR HVWLPDWH WKH VWDWHV $OWKRXJK WKH REVHUYHU KDG D n[HG JDLQ ZKLOH
SDUDPHWHUV ZHUH YDU\LQJ WKH SHUIRUPDQFH RI WKH REVHUYHU ZDV IDLUO\ UREXVW WR SDUDPHWHU
FKDQJHV HVSHFLDOO\ ZKHQ FRPSDUHG WR D VLPSOH GLmHUHQWLDWLQJ nOWHU IRU VWDWH HVWLPDWLRQ
7KH ODUJHVW $+6 HmRUW LV FXUUHQWO\ EHLQJ XQGHUWDNHQ DW 3$7+ 3URJUDP IRU $GYDQFHG
7HFKQRORJ\ IRU WKH +LJKZD\ LQ &DOLIRUQLD 7KH 3$7+ DSSURDFK WR DXWRPDWLF ODWHUDO FRQWURO
UHOLHV RQ VHQVLQJ WKH ORFDWLRQ RI EXULHG PDJQHWV VSDFHG PHWHU DSDUW
,Q DGGLWLRQ WR
SURYLGLQJ ODWHUDO SRVLWLRQ HUURU GDWD WKH PDJQHWV DUH DOVR FRGHG XVLQJ SRODULW\ FKDQJHV WR
SURYLGH URDG FXUYDWXUH LQIRUPDWLRQ WR WKH YHKLFOH ODWHUDO FRQWURO V\VWHP 7KH XVH RI SUHYLHZ
FRQWURO ZDV GHHPHG QHFHVVDU\ WR LPSURYH SHUIRUPDQFH RQ VKDUS FXUYHV HVSHFLDOO\ DW KLJK
VSHHGV >@ 7KH PDJQHWLF UHIHUHQFH V\VWHP LV GHVFULEHG LQ JUHDW GHWDLO LQ >@
7KH RYHUDOO ODWHUDO FRQWUROOHU GHVLJQHG DW 3$7+ FRQVLVWV RI D IHHGEDFN DQG D IHHGIRUZDUG
FRPSRQHQW 7KH IHHGEDFN FRPSRQHQW RI WKH FRQWURO V\VWHP ZDV GHVLJQHG XVLQJ IUHTXHQF\
VKDSHG OLQHDU TXDGUDWLF )6/4 FRQWURO WKHRU\ ZKLOH WKH IHHGIRUZDUG FRQWUROOHU ZDV GH
VLJQHG WR JHQHUDWH D SUHYLHZ VWHHULQJ FRPPDQG EDVHG RQ WKH URDG FXUYDWXUH LQIRUPDWLRQ
>@
$ VL[ GHJUHHRIIUHHGRP FRPSOH[ PRGHO ZDV XVHG IRU VLPXODWLRQV ZKLOH D VLPSOLnHG
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+ WZR GHJUHHRIIUHHGRP PRGHO ZDV XVHG IRU WKH FRQWUROOHU GHVLJQ
2SHQORRS VLPXODWLRQV
ZHUH FRQGXFWHG WR YHULI\ WKDW WKH VLPSOLnHG DQG FRPSOH[ PRGHOV SHUIRUPHG VLPLODUO\ XQGHU
W\SLFDO RSHUDWLQJ FRQGLWLRQV
)6/4 FRQWURO WKHRU\ ZDV FKRVHQ IRU ODWHUDO YHKLFOH FRQWURO DW 3$7+ EHFDXVH IUHTXHQF\
GHSHQGHQW ZHLJKWLQJ IDFWRUV FDQ EH SODFHG RQ WKH WUDFNLQJ HUURU ODWHUDO DFFHOHUDWLRQ DQG
FRQWURO HmRUW >@ ,Q DGGLWLRQ ZHLJKWLQJ IDFWRUV RQ WKH WUDFNLQJ HUURU WHUPV FDQ EH VKDSHG
LQ WKH IUHTXHQF\GRPDLQ WR LQFUHDVH WKH UREXVWQHVV RI WKH SODQW WR KLJK IUHTXHQF\ QRLVH DQG
XQPRGHOHG G\QDPLFV 7KH ZHLJKWLQJ IDFWRU RQ WKH DFFHOHUDWLRQ WHUP FDQ DOVR EH ZHLJKWHG
LQ WKH IUHTXHQF\ GRPDLQ WR HQVXUH JRRG ULGH TXDOLW\ LQ WKH IUHTXHQF\ UDQJH VHQVLWLYH WR
SDVVHQJHUV >@
)6/4 WKHRU\ LV DQ H[WHQVLRQ RI OLQHDUTXDGUDWLF JDXVVLDQ PHWKRGV >@
7UDGLWLRQDO
OLQHDU TXDGUDWLF UHJXODWRU /45 GHVLJQV DUH EDVHG RQ WKH OLQHDU PRGHO DQG WKH
TXDGUDWLF SHUIRUPDQFH LQGH[
[B
$[ %X [
= WI r
-
[
W WI
s
[7 4[ X7 5X GW [7 WI 0 [WI
7KH G\QDPLFV RI WKH SODQW DUH GHVFULEHG E\ $ % DQG WKH GHVLJQ REMHFWLYH LV WR
PLQLPL]H WKH FRVW LQGH[
5
!
DQG
0
-
ZLWK
4
SRVLWLYH VHPLGHnQLWH 4
SRVLWLYH VHPLGHnQLWH 0
w
w
5
SRVLWLYH GHnQLWH
,I WKH VWDQGDUG /45 FRVW IXQFWLRQ LV
ZULWWHQ LQ WKH IUHTXHQF\ GRPDLQ XVLQJ 3DUVHYDO V WKHRUHP ZLWK WKH ZHLJKWLQJ PDWULFHV
DQG
5
4
IXQFWLRQV RI IUHTXHQF\ DQG ZLWK QR ZHLJKWLQJ RQ WKH nQDO VWDWH WKH UHVXOW LV
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
>@
4MZ LI
5MZ
DQG
5MZ
= K >
L
[+ MZ 4MZ [MZ X+ MZ 5MZ XMZ GZ
PXVW EH +HUPLWLDQ
LV SRVLWLYH GHnQLWH DQG
4MZ
DW DOO IUHTXHQFLHV DQG D VROXWLRQ LV JXDUDQWHHG
LV SRVLWLYH VHPLGHnQLWH DW DOO EXW D nQLWH QXPEHU RI
GLVFUHWH IUHTXHQFLHV >@ 7KH G\QDPLF HTXDWLRQ DQG WKH FRVW IXQFWLRQ PD\ EH
ZULWWHQ LQ WHUPV RI DQ H[WHQGHG VWDWH YHFWRU 7KH FRQWURO ODZ LV WKHQ REWDLQHG E\ VROYLQJ
D PRGLnHG DOJHEUDLF 5LFFDWL HTXDWLRQ >@
([SHULPHQWDO UHVXOWV IRU WKH )6/4 FRQWUROOHU DSSURDFK DUH GHVFULEHG LQ >@ 6HQVLWLYLW\
UHGXFWLRQ ZDV XVHG WR OHVVHQ WKH HmHFWV RI SHUWXUEDWLRQV LQ YHORFLW\ DQG FRUQHULQJ VWLmQHVV
2SHQORRS WHVWV ZHUH FRQGXFWHG WR GHWHUPLQH WLUH PRGHO SDUDPHWHUV VWHHULQJ DFWXDWRU SD
UDPHWHUV DQG RYHUDOO YHKLFOH UHVSRQVH
7KH PDJQHWLF VHQVRU V\VWHP ZDV FDOLEUDWHG XVLQJ
D YLGHR VWULSH VHQVLQJ V\VWHP $ SURSRUWLRQDOLQWHJUDOGHULYDWLYH 3,' FRQWUROOHU ZDV DOVR
WHVWHG IRU FRPSDULVRQ SXUSRVHV
7HVW VSHHGV ZHUH UHODWLYHO\ VORZ
b NPSK
PSK DQG WKH FRQWURO V\VWHP FRXOG QRW NHHS WKH YHKLFOH ZLWKLQ WKH UDQJH RI WKH PDJQHWLF
h FP
PDUNHU V\VWHP
LQ WKH KLJK VSHHG WHVWV RI
NPSK
,Q VXEVHTXHQW WHVWLQJ WKH
SHUIRUPDQFH ZDV LPSURYHG DW KLJKHU VSHHGV DQG WKH PD[LPXP YHORFLW\ ZDV LQFUHDVHG WR
NPSK
>@
2WKHU ODWHUDO FRQWURO UHVHDUFK FRQGXFWHG E\ 3$7+ UHVHDUFKHUV KDV DQDO\]HG WKH XVH RI
ODWHUDO YHORFLW\ DQG \DZUDWH DV WZR LQGHSHQGHQW FRQWURO LQSXWV >@ 7KLV DSSURDFK UHTXLUHV
DQ H[WUD LQSXW LQ DGGLWLRQ WR IURQW VWHHULQJ DQJOH ZKLFK PLJKW FRQVLVW RI UHDU LQGHSHQGHQW
GHI RI +HUPLWLDQ LV $+ MZ
$MZ Z ZKHUH $+ LV WKH FRPSOH[ FRQMXJDWH WUDQVSRVH RI $
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
VWHHULQJ IURQW GLmHUHQWLDO WRUTXH RU UHDU GLmHUHQWLDO WRUTXH >@ 7KHVH FRPELQDWLRQV ZRXOG
DOORZ LQGHSHQGHQW FRQWURO RI ODWHUDO DQG \DZ PRWLRQV
7KH UDQJH RI VWHDG\VWDWH ODWHUDO
YHORFLW\ DQG \DZUDWH ZHUH DQDO\]HG IRU WKUHH GLmHUHQW FDVHV
FRQYHQWLRQDO IURQWZKHHO
VWHHULQJ IURQWZKHHO VWHHULQJ DQG IURQWGLmHUHQWLDO IRUFH DQG IURQW DQG UHDU LQGHSHQGHQW
VWHHULQJ
7KH FDVH RI LQGHSHQGHQW IURQW DQG UHDU ZKHHO VWHHULQJ DOORZHG ZLGHVW UDQJH RI
UHDFKDEOH VWHDG\VWDWH \DZUDWH DQG ODWHUDO YHORFLW\ $Q RSWLPDO FRQWUROOHU ZDV GHYHORSHG
IRU WKH IURQW DQG UHDU LQGHSHQGHQW VWHHULQJ V\VWHP DQG ZDV HYDOXDWHG XVLQJ VLPXODWLRQV DV
ZHOO DV H[SHULPHQWV RQ D VPDOO PRGHO FDU $Q HVWLPDWRU ZDV DOVR GHVLJQHG WR HVWLPDWH WKH
FRUQHULQJ VWLmQHVV RI WKH WLUHV IRU XVH LQ WKH FRQWURO DOJRULWKP *DLQVFKHGXOLQJ ZDV XVHG WR
DFFRXQW IRU YDU\LQJ YHORFLWLHV DQG FRUQHULQJ VWLmQHVV >@ 7KH FRQWURO ODZ DOVR LQFRUSRUDWHG
D IHHGIRUZDUG WHUP WR FRPSHQVDWH IRU FHQWULIXJDO IRUFH ,Q WKH DFWXDO H[SHULPHQWV \DZUDWH
ZDV PHDVXUHG E\ DQ DQJXODU YHORFLW\ VHQVRU DQG ODWHUDO YHORFLW\ ZDV REWDLQHG E\ LQWHJUDWLQJ
GDWD IURP DQ DFFHOHURPHWHU >@
7KH XVH RI JDLQVFKHGXOLQJ DQG VXERSWLPDO HVWLPDWLRQ
ZLWKRXW ORRS WUDQVIHU UHFRYHU\ UHVXOWV LQ WKH ORVV RI DQ\ LQKHUHQW UREXVWQHVV SURSHUWLHV LQ
WKH RSWLPDO FRQWUROOHU GHVLJQ
$ WRSLF UHODWHG WR ODWHUDO FRQWURO UREXVW IDXOW GHWHFWLRQ LQ ODWHUDO FRQWURO V\VWHPV ZDV
DOVR DQDO\]HG DV SDUW RI WKH 3$7+ SURJUDP >@
7KH DSSURDFK WDNHQ LQYROYHV GHVLJQLQJ
WKUHH REVHUYHUV HDFK RI ZKLFK XVHV WZR RXW RI WKH WKUHH DYDLODEOH VHQVRU PHDVXUHPHQWV
6KRXOG RQH RI WKH VHQVRUV IDLO RQO\ RQH REVHUYHU ZRXOG EH DmHFWHG
7KH REVHUYHU ZDV
GHVLJQHG E\ ZULWLQJ WKH V\VWHP G\QDPLFV LQ WKH IRUP
[B
$[ %X (G
\
&[ 'X IV
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+ ZKHUH WKH
DQG
IV
(
PDWUL[ DFFRXQWV IRU WKH SDUDPHWHU XQFHUWDLQWLHV
G
LV WKH GLVWXUEDQFH LQSXW
UHSUHVHQWV WKH VHQVRU IDXOW YHFWRU 'HnQLQJ DQ REVHUYHU DV
B [ A
$[ A A %X . \ b \
\ A
&[ A 'X
7KH REVHUYHU HUURU G\QDPLFV EHFRPH
HB
'HnQLQJ WKH UHVLGXH
WR
U
DV
$
U
b .& H (G .IV )
+H
$
b .&
\LHOGV WKH IROORZLQJ WUDQVIHU IXQFWLRQ IURP XQFHUWDLQW\
G
U + V,
*UG V ZKHUH
)
b ) > (
$
b .&
)RU WKH UHVLGXH WR EH LQVHQVLWLYH WR XQFHUWDLQWLHV
*UG V
7KH
.
DQG
:
+ V,
b ) > (
*UG
VKRXOG EH ]HUR DV VKRZQ LQ
: & V,
b ) >(
PDWULFHV DUH WKHQ FKRVHQ XVLQJ HLJHQVWUXFWXUH DVVLJQPHQW DV GHVFULEHG LQ
> @
6LPXODWLRQ DQG H[SHULPHQWDO UHVXOWV RI WKH VHQVRU IDXOW GHWHFWLRQ DOJRULWKP DUH GLVFXVVHG
LQ >@ 7KH VDPH PRGHO FDU XVHG LQ >@ ZDV XVHG IRU WHVWLQJ WKH IDXOW GHWHFWLQJ REVHUYHU
VFKHPH $V LQ >@ QRLV\ DFFHOHUDWLRQ GDWD ZDV D SUREOHP DQG ODWHUDO DFFHOHUDWLRQ VHQVRU
IDXOWV ZHUH QRW HDVLO\ GHWHFWHG
$ QRQOLQHDU FRPELQHG ODWHUDO DQG ORQJLWXGLQDO FRQWUROOHU IRU ODWHUDO FRQWURO SURSRVHG
E\ 3$7+ UHVHDUFKHUV LV GHVFULEHG LQ >@
$ QRQOLQHDU PRGHO ZKLFK WDNHV LQWR DFFRXQW
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
HQJLQH G\QDPLFV VWHHULQJ DFWXDWRU G\QDPLFV DQG ODWHUDO G\QDPLFV ZDV XVHG 7KH SURSRVHG
QRQOLQHDU FRQWURO ODZ LV YHU\ VLPLODU WR FRPSXWHGWRUTXH FRQWURO ODZV LQ URERWLFV
7KLV
DSSURDFK LV RXWOLQHG E\ HTXDWLRQV
0 T 1 T NT
XW
XW
1 T /TB
,I WKH G\QDPLFV RI D V\VWHP DUH GHVFULEHG E\ ZKHUH
1 T
LV D NQRZQ QRQOLQHDULW\ D
IHHGEDFN ODZ RI WKH IRUP RI FDQ EH XVHG WR FDQFHO WKH QRQOLQHDULW\ DQG SODFH WKH SROHV
RI WKH UHPDLQLQJ OLQHDU V\VWHP +RZHYHU WKH UREXVWQHVV RI WKH V\VWHP LV DmHFWHG E\ LQH[DFW
FDQFHOODWLRQ RI WKH QRQOLQHDULWLHV 7KLV DSSURDFK LV WDNHQ LQ >@ EXW DSSUR[LPDWLRQV RI WKH
VLQH DQG FRVLQH WHUPV DUH PDGH LQ RUGHU WR DUULYH DW WKH FRQWURO ODZ 7KH FRQWURO ODZ ZDV
VLPXODWHG IRU D SODWRRQ RI YHKLFOHV DFFHOHUDWLQJ RQ D FXUYHG URDG VHFWLRQ
7KH FRQWURO
V\VWHP SHUIRUPHG ZHOO LQ VLPXODWLRQ DQG IXUWKHU ZRUN ZLOO DGGUHVV WKH UREXVWQHVV RI WKH
FRQWUROOHU WR PHDVXUHPHQW QRLVH DQG FRPPXQLFDWLRQ GHOD\V EHWZHHQ YHKLFOHV >@
)X]]\ ORJLF KDV DOVR EHHQ DSSOLHG WR WKH ODWHUDO FRQWURO SUREOHP E\ UHVHDUFKHUV DW 3$7+
>@
)X]]\ ORJLF ZDV XVHG WR GHYHORS IHHGEDFN SUHYLHZ DQG JDLQ VFKHGXOLQJ UXOH EDVHV
7KH IX]]\ ORJLF FRQWUROOHU ZDV WKHQ WHVWHG RQ D 7R\RWD &HOLFD GHYHORSHG E\ ,05$ $PHULFD
7HVWLQJ ZDV SHUIRUPHG DW
NPSK
NPSK
NPSK
DQG
NPSK
7KH IX]]\ ORJLF
FP
DW VSHHGV XS WR
FRQWUROOHU ZDV FDSDEOH RI PDLQWDLQLQJ ODWHUDO HUURUV RI OHVV WKDQ
NPSK
7KH H[SHULPHQWDO SHUIRUPDQFH RI WKH IX]]\ ORJLF FRQWUROOHU ZDV FRPSDUDEOH WR
WKH 3,' DQG )6/4 FRQWUROOHUV SUHYLRXVO\ WHVWHG E\ 3$7+
5REXVW FRQWURO WHFKQLTXHV DSSOLHG WR YHKLFOH ODWHUDO FRQWURO DUH GHVFULEHG LQ > @
,Q >@ D JDLQVFKHGXOHG FRQWUROOHU IRU IRXUZKHHO VWHHULQJ WKDW \LHOGV YHORFLW\LQGHSHQGHQW
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
\DZ HLJHQYDOXHV LV SUHVHQWHG 7KH ELF\FOH PRGHO LV XVHG WR PRGHO YHKLFOH ODWHUDO G\QDPLFV
$ UHVXOW SUHVHQWHG LQ >@ ZKLFK VWDWHV WKDW D IHHGEDFN FRPSHQVDWRU
+I V
V
IRU WKH IURQW
ZKHHO VWHHULQJ DQJOH GHFRXSOHV WKH \DZ PRGH IURP WKH ODWHUDO PRGH RI WKH IURQW D[OH LV XVHG
LQ >@ 8VLQJ WKLV FRPSHQVDWRU WKH \DZUDWH DQG IURQW VWHHULQJ DQJOH DUH XQREVHUYDEOH IURP
WKH DFFHOHUDWLRQ RI WKH IURQW D[OH DQG WKH DFFHOHUDWLRQ RI WKH IURQW D[OH LV QRW FRQWUROODEOH
IURP WKH UHDU VWHHULQJ DQJOH >@ $ FRQWUROOHU GHVFULEHG E\ LV WKHQ SURSRVHG IRU WKH
UHDU VWHHULQJ ZKLFK UHVXOWV LQ UREXVW \DZ GDPSLQJ E\ \DZUDWH IHHGEDFN
t pU
O 9[
b N'
u ZU
b l]
ZKHUH
pU O
UHDU ZKHHO VWHHULQJ DQJOH
ZKHHOEDVH
9[
ORQJLWXGLQDO YHORFLW\
N'
FRQWUROOHU SDUDPHWHU DGMXVWHG WR REWDLQ WKH GHVLUHG GDPSLQJ
ZU
FRPPDQGHG UHDU \DZUDWH
l]
YHKLFOH \DZUDWH
1RWH WKDW WKH FRQWUROOHU GHVFULEHG E\ UHTXLUHV JDLQVFKHGXOLQJ IRU WKH YHORFLW\
WHUP 7KH FRQWUROOHU GRHV KRZHYHU HOLPLQDWH WKH YHORFLW\ GHSHQGHQFH RI WKH FKDUDFWHULVWLF
SRO\QRPLDO RI WKH FORVHGORRS V\VWHP >@ 'HFRXSOLQJ IHHGEDFN +I V
V
\LHOGV D YHORFLW\
LQGHSHQGHQW QDWXUDO IUHTXHQF\ EXW ORZ GDPSLQJ $GGLQJ UHDUZKHHO VWHHULQJ ZLWK WKH \DZ
UDWH IHHGEDFN VKRZQ LQ \LHOGV YHORFLW\ LQGHSHQGHQW HLJHQYDOXHV DQG EHWWHU GDPSLQJ
FRPSDUDEOH WR WKH HLJHQYDOXH UHJLRQ RI D FRQYHQWLRQDO FDU >@
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
,Q >@ \DZUDWH IHHGEDFN LQ FRQMXQFWLRQ ZLWK VLPXOWDQHRXV SROH UHJLRQ DVVLJQPHQW IRU
IRXU H[WUHPDO SODQWV LV DSSOLHG WR LPSURYH WKH UREXVWQHVV RI D EXV ODWHUDO FRQWURO V\VWHP
7KH IRXU H[WUHPDO SODQWV FRQVLVW RI FRPELQDWLRQV RI WKH PD[LPXPPLQLPXP YHORFLW\ DQG
PDVV
Y>
P
Y
P
> Y >
P
> Y
P
$ K\SHUEROD ZDV FKRVHQ DV WKH VWDELOLW\
ERXQGDU\ 7KH FORVHGORRS SROHV RI WKH V\VWHP ZHUH SODFHG WR WKH OHIW RI WKH K\SHUEROD IRU
WKH IRXU H[WUHPDO SODQWV 6LPXODWLRQ UHVXOWV VKRZHG WKDW WKH UREXVW FRQWUROOHU GHVLJQHG ZLWK
\DZUDWH IHHGEDFN SHUIRUPHG EHWWHU WKDQ D IHHGEDFN V\VWHP ZKLFK RQO\ XVHV ODWHUDO HUURU
7KH LPSURYHPHQWV LQFOXGHG UHGXFHG PD[LPDO GLVSODFHPHQWV UHGXFHG RVFLOODWRU\ WHQGHQFLHV
DQG PRUH XQLIRUP UHVSRQVHV RYHU WKH UDQJH RI RSHUDWLRQ FRQGLWLRQV P Y >@
,Q >@ VOLGLQJ PRGH FRQWURO LV DSSOLHG WR WKH ODWHUDO FRQWURO SUREOHP $ ELF\FOH PRGHO ZDV
XVHG IRU WKH FRQWUROOHU GHVLJQ EXW WKH VLPXODWLRQV ZHUH FRQGXFWHG ZLWK DQ H[WHQGHG QRQOLQ
HDU WZRWUDFN PRGHO 7ZR GLmHUHQW DSSURDFKHV ZHUH WDNHQ IRU WKH VOLGLQJ PRGH FRQWUROOHU
GHVLJQ
7KH nUVW DVVXPHG ODWHUDO GLVSODFHPHQW DQG VWHHULQJ DQJOH DV WKH WZR PHDVXUDEOH
VWDWHV 7KH VHFRQG DSSURDFK DVVXPHG WKDW ODWHUDO GLVSODFHPHQW DQG \DZUDWH ZHUH WKH WZR
PHDVXUDEOH VWDWHV 7KH UREXVWQHVV RI WKLV DSSURDFK FRPHV IURP WKH DSSOLFDWLRQ RI VOLGLQJ
PRGH FRQWURO EXW WKH FRQWUROOHU SDUDPHWHUV ZHUH KDQGWXQHG WR REWDLQ D VXLWDEOH WUDGHRm
EHWZHHQ WUDFNLQJ SHUIRUPDQFH DQG ULGH TXDOLW\ >@
5HVHDUFK RQ SDVVHQJHU ULGH FRPIRUW GXULQJ ODQH FKDQJHV KDV EHHQ VWXGLHG E\ 0LWVXELVKL
>@ ([SHULPHQWDO WHVWV ZHUH FRQGXFWHG WR GHWHUPLQH WKH SURnOH RI W\SLFDO DQG HPHUJHQF\
ODQH FKDQJHV
%DVHG RQ WKH ODWHUDO DFFHOHUDWLRQ DQG MHUN SURnOH RI D W\SLFDO ODQH FKDQJH
D ODWHUDO FRQWUROOHU DQG WUDMHFWRU\ JHQHUDWRU ZHUH GHVLJQHG 7KH WUD MHFWRU\ JHQHUDWRU FRP
PDQGV WKH VWHHULQJ DFWXDWRU SRVLWLRQ DQG YHORFLW\ WR REWDLQ WKH V\PPHWULF DFFHOHUDWLRQ DQG
MHUN WUD MHFWRULHV VHHQ LQ WKH WHVW GDWD
7KH VWHHULQJ SRVLWLRQ FRQWURO LV RQO\ XVHG GXULQJ
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
ODQH FKDQJHV QRW GXULQJ QRUPDO ODWHUDO FRQWURO DQG LQYROYHV WKH XVH RI D IHHGIRUZDUG WHUP
WR WKH VWHHULQJ DFWXDWRU %RWK VLPXODWLRQV DQG nHOG WHVWV ZHUH XVHG WR HYDOXDWH WKH FRQWURO
V\VWHP SHUIRUPDQFH
7KH DSSOLFDWLRQ RI PRGHOUHIHUHQFH DGDSWLYH FRQWURO 05$& WR WKH ODWHUDO FRQWURO SURE
OHP LV GHVFULEHG LQ >@ $GDSWLYH FRQWURO LV SURPLVLQJ EHFDXVH LW DOORZV IRU DGDSWDWLRQ DV
SDUDPHWHUV FKDQJH YHORFLW\ FRUQHULQJ VWLmQHVV PDVV HWF
$OWKRXJK PRGHOUHIHUHQFH
DGDSWLYH FRQWURO JXDUDQWHHV VWDELOLW\ DQG SHUIRUPDQFH DIWHU DGDSWDWLRQ SHUIRUPDQFH LV QRW
JXDUDQWHHG GXULQJ DGDSWDWLRQ 7KHUH DUH DOVR VHYHUDO OLPLWDWLRQV WR SUDFWLFDO LPSOHPHQWD
WLRQ
7KHVH LQFOXGH LQVWDELOLW\ FDXVHG E\ VWHHULQJ DFWXDWRU VDWXUDWLRQ GXULQJ DGDSWDWLRQ
DQG D WUDGHRm EHWZHHQ FRQWURO DPSOLWXGH DQG IUHTXHQF\ FRQWHQW GXULQJ DGDSWDWLRQ 7KHVH
WZR LVVXHV UHTXLUH IXUWKHU UHVHDUFK EHIRUH PRGHOUHIHUHQFH DGDSWLYH FRQWURO LV VXLWDEOH IRU
ODWHUDO FRQWURO RI YHKLFOHV
2QH SRVVLEOH DSSURDFK IRU KDQGOLQJ DFWXDWRU VDWXUDWLRQ LV GH
VFULEHG LQ > @ 7KLV LQYROYHV XVLQJ WKH VXP RI VHYHUDO VDWXUDWLRQ IXQFWLRQV WR REWDLQ WKH
FRQWURO LQSXW
7KHUH KDV DOVR EHHQ D VLJQLnFDQW DPRXQW RI UHVHDUFK FRQGXFWHG RQ YLVLRQEDVHG ODWHUDO
DQG ORQJLWXGLQDO FRQWURO RI YHKLFOHV > @
0XFK RI WKLV ZRUN KDV IRFXVHG RQ WKH YLVLRQ DVSHFWV DQG OLWWOH DWWHQWLRQ KDV EHHQ SDLG WR WKH
DFWXDO FRQWURO DOJRULWKP ,Q RWKHU FDVHV WKH ODWHUDO FRQWURO DOJRULWKP LV ?KLGGHQ LQ D QHXUDO
QHWZRUN YLVLRQ DOJRULWKP DQG LV GLpFXOW WR DQDO\]H >@ 0XFK RI WKH YLVLRQEDVHG QDYLJDWLRQ
ZRUN GRQH LQ WKH V ZDV SDUW RI WKH $XWRQRPRXV /DQG 9HKLFOH $/9 SURMHFW >
@ 7KH PRVW VXFFHVVIXO YLVLRQEDVHG URDG IROORZLQJ UHVHDUFK LV
FXUUHQWO\ EHLQJ FRQGXFWHG DW &DUQHJLH 0HOORQ 8QLYHUVLW\ &08 DQG LQ *HUPDQ\ > @
7KH &08 DSSURDFK XVHV QHXUDO QHWZRUNV ZKLOH WKH *HUPDQV DUH XVLQJ PRUH FODVVLFDO YLVLRQ
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
WHFKQLTXHV OLQH DQG VWULSH IROORZLQJ HGJH GHWHFWLRQ %RWK KDYH GHPRQVWUDWHG VXFFHVVIXO
ODWHUDO FRQWURO DW KLJKZD\ VSHHGV
PSK SOXV
7KH 1DWLRQDO ,QVWLWXWH RI 6WDQGDUGV 1,67
KDV DOVR FRQGXFWHG VRPH YLVLRQEDVHG URDG IROORZLQJ UHVHDUFK LQFOXGLQJ H[SHULPHQWDO ZRUN
ZLWK D +LJK 0RELOLW\ 0XOWLSXUSRVH :KHHOHG 9HKLFOH +00:9 ^ WKH $UP\ MHHS
6XPPDU\ DQG &RQFOXVLRQV $ VXPPDU\ RI WKH KLVWRU\ RI ODWHUDO FRQWURO UHVHDUFK DSSHDUV LQ 7DEOH
0DQ\ RI WKH
FRQFHSWV SRSXODU WRGD\ RSWLPDO FRQWURO DQG YHORFLW\ JDLQVFKHGXOLQJ KDYH WKHLU RULJLQV LQ
WKH HDUO\ UHVHDUFK 7KLV LV VRPHZKDW GULYHQ E\ WKH UHTXLUHPHQWV DQG SUREOHPV HQFRXQWHUHG
ZKHQ GHVLJQLQJ D ODWHUDO FRQWURO V\VWHP 7DEOH VXPPDUL]HV WKH EDVLF UHTXLUHPHQWV DQG
SUREOHPV
$V VHHQ LQ 7DEOH WKHUH DUH PDQ\ XQVROYHG SUREOHPV
7KHVH LQFOXGH GHDOLQJ ZLWK
QRQOLQHDULWLHV DQG WLPH YDU\LQJ SDUDPHWHUV $OWKRXJK JDLQVFKHGXOLQJ LV RIWHQ XVHG WR VROYH
WKH YHORFLW\ GHSHQGHQW SUREOHPV WKHUH DUH QR JXDUDQWHHV RI VWDELOLW\ 7KHUHIRUH H[WHQVLYH
VLPXODWLRQ DQG nHOG WHVWLQJ PXVW EH FRQGXFWHG WR HQVXUH WKH VWDELOLW\ RI D JDLQVFKHGXOLQJ
FRQWURO V\VWHP $GDSWLYH FRQWURO FDQ EH DSSOLHG WR VROYH VRPH RI WKH WLPH YDU\LQJ LVVXHV
EXW WKHUH DUH QR SHUIRUPDQFH JXDUDQWHHV ZKLOH WKH V\VWHP LV DGDSWLQJ
7KLV FDQ OHDG WR
RVFLOODWLRQV DQG LQ WKH FDVH RI VDWXUDWLRQ RI WKH VWHHULQJ DFWXDWRU LQVWDELOLW\ 5REXVW FRQWURO
WHFKQLTXHV FDQ JXDUDQWHH VWDELOLW\ IRU D ZLGH UDQJH RI SDUDPHWHU FKDQJHV EXW SHUIRUPDQFH
PD\ YDU\ JUHDWO\
,Q VXPPDU\ DOWKRXJK WKHUH KDV EHHQ D VLJQLnFDQW DPRXQW RI UHVHDUFK
RQ ODWHUDO FRQWURO RYHU WKH ODVW \HDUV WKH ?LGHDO VROXWLRQ VWLOO GRHV QRW H[LVW 7KHUHIRUH
WKLV GLVVHUWDWLRQ PDNHV D FRQWULEXWLRQ E\ H[SORULQJ WKH PHULWV RI UREXVW FRQWUROOHUV ZKLFK
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
'HVLJQ 5HTXLUHPHQWV q
PLQLPL]H ODWHUDO HUURU
q
IXQFWLRQ RYHU D ZLGH UDQJH RI SDUDPHWHU FKDQJHV YHORFLW\ FRUQHULQJ VWLmQHVV PDVV HWF
q
JRRG ULGH FRPIRUW
q
JUDFHIXO GHJUDGDWLRQ DQG UREXVWQHVV WR VHQVRU DFWXDWRU DQG FRQWUROOHU IDXOWV
'LpFXOWLHV q
GHYHORSLQJ D VXLWDEOH PRGHO LV WRXJK PRVW FRQWUROOHU GHVLJQV DUH SHUIRUPHG XVLQJ D OLQ
HDUL]HG WZR '2) ELF\FOH PRGHO
SXUSRVHV
+LJKHU RUGHU QRQOLQHDU PRGHOV DUH XVHG IRU VLPXODWLRQ
7KHVH LQFOXGH WHUPV IRU UROO VWHHULQJ DQG WLUH PRGHOV
6WLOO WKHVH PRGHOV DUH
QRW YDOLG IRU DOO PRGHV RI RSHUDWLRQ 7KH QRQOLQHDULWLHV DUH DOVR GLpFXOW WR GHDO ZLWK XVLQJ
PRGHUQ FRQWURO WHFKQLTXHV
q
V\VWHP LV WLPH YDU\LQJ SDUDPHWHUV OLNH YHORFLW\ FRUQHULQJ VWLmQHVV PDVV HWF
q
VRPH SDUDPHWHUV DUH QRW HDVLO\ PHDVXUHG OLNH FRUQHULQJ VWLmQHVV DQG ODWHUDO YHORFLW\ UH
TXLULQJ VRPH VRUW RI HVWLPDWLRQ
7DEOH 6XPPDU\ RI &RQWUROOHU 'HVLJQ 5HTXLUHPHQWV DQG 'LpFXOWLHV
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
FDQ RYHUFRPH PDQ\ RI WKH SUREOHPV DVVRFLDWHG ZLWK RWKHU FRQWUROOHUV ZKLOH VWLOO XVLQJ D
n[HG FRQWURO ODZ
7KH QH[W FKDSWHU GLVFXVVHV UREXVW FRQWURO RI SODQWV ZLWK XQVWUXFWXUHG DGGLWLYH SHUWXU
EDWLRQV LQ WKH IUHTXHQF\GRPDLQ
&+$37(5 5(9,(: 2) /$7(5$/ 9(+,&/( &21752/ 5(6($5&+
3URJUDP b T aV S a V @n n GVL GL
ZKHUH
L
b
P b
P
V mL
5HRUJDQL]LQJ HTXDWLRQ \LHOGV
n n n >T aV @n n GVL GL
XV
wnn n n GVL SaV n GL
V mL
ZKHUH
L
V mL
LV GHnQHG DV
TaV UP V
XV
7KHUHIRUH
n n n >XV @n n GVL GL
n n n >T aV UP V @n n GVL GL
V mL
ZKHUH
L
P
V mL
b
8VLQJ HTXDWLRQ HTXDWLRQ PD\ EH ZULWWHQ DV
n n n >XV @n L n GV GL
V mL
GL
GVL
n
w UP V nn n
SaV n
ZKHUH
V mL
L
P
b
(TXDWLRQ LV LPSRUWDQW EHFDXVH LW DOORZV WKH FDOFXODWLRQ RI WKH GHVLUHG GHULYDWLYHV RI
XV
DW WKH LQWHUSRODWLRQ SRLQW IURP NQRZQ LQIRUPDWLRQ T aV KDV QRW EHHQ FRQVWUXFWHG \HW
&+$37(5 52%867 &21752/
,Q DGGLWLRQ WR WKH LQWHUSRODWLRQ FRQGLWLRQV SODFHG RQ WKH 6%5 IXQFWLRQ
PD\ DOVR EH SODFHG RQ WKH UHODWLYH GHJUHH RI
XV
WKH FRQWUROOHU FDQ EH H[SUHVVHG LQ WHUPV RI
FV
7KH FRQWUROOHU LV SURSHU RQO\ LI
TV
TV
WR PDNH WKH FRPSHQVDWRU SURSHU )URP
TV
UP V
b SV TV
LV SURSHU )URP DQG
%V XV
UP V
WR EH SURSHU WKH UHODWLYH GHJUHH RI
WR WKH UHODWLYH GHJUHH RI
FRQVWUDLQWV
TV
TV
,Q RUGHU IRU
XV
XV
PXVW EH JUHDWHU WKDQ RU HTXDO
7KH 1HYDQOLQQD3LFN LQWHUSRODWLRQ GLVFXVVHG LQ WKH QH[W
VHFWLRQ JHQHUDOO\ \LHOGV D IXQFWLRQ ZLWK UHODWLYH GHJUHH 7KHUHIRUH LI WKH UHODWLYH GHJUHH
RI
UP V
LV JUHDWHU WKDQ LQWHUSRODWLRQ FRQGLWLRQV DW
DUH UHTXLUHG IRU
UHODWLYH GHJUHH JUHDWHU WKDQ RU HTXDO WR WKH UHODWLYH GHJUHH RI
FRQGLWLRQV DW
HQVXUH WKDW
TV
UP V
XV
WR KDYH D
7KHVH LQWHUSRODWLRQ
LV SURSHU
,QWHUSRODWLRQ 7KHRU\ ,QWHUSRODWLRQ WKHRU\ LV XVHG WR JHQHUDWH D IXQFWLRQ
FRQGLWLRQV
XmL
nL
IRU
L
P
XV
ZKLFK PHHWV WKH LQWHUSRODWLRQ
([DPSOHV LQFOXGH /DJUDQJH LQWHUSRODWLRQ RI UDWLRQDO
WUDQVIHU IXQFWLRQV >@ LQWHUSRODWLRQ RI SRVLWLYH UHDO IXQFWLRQV > @ DQG LQWHUSRODWLRQ RI
UDWLRQDO 6FKXU IXQFWLRQV ^ WKH FODVVLFDO 1HYDQOLQQD3LFN SUREOHP > @ $SSOLFDWLRQV
RI WKH 1HYDQOLQQD3LFN LQWHUSRODWLRQ SUREOHP LQ FLUFXLW DQG V\VWHP WKHRU\ DUH GHVFULEHG LQ
>@
7KH UREXVW FRQWURO SUREOHP SUHVHQWHG LQ WKH SUHYLRXV VHFWLRQ UHTXLUHV LQWHUSRODWLRQ
ZLWK 6%5 IXQFWLRQV :KHQ WKH LQWHUSRODWLRQ SRLQWV DUH RQ WKH UHDO D[LV WKH 1HYDQOLQQD
&+$37(5 52%867 &21752/
3LFN DSSURDFK \LHOGV 6%5 IXQFWLRQV
2WKHUZLVH HTXDWLRQ PD\ EH XVHG WR REWDLQ
ERXQGHG UHDO IXQFWLRQV IURP 6FKXU IXQFWLRQV
Z%5 V
V @ x6FKXU x >Z6FKXU V Z
$ PRGLnHG YHUVLRQ RI WKH 1HYDQOLQQD3LFN DOJRULWKP ZKLFK GLUHFWO\ JLYHV ERXQGHG UHDO
IXQFWLRQV LV GHVFULEHG LQ >@
7KH LQWHUSRODWLRQ RI IXQFWLRQV DQDO\WLF LQ WKH XQLW FLUFOH ZLWK D PRGXOXV QRW JUHDWHU
WKDQ
0
LV GHVFULEHG LQ JUHDW GHWDLO LQ >@
)URP >@ LQWHUSRODWLRQ LQ WKH XQLW FLUFOH LV
UHGXFHG IURP WKH SUREOHP RI nQGLQJ D IXQFWLRQ
D IXQFWLRQ
]
Z ]
WKDW WDNHV RQ
Pb
Z]
WKDW WDNHV RQ
P
JLYHQ YDOXHV WR nQGLQJ
JLYHQ YDOXHV XVLQJ WKH PDSSLQJ EHORZ 7KH YDULDEOH
ZLOO EH XVHG IRU IXQFWLRQV DQDO\WLF LQ WKH XQLW FLUFOH ZKLOH WKH YDULDEOH
V
ZLOO EH XVHG IRU
IXQFWLRQV DQDO\WLF LQ WKH ULJKWKDOISODQH
Z mN
ZN
s 0
ZN
0
t
b Z
x Z bZ N
ZKHUH
u x mN bm N mN b m
P
Z mL
ZL
7KLV JLYHV D UHFXUUHQW PHWKRG IRU WKH JHQHUDO VROXWLRQ WR WKH SUREOHP VKRZQ E\ DQG
Y
ZN
s ZY mN
ZY ]
0
Y>
ZN
0
s 0
Y >
b ZY
Y>
xY bZ
t
ZY>] Y>
ZY>] b ZY 0
Y>
xY bZ
u xY ] bm N ] b mY
ZY > ]
t
Y Y
P
u xY ] bm Z ] s Z] ] b mY
(TXDWLRQ LV XVHG WR UHGXFH WKH LQWHUSRODWLRQ SUREOHP UHFXUVLYHO\ XQWLO WKHUH LV RQO\
RQH LQWHUSRODWLRQ SRLQW
7KHQ HTXDWLRQ LV XVHG WR EDFN RXW WR WKH VROXWLRQ
Z]
(TXDWLRQV DQG DUH FRQFHUQHG ZLWK LQWHUSRODWLRQ RI IXQFWLRQV DQDO\WLF
&+$37(5 52%867 &21752/
0
LQVLGH WKH XQLW FLUFOH ,Q RUGHU WR JHQHUDWH ERXQGHG
DQG ZLWK PRGXOXV QRW JUHDWHU WKDQ
UHDO IXQFWLRQV DQDO\WLF LQ WKH ULJKWKDOISODQH WKH ELOLQHDU PDSSLQJ
Vb
]
V
PD\ EH XVHG WR PDS WKH XQLW FLUFOH LQWR WKH ULJKWKDOISODQH $OVR WKH ERXQG
0
LQ HTXDWLRQV
DQG HTXDOV
8VLQJ WR PRGLI\ FKDQJHV WKH DQDO\WLF UHJLRQ WR WKH ULJKWKDOISODQH DQG
\LHOGV
X V
X V b X
s
t
x bX X V
Vm x
ut
V b m
m m x
t
u
u V
mN N
P
RU
X V
s
X V b X
HMt
V b m
x X V bX
WDQ
GRHV QRW DmHFW WKH PDJQLWXGH RI
ZKLOH VWLOO JXDUDQWHHLQJ WKDW
X V
HMt V ,P
>
t
ZKHUH
7KH
Vm x
X V
mN N
P
m
5H
m
7KHUHIRUH PD\ EH ZULWWHQ DV
LV D 6FKXU IXQFWLRQ
X V
s
X V b X
t
Vm x
u
V b m
x XV bX
7KH VLPSOHU IRUP RI HTXDWLRQ LV W\SLFDOO\ XVHG 7KH HTXDWLRQV WKDW FKDUDFWHUL]H WKH
JHQHUDO VROXWLRQ ZKLFK LV DQDO\WLF LQVLGH WKH XQLW FLUFOH DQG PDS WR HTXDWLRQV
DQG IRU WKH JHQHUDO VROXWLRQ ZKLFK LV DQDO\WLF LQ WKH ULJKWKDOISODQH
Y
XN
s XY V MV mN
t
Y >
XY>V b XY
Y >
xY bX
XY>V
s
r
N
V mN
Y
XY
Y P
s
V b mY XY V V m x r s Y V b mY Y XYV X x Y V m x Y Y
XY V
unn n n V b mY n Vm xY
&+$37(5 52%867 &21752/
m
X
Xm
ccc
m n
X m
X
n
c c c XP
XmP
ccc
X m
X
mP
XP
nP
X mP
P>
XP
XP> mP
X V X V
XP> V
)LJXUH )HQ\YHV $UUD\
7KH LQWHUSRODWLRQ SUREOHP ERRNNHHSLQJ LV VLPSOLnHG E\ XVLQJ WKH VR FDOOHG ?)HQ\YHV DUUD\
VKRZQ LQ )LJXUH >@
/HPPD
>@ 7KHUH LV D VWULFWO\ ERXQGHG UHDO 6%5 VROXWLRQ WR WKH 1HYDQOLQQD3LFN
SUREOHP LI DQG RQO\ LI DOO WKH HOHPHQWV RI WKH )HQ\YHV DUUD\ DUH VWULFWO\ OHVV WKDQ RQH LH
n n n Y n nXN n
/HPPD
>@ ,I DQ HOHPHQW RI WKH )HQ\YHV DUUD\ LV HTXDO WR RQH WKHQ D ERXQGHG
UHDO %5 VROXWLRQ H[LVWV RQO\ LI WKH ZKROH URZ RI WKH )HQ\YHV DUUD\ KDV WHUPV HTXDO WR RQH
$Q HTXLYDOHQW PHWKRG IRU GHWHUPLQLQJ WKH H[LVWHQFH RI D VROXWLRQ WR WKH 1HYDQOLQQD3LFN
SUREOHP LV WR ORRN DW WKH 3LFN PDWUL[
3
3
VKRZQ EHORZ >@
>n nx m mx
>nP nx mP mx
ccc
ccc
>n nxP m mxP
>nP nxP mP mxP
&+$37(5 52%867 &21752/
/HPPD LI WKH PDWUL[
3
>@ 7KH 1HYDQOLQQD3LFN SUREOHP LV VROYDEOH IRU 6%5 IXQFWLRQV LI DQG RQO\
LV SRVLWLYH GHnQLWH
$Q DSSOLFDWLRQ RI WKH 1HYDQOLQQD3LFN LQWHUSRODWLRQ WKHRU\ DSSOLHG WR WKH UREXVW FRQWURO
SUREOHP LV GHVFULEHG LQ ([DPSOH
([DPSOH ^ 5REXVW &RQWURO RI 3ODQW ZLWK 5HODWLYH 'HJUHH *LYHQ WKH IROORZLQJ XQVWDEOH SODQW
V V
S V
b V b V
ZLWK WKH XQFHUWDLQW\ RI WKH SODQW JLYHQ E\
UV
V V
V V
)LQG WKH UREXVWO\ VWDELOL]LQJ FRPSHQVDWRU
6WHS DQG
^ &RPSXWH
m
UP V Sa V
WKHUHIRUH
% V
DQG
% V
%V S a V
UV
6WHS RI
S V
b V b V
V V
FDQ EH ZULWWHQ
S a V
6LQFH
m
FDQ EH ZULWWHQ
% V
*LYHQ
/RRNLQJ DW WKH XQVWDEOH SROHV DUH
S V %V
V V
V V
LV D VWDEOH PLQLPXP SKDVH SURSHU WUDQVIHU IXQFWLRQ
^ )LQG DQ 6%5 IXQFWLRQ
XV
VXFK WKDW
XmL
nL
LQ WKH 5+3 6ROYH WKH 1HYDQOLQQD3LFN SUREOHP
UP V
UP mL Sa mL
UV
ZKHUH
)LUVW FDOFXODWH
mL
DUH WKH SROHV
XmL
DQG WKHQ
&+$37(5 52%867 &21752/
m
m
X V
X V
)LJXUH )HQ\YHV $UUD\ IRU ([DPSOH
FRQVWUXFW WKH )HQ\YHV DUUD\
UP mL
XmL 1RWH WKDW
XmL
SamL
LV D FRQVWDQW IRU WKLV FDVH EHFDXVH RI WKH FKRLFH RI
UP V
7KH FRUUHVSRQGLQJ
)HQ\YHV DUUD\ FRQVWUXFWHG XVLQJ LV VKRZQ LQ )LJXUH 7KH 6%5 IXQFWLRQ
LQWHUSRODWH WR DW
V
7KHUHIRUH D VXLWDEOH \HW DUELWUDU\ FKRLFH RI
XV
V
PXVW
LV
Vb
XV
8VLQJ
X V
XV
LV
XV $QRWKHU SRVVLEOH VROXWLRQ IRU
bV V b
XV
V
X V ZKLFK PHHWV DOO RI
7KLV FKRLFH LV REWDLQHG LI
XV
V WKH LQWHUSRODWLRQ FRQGLWLRQV LV
XV
LV XVHG LQ WKH )HQ\YHV $UUD\ RU E\ LQVSHFWLRQ 7KLV
VROXWLRQ KRZHYHU \LHOGV DQ LQnQLWH JDLQ FRPSHQVDWRU ZKLFK VWDELOL]HV WKH QRPLQDO SODQW
EXW LV LPSUDFWLFDO WR LPSOHPHQW
6WHS
^ &RPSXWH
TV
TV
6WHS
^ &RPSXWH
% V XV UP V
b V b V
V V
bV V b V
V
FV FV
TV
b SV TV
bV V b
V V
&+$37(5 52%867 &21752/
7KH FKDUDFWHULVWLF SRO\QRPLDO RI WKH QRPLQDO FORVHGORRS V\VWHP LV
V
V ZKLFK LV
+XUZLW] DV H[SHFWHG
UP V
,Q WKH SUHYLRXV H[DPSOH WKH UHODWLYH GHJUHH RI
ZDV HTXDO WR
7KHUHIRUH QR
LQWHUSRODWLRQ SRLQWV DW LQnQLW\ ZHUH UHTXLUHG 7KH FDVH UHTXLULQJ DQ LQWHUSRODWLRQ SRLQW DW
LQnQLW\ LV VKRZQ LQ ([DPSOH
([DPSOH ^ 5REXVW &RQWURO ZLWK 5HODWLYH 'HJUHH RI 728 *LYHQ WKH IROORZLQJ XQVWDEOH SODQW
S V
V
b V b V
ZLWK WKH XQFHUWDLQW\ RI WKH SODQW JLYHQ E\
UV
V
V V
)LQG WKH UREXVWO\ VWDELOL]LQJ FRPSHQVDWRU
6WHS m
^ &RPSXWH
WKHUHIRUH
UP V S a V
% V
DQG
% V
%V S a V
UV
b V b V
V V
S V %V
V
UP V
V V
LV D VWDEOH PLQLPXP SKDVH SURSHU WUDQVIHU IXQFWLRQ
UHODWLYH GHJUHH RI
FDQ EH ZULWWHQ
S a V
6LQFH
m
FDQ EH ZULWWHQ
% V
*LYHQ
/RRNLQJ DW WKH XQVWDEOH SROHV DUH
UP V
UV
1RWH WKDW WKH
LV ZKLFK DGGV DQ DGGLWLRQDO LQWHUSRODWLRQ FRQGLWLRQ DW LQnQLW\
&+$37(5 52%867 &21752/
m
m
m
XV
b
XV
b
XV
)LJXUH )HQ\YHV $UUD\ IRU ([DPSOH
6WHS RI
S V
^ )LQG DQ 6%5 IXQFWLRQ
XV
VXFK WKDW
XmL
UP mL Sa mL
nL
LQ WKH 5+3 6ROYH WKH 1HYDQOLQQD3LFN SUREOHP
ZKHUH
)LUVW FDOFXODWH
mL
DUH WKH SROHV
XmL
DQG WKHQ
FRQVWUXFW WKH )HQ\YHV DUUD\
UP mL
XmL 1RWH WKDW
SamL
XmL LV D FRQVWDQW IRU WKLV FDVH EHFDXVH RI WKH FKRLFH RI UP V
$OVR EHFDXVH
UP V
KDV UHODWLYH GHJUHH WKHUH LV DQ DGGLWLRQDO LQWHUSRODWLRQ SRLQW DW LQnQLW\ 7KH FRUUHVSRQGLQJ
)HQ\YHV DUUD\ LV VKRZQ LQ )LJXUH 7KH 6%5 IXQFWLRQ
LQnQLW\ 7KHUHIRUH D VXLWDEOH \HW DUELWUDU\ FKRLFH RI
X V
8VLQJ
XV
XV
X V
PXVW LQWHUSRODWH WR DW
LV
bV b V
LV
X V
8VLQJ
X V
V b V
V V
LV
XV
1RWH WKDW WKH UHODWLYH GHJUHH RI
LQnQLW\ HQVXULQJ WKDW
TV
XV X V
LV SURSHU
V
V
V V V
LV ZKLFK LV D UHVXOW RI WKH LQWHUSRODWLRQ FRQGLWLRQ DW
&+$37(5 52%867 &21752/
6WHS
^ &RPSXWH
TV % V XV
TV
6WHS
^ &RPSXWH
UP V
b V b V
V
V
V
V V V
FV FV
V
TV
b SV TV
V
V V
7KH FKDUDFWHULVWLF SRO\QRPLDO RI WKH QRPLQDO FORVHGORRS V\VWHP LV V
V
V
ZKLFK LV +XUZLW] DV H[SHFWHG
7KH SUHYLRXV WZR H[DPSOHV KDYH VKRZQ KRZ 1HYDQOLQQD3LFN LQWHUSRODWLRQ FDQ EH XVHG
WR VROYH WKH UREXVW FRQWURO SUREOHP ZLWK XQVWUXFWXUHG DGGLWLYH SHUWXUEDWLRQV /LPLWDWLRQV
RI WKH DSSURDFK LQFOXGH QRW EHLQJ DEOH WR KDQGOH SROHV RQ WKH
PXOWLSOLFLW\ $Q DSSURDFK IRU KDQGOLQJ RQH W\SH RI SROH RQ WKH
LQWHJUDWRU LV RXWOLQHG LQ >@
MZ
MZ
D[LV DQG SROHV ZLWK
D[LV VSHFLnFDOO\ D VLQJOH
7KLV LQYROYHV GLYLGLQJ WKH LQWHJUDWRU RXW RI WKH QRPLQDO
SODQW DQG WKH SODQW XQFHUWDLQW\ DQG DGGLQJ DQ LQWHUSRODWLRQ SRLQW DW WKH RULJLQ
7KH
LQWHUSRODWLRQ SRLQW DW WKH RULJLQ PXVW EH KDQGOHG OLNH WKH SRLQW DW LQnQLW\ LQ ([DPSOH
7KH LQWHUSRODWLRQ SRLQWV DW ]HUR DQG LQnQLW\ PXVW EH LQ WKH ODVW WZR FROXPQV RI WKH )HQ\YHV
DUUD\ VR WKDW WKH ODVW IXQFWLRQ
XQ> V
FDQ EH FUDIWHG XVLQJ WKH HTXDWLRQ EHORZ
XQ> V
%\ VHOHFWLQJ
p
DQG
w
pV w
V
WKH LQWHUSRODWLRQ FRQGLWLRQV IRU
XQ>
DW ]HUR DQG LQnQLW\ FDQ EH PHW
SURYLGHG WKHUH LV D VROXWLRQ WR WKH 1HYDQOLQQD3LFN SUREOHP
2QH DSSURDFK IRU KDQGOLQJ LQWHUSRODWLRQ SRLQWV RQ WKH
MZ
D[LV LV GHVFULEHG LQ >@ 7KLV
LQYROYHV XVLQJ D PDSSLQJ ZKLFK LQWHUSRODWHV SRVLWLYHUHDO IXQFWLRQV RQ WKH
MZ
D[LV 7KHQ
&+$37(5 52%867 &21752/
WKH SRVLWLYH UHDO IXQFWLRQ LV PDSSHG WR D ERXQGHG UHDO IXQFWLRQ
LQWHUSRODWLRQ SRLQWV ZLWK PXOWLSOLFLW\ RQ WKH
MZ
$ PHWKRG IRU KDQGOLQJ
D[LV ZDV QRW GLVFXVVHG
$ JHQHUDO DSSURDFK IRU KDQGOLQJ LQWHUSRODWLRQ SRLQWV RQ WKH
MZ
D[LV LV RXWOLQHG LQ WKH
QH[W VHFWLRQ 7KLV DSSURDFK LV DOVR DEOH WR GHDO ZLWK PXOWLSOLFLW\ ZKLFK LV GHVFULEHG LQ D
VXEVHTXHQW VHFWLRQ
,QWHUSRODWLRQ 3RLQWV RQ WKH MZ $[LV 7KH FODVVLFDO VROXWLRQ RI WKH 1HYDQOLQQD3LFN LQWHUSRODWLRQ SUREOHP LV FRQFHUQHG ZLWK LQ
WHUSRODWLQJ IXQFWLRQV DQDO\WLF KDYLQJ QR SROHV LQ WKH XQLW FLUFOH RU WKH ULJKWKDOISODQH
)XQFWLRQV DQDO\WLF LQ WKH XQLW FLUFOH DUH XVHIXO LQ GLVFUHWHWLPH SUREOHPV ZKLOH IXQFWLRQV DQ
DO\WLF LQ WKH ULJKWKDOISODQH DUH XVHIXO IRU FRQWLQXRXVWLPH SUREOHPV 7KH ELOLQHDU PDSSLQJ
EHORZ LV W\SLFDOO\ XVHG WR PDS WKH XQLW FLUFOH LQWR WKH ULJKWKDOISODQH
]
Vb
V
)URP WKH SUHYLRXV VHFWLRQ WKH PDSSLQJ XVHG IRU LQWHUSRODWLRQ RI IXQFWLRQV DQDO\WLF LQ WKH
ULJKWKDOISODQH LV JLYHQ E\
X V
X V b X
x bX X V
t
Vm x
u
V b m
$OWKRXJK WKLV PDSSLQJ LV YHU\ XVHIXO LW KDV VHYHUDO VKRUWFRPLQJV
LQWHUSRODWH SRLQWV ZLWK PXOWLSOLFLW\ ZLWKRXW PRGLnFDWLRQ
WHUSRODWH RQ WKH
MZ
D[LV
,W FDQQRW EH XVHG WR
,W DOVR FDQQRW EH XVHG WR LQ
)LQDOO\ DOWKRXJK WKH IXQFWLRQV JHQHUDWHG DUH DQDO\WLF LQ WKH
ULJKWKDOISODQH LW LV VRPHWLPHV GHVLUDEOH WR JHQHUDWH IXQFWLRQV WKDW DUH DQDO\WLF LQ D UHJLRQ
RWKHU WKDQ WKH ULJKWKDOISODQH %DVHG RQ WKLV PRWLYDWLRQ D PRGLnHG PDSSLQJ LV SURSRVHG
&+$37(5 52%867 &21752/
WR RYHUFRPH WKHVH VKRUWFRPLQJV ,QVWHDG RI PDSSLQJ WKH XQLW FLUFOH LQWR WKH ULJKWKDOISODQH
D PRGLnHG YHUVLRQ RI LV XVHG WR PDS WKH XQLW FLUFOH LQWR D UHJLRQ
'
ZKLFK LQFOXGHV
WKH ULJKWKDOISODQH 7KLV LQYROYHV PRGLI\LQJ WKH ELOLQHDU PDSSLQJ DV VKRZQ EHORZ
V b b q
]
V q
$SSO\LQJ WR \LHOGV
X V
/HPPD
,I
X V
X V b X
t
Vm x
x bX XV
LV D 6FKXU IXQFWLRQ DQG
q
u
V b m
X m
X
WKHQ
X V
LV D 6FKXU
IXQFWLRQ
3URRI RI /HPPD
%HFDXVH RI WKH 0D[LPXP 0RGXOXV 7KHRUHP >@ WKH PD[LPXP
YDOXH RI WKH IXQFWLRQ RFFXUV RQ WKH ERXQGDU\ RI WKH DQDO\WLF UHJLRQ 7KLV RFFXUV DW
IRU 7KHUHIRUH LW LV QHFHVVDU\ WR GHnQH D QHZ QRUP WKH
NXV Nq s VXS MXV M V
MZ b q
+q
MZ bq
V
QRUP DV VKRZQ EHORZ
Z
%HFDXVH RI WKH 0D[LPXP 0RGXOXV 7KHRUHP WKH IROORZLQJ UHODWLRQVKLS EHWZHHQ WKH
QRUP DQG WKH VWDQGDUG
+
QRUP H[LVWV IRU IXQFWLRQV DQDO\WLF LQ WKH UHJLRQ
'
+q
VHH )LJXUH
NXV N NXV Nq 7KH XVH RI WKH
+q
QRUP PDNHV WKH UREXVW VWDELOLW\ FRQGLWLRQ PRUH FRQVHUYDWLYH DV
LQ PDJQLWXGH %\ LQFUHDVLQJ
XV
q
WKH OLNHOLKRRG RI D VROXWLRQ H[LVWLQJ LV GHFUHDVHG
LV D 6FKXU IXQFWLRQ LI DQG RQO\ LI
q
JURZV
&+$37(5 52%867 &21752/
XV
+
Z
SURYHV
MZ b q
x V X V w V bX
%\ DVVXPSWLRQ
DQG
7KH SROH
XV
x M MX
V
m
DQG
Z ,5
MX V M
7KHUHIRUH
x X V bX
IRU
V
LQ WKH 5+3 LV FDQFHOHG E\ WKH LQWHUSRODWLRQ FRQGLWLRQ DW
MZ m
b q
7KLV
+
1H[W IRU
V
MZ b q
x V X V bX
FDQ EH ZULWWHQ DV
r
x V X V bX
sb c b MX M b MXV M n n n n X V x n b X n
EHFDXVH
n n nV m x q n n n s ZKHQ V n Vbm n
MZ b q
(TXDWLRQ LV QRQQHJDWLYH VLQFH E\ DVVXPSWLRQ
Z ,5
MX M
DQG
MXV M
7KH LQYHUVH PDSSLQJ LV JLYHQ E\
X V
/HPPD X m
X
,I
X V LV
r
X V
D 6FKXU IXQFWLRQ WKHQ
LQGHSHQGHQWO\ RI
s
V b m Vm x q r s V b m X X V x Vm x q
X
X V LV DOVR D 6FKXU IXQFWLRQ
,Q DGGLWLRQ
X V
3URRI RI /HPPD X V
LV D 6KXU IXQFWLRQ LI DQG RQO\ LI
&+$37(5 52%867 &21752/
jw
−ε
σ
Region D
)LJXUH $QDO\WLF 5HJLRQ
XV
+ MZ b q
x V X V w V bX
)URP WKH IDFW WKDW
X V
7KHUHIRUH
'
XV
LV 6FKXU
X X V x
t
Z ,5
x MX M
u
V b m Vm x
DQG WKH 0D[LPXP 0RGXOXV 7KHRUHP
q
V
MZ b q
V
+ MZ b q
x V X V FDQ EH ZULWWHQ bX r s c b b MX x M b MX V M V bX x V X V n n n n x X V n n X
1H[W IRU
Z ,5
ZKLFK LV QRQQHJDWLYH EHFDXVH
MX M
DQG
X V
MZ b q
Z ,5
E\ DVVXPSWLRQ
$Q DSSOLFDWLRQ RI WKH PDSSLQJ GHVFULEHG E\ WR WKH UREXVW FRQWURO SUREOHP LV
VKRZQ LQ ([DPSOH %\ XVLQJ WKLV PDSSLQJ LW LV QRZ SRVVLEOH WR KDQGOH SROHV RQ WKH
D[LV
MZ
&+$37(5 52%867 &21752/
([DPSOH ^ 5REXVW &RQWURO RI D 3ODQW ZLWK 3ROHV RQ WKH MZ $[LV *LYHQ WKH IROORZLQJ SODQW
V V V
SV
V V
ZLWK WKH XQFHUWDLQW\ RI WKH SODQW JLYHQ E\
V V V V
UV
V V V
)LQG WKH UREXVWO\ VWDELOL]LQJ FRPSHQVDWRU
,W LV DVVXPHG WKDW WKH SROH RQ WKH
MZ
D[LV LV
SUHVHUYHG XQGHU SHUWXUEDWLRQV
6WHS
^ &RPSXWH
UP V S a V
DQG
V UP
UV
V
V UP
:ULWH
V V V V
V V V V
V
S V
V V V
SV
^ )LQG DQ 6%5 IXQFWLRQ
XV
V
%HFDXVH WKH SODQW KDV QR SROHV LQ WKH RSHQ 5+3
RI
V V
LV D PLQLPXP SKDVH IXQFWLRQ 7KHQ S a V FDQ EH ZULWWHQ
Sa V
6WHS
V V V
V UP ZKHUH
%V
VXFK WKDW
%V
XmL
nL
UP mL Sa mL
ZKHUH
mL
DUH WKH SROHV
LQ WKH FORVHG 5+3 6ROYH WKH 1HYDQOLQQD3LFN SUREOHP
)RU WKLV H[DPSOH WKHUH DUH QR LQWHUSRODWLRQ SRLQWV LQ WKH RSHQ 5+3 EHFDXVH WKH SODQW
KDV QR SROHV LQ WKH RSHQ 5+3 +RZHYHU WKHUH DUH WZR LQWHUSRODWLRQ SRLQWV RQ WKH
m
M
DQG
m
MZ
D[LV
bM XmL
mL
mL
&+$37(5 52%867 &21752/
M
m
bM
m
M
>M
XV
q>M M
XV
)LJXUH )HQ\YHV $UUD\ IRU ([DPSOH
HYDOXDWLQJ RQH REWDLQV
XM
M
XbM
bM
8VLQJ DQG WKH FRUUHVSRQGLQJ )HQ\YHV DUUD\ LV VKRZQ LQ )LJXUH ,Q RUGHU
IRU D VROXWLRQ WR H[LVW DOO WKH HOHPHQWV RI WKH )HQ\YHV DUUD\ PXVW EH OHVV WKDQ RU HTXDO WR
LQ PDJQLWXGH 7KLV SXWV WKH IROORZLQJ FRQVWUDLQW RQ WKH VL]H RI
q
6ROYLQJ IRU
X V
LQ WHUPV RI
XV
X V
q
q
RQH REWDLQV
V> q b M @ >q b M b M q@ V> q b M q@ >q b M M q@
8VLQJ RQH FDQ VDIHO\ FKRRVH DQ
q
XV
XV LV D
DQG EH JXDUDQWHHG WKDW D VROXWLRQ WR WKH
1HYDQOLQQD3LFN LQWHUSRODWLRQ SUREOHP H[LVWV 7KLV \LHOGV WKH IROORZLQJ
%HFDXVH
V> b M @ >b b M @ V> b M @ > b M @
XV
6FKXU IXQFWLRQ HTXDWLRQ PXVW EH XVHG WR JHQHUDWH DQ 6%5 IXQFWLRQ
7KLV \LHOGV
X V
V
V
V
V
&+$37(5 52%867 &21752/
6WHS
^ &RPSXWH
TV
6WHS
TV
XVLQJ HTXDWLRQ
V
%V XV
FV
FV
V V
V
V V V V V V
UV
^ &RPSXWH
7KH FRPSHQVDWRU LV VKRZQ LQ HTXDWLRQ
V
TV
b S V TV
V
V V
b V V V
1RWH WKDW WKH VWDELOL]LQJ FRPSHQVDWRU LV XQVWDEOH GXH WR WKH SROH ORFDWHG DW
V
+RZHYHU LI RQH FKHFNV WKH IRXU WUDQVIHU IXQFWLRQV LQ WKH V\VWHP ZLOO VWLOO EH LQWHUQDOO\
VWDEOH DV H[SHFWHG 7KH SROHV RI WKH FORVHGORRS QRPLQDO V\VWHP DUH DW
b
DQG
b h
M
7KH QH[W VHFWLRQ SUHVHQWV DQ DSSURDFK IRU KDQGOLQJ SODQWV ZLWK D PXOWLSOLFLW\ RI SROHV
LQ WKH ULJKWKDOISODQH
,QWHUSRODWLRQ 3RLQWV ZLWK 0XOWLSOLFLW\ )RU WKH FDVH ZKHUH WKH
mL V
DUH GLVWLQFW HTXDWLRQV DQG DUH HDVLO\ DSSOLHG
+RZHYHU IRU WKH FDVH ZKHUH WKH
EH XVHG
mL
mL V
DUH QRW GLVWLQFW HTXDWLRQV DQG PD\ QRW
7KH FDVH RI PXOWLSOLFLW\ HTXDO WR WZR LV GHVFULEHG E\ :DOVK LQ >@
DUH QRW GLVWLQFW FRQVWUDLQWV DUH IRUFHG RQ WKH GHULYDWLYHV RI
XV
:KHQ WKH
$ VLPSOH DSSURDFK WR
KDQGOH SRLQWV ZLWK PXOWLSOLFLW\ XVLQJ D PRGLnHG )HQ\YHV DUUD\ LV GHVFULEHG E\ 7KHRUHP
7KHRUHP SOLFLW\
P
7KH VROXWLRQ WR WKH 1HYDQOLQQD3LFN LQWHUSRODWLRQ SUREOHP ZLWK PXOWL
LV REWDLQHG E\ FRQVWUXFWLQJ D PRGLnHG )HQ\YHV DUUD\ VKRZQ LQ )LJXUH ZKRVH
&+$37(5 52%867 &21752/
WHUPV DUH JLYHQ E\ HTXDWLRQ
XN m
ZKHUH
X N > m
m x
m
X m N b MXN>m M N> XN> V
UHSUHVHQWV WKH nUVW GHULYDWLYH RI
P
b
HYDOXDWHG DW
m
XV
2QFH WKH )HQ\YHV DUUD\ LV FRQVWUXFWHG WKH GHVLUHG IXQFWLRQ
LV REWDLQHG LQ WKH XVXDO
PDQQHU
1RWH
$OWKRXJK JLYHV WKH IRUPXOD IRU FRQVWUXFWLQJ WKH PRGLnHG )HQ\YHV $UUD\
WKH IXQFWLRQV
XN V
DUH QRW FRQVWUXFWHG XQWLO DIWHU WKH )HQ\YHV $UUD\
+RZHYHU
PD\ EH HYDOXDWHG E\ DSSO\LQJ WKH PDSSLQJ DQG GLmHUHQWLDWLQJ ,QWHUSRODWLRQ ZLWK
PXOWLSOLFLW\
P
Pb
UHTXLUHV PDWFKLQJ WKH nUVW
WKH IXQFWLRQ WKDW
XV
ZLOO PXOWLSO\
GHULYDWLYHV RI
X V
ZLWK WKH GHULYDWLYHV RI
,Q RWKHU ZRUGV HDFK DGGLWLRQDO LQWHUSRODWLRQ SRLQW
ZLWK PXOWLSOLFLW\ SODFHV FRQVWUDLQWV RQ WKH QH[W KLJKHU RUGHU GHULYDWLYH RI
3URRI RI 7KHRUHP
X V
7ZR GLmHUHQW PHWKRGV PD\ EH XVHG IRU WKH SURRI E\ LQGXFWLRQ
7KH nUVW DSSURDFK LQYROYHV DVVXPLQJ WKDW WKH LQWHUSRODWLRQ SRLQWV DUH VHSDUDWHG E\ D VPDOO
LQFUHPHQW
q
DQG WKHQ WDNLQJ WKH OLPLW DV
q
DSSURDFKHV ]HUR 7KH VHFRQG DSSURDFK LQYROYHV
DSSO\LQJ / +RSLWDO V 5XOH WR HYDOXDWH WHUPV LQ WKH )HQ\YHV $UUD\ 7KH SURRI E\ LQGXFWLRQ
XVLQJ WKH OLPLW DSSURDFK LV RXWOLQHG LQ )LJXUH DQG LV GLVFXVVHG QH[W
7KH PDSSLQJ W\SLFDOO\ XVHG WR FRQVWUXFW WKH )HQ\YHV DUUD\ LV
XY V MV mL $VVXPH WKDW WKH
mL
Y>
XY > V b XY
Y>
xY bX
t
XY > V
DUH VHSDUDWHG E\ D VPDOO LQFUHPHQW
mM
b mM
q M
unn n n V b mY n Vm xY
q
V mL
VR WKDW
P b
&+$37(5 52%867 &21752/
ccc
m
ccc
mM
mM
mP
X m
X mP
X V
XM > mM
XM > mM XM mM
q
XM > V
q
XM V
XP> mP ZKHUH
mM
b mM
q
DQG
mP
m
P
XP>V
b q
)LJXUH 0RGLnHG )HQ\YHV $UUD\
7KHQ DQ\ GLDJRQDO HOHPHQW RI WKH )HQ\YHV DUUD\
M >
XM
FDQ EH HYDOXDWHG XVLQJ HTXDWLRQ
XM mM
XM mM
7DNLQJ WKH OLPLW DV
q q
q
XM > mM
q b XM > mM
xM > mM XM > mM bX XM >mM q b XM > mM
q
q
mM
mM
mM
qm xM
q b mM
qm xM
xM > mM XM > mM bX
DSSURDFKHV ]HUR LQ HTXDWLRQ DQG QRWLQJ WKDW DOO
XM m
m x
m
q mL
m
X m b MXM > m M M >
\LHOGV
ZKLFK LV WKH VDPH UHVXOW VWDWHG E\ HTXDWLRQ
,W VKRXOG EH QRWHG WKDW WKLV DSSURDFK FDQ RQO\ DSSOLHG ZKHQ WKH GHULYDWLYHV RI
KDYH PHDQLQJ LH DUH nQLWH %HFDXVH
X V
XV
LV DQDO\WLF LQ WKH 5+3 WKLV VKRXOG QHYHU EH D
&+$37(5 52%867 &21752/ SUREOHP
7KH FDVH ZKHUH D GHULYDWLYH LV ]HUR LV HDVLO\ KDQGOHG
7KLV FDVH \LHOGV D URZ RI
WKH PRGLnHG )HQ\YHV $UUD\ ZKHUH DOO RI WKH WHUPV DUH ]HUR $ ERXQGHG UHDO IXQFWLRQ ZLWK
D PXOWLSOLFLW\ RI ]HURV DW WKH VDPH SRLQW FDQ EH FRQVWUXFWHG E\ LQVSHFWLRQ 7KLV LV VKRZQ
LQ H[DPSOH
([DPSOH ^ 5REXVW &RQWURO ZLWK 8QVWUXFWXUHG 8QFHUWDLQW\ 2 *LYHQ WKH IROORZLQJ XQVWDEOH SODQW
V V
S V
V
b
ZLWK WKH XQFHUWDLQW\ RI WKH SODQW JLYHQ E\
UV
V V
V
SaV
)LQG WKH UREXVWO\ VWDELOL]LQJ FRPSHQVDWRU
6WHS m
^ &RPSXWH
DQG
m
UP V S a V
7KHUHIRUH
DQG
% V
% V
/RRNLQJ DW WKH XQVWDEOH SROHV DUH
% V
%V S a V
UV
6WHS S V
u Vb
V
FDQ EH ZULWWHQ
V V
Sa V
6LQFH
LV D PLQLPXP SKDVH SURSHU WUDQVIHU IXQFWLRQ
^ )LQG DQ 6%5 IXQFWLRQ
XV
V
VXFK WKDW
XmL
LQ WKH 5+3 6ROYH WKH 1HYDQOLQQD3LFN SUREOHP
X
mL
FDQ EH ZULWWHQ
t
*LYHQ
m
UP V
UP mL Sa mL
UV ZKHUH
)LUVW FDOFXODWH
mL
DUH WKH SROHV RI
XmL X mL
DQG
7KHQ FRQVWUXFW WKH )HQ\YHV $UUD\
XmL
UP mL SamL
&+$37(5 52%867 &21752/
m
m
m
X V
X V
)LJXUH )HQ\YHV $UUD\ IRU ([DPSOH
X mL
X mL
7KH FRUUHVSRQGLQJ )HQ\YHV $UUD\ FRQVWUXFWHG XVLQJ LV VKRZQ LQ )LJXUH
/RRNLQJ DW WKH )HQ\YHV DUUD\ LQ )LJXUH WKHUH DUH WZR SRVVLEOH VROXWLRQV
E\ LQVSHFWLRQ
X V
VDWLVnHV WKH LQWHUSRODWLRQ FRQGLWLRQV DQG WKH FRQVWUDLQWV RQ
WKH nUVW DQG VHFRQG GHULYDWLYHV RI
JDLQ FRPSHQVDWRU
WR LPSOHPHQW
)LUVW
XV
+RZHYHU WKLV FKRLFH RI
XV
\LHOGV DQ LQnQLWH
,Q WKHRU\ WKLV VWDELOL]HV WKH SODQW EXW VXFK D FRQWUROOHU LV GLpFXOW
7KH VHFRQG SRVVLEOH VROXWLRQ PD\ EH REWDLQHG IURP WKH VHFRQG URZ RI WKH
PRGLnHG )HQ\YHV $UUD\ ,I RQH ZHUH WR FRQWLQXH WKH DUUD\ WR WKH WKLUG URZ WKH ODVW WHUP LQ
WKH DUUD\ ZRXOG DOVR EH ]HUR 8VLQJ HTXDWLRQ WKH FRQVWUDLQW RQ WKH nUVW GHULYDWLYH
RI
X V
DW
V
m
LV
X m 7KHUHIRUH
X V
PD\ EH FRQVWUXFWHG E\ LQVSHFWLRQ DQ\ ERXQGHG UHDO IXQFWLRQ ZLWK WZR
]HURV DW ZLOO VXpFH )RU WKLV H[DPSOH WKH
X V
XV V
EHORZ ZLOO EH FKRVHQ
b
V
,W VKRXOG EH QRWHG WKDW LI WKH )HQ\YHV $UUD\ LV FRPSOHWHG WR WKH WKLUG URZ WKH LQYHUVH
PDSSLQJ \LHOGV WKH FRQVWDQW VROXWLRQ
XV
7R JHW WKH RWKHU VROXWLRQ ZLWK WKH FDVH RI
]HUR GHULYDWLYHV WKH FRQVWUXFWLRQ RI WKH )HQ\YHV $UUD\ PXVW EH VWRSSHG DW WKH nUVW URZ RI
&+$37(5 52%867 &21752/
DOO ]HURV ZKHUH WKH GHULYDWLYH FRQVWUDLQWV FDQ EH HDVLO\ LQFRUSRUDWHG LQWR D UDWLRQDO IXQFWLRQ
E\ LQVSHFWLRQ 8VLQJ
X V
LV
V
X V
6WHS
^ &RPSXWH
TV
6WHS
V V V
TV
t
% V XV UP V
^ &RPSXWH
b V V
u Vb
V V
V
b V V
V
V
SaV
FV
FV
bV b V V
TV
V V
b SV TV
7KH SROHV RI WKH QRPLQDO FORVHGORRS V\VWHP DUH ORFDWHG DW
b h M DQG b
7KH FDVH RI QRQ]HUR GHULYDWLYHV LQ WKH LQWHUSRODWLRQ FRQGLWLRQV LV H[DPLQHG LQ WKH QH[W
H[DPSOH
([DPSOH ^ ,QWHUSRODWLRQ ZLWK 1RQ]HUR 'HULYDWLYHV *LYHQ WKH IROORZLQJ XQVWDEOH SODQW
SV
V V V V
b
ZLWK WKH XQFHUWDLQW\ RI WKH SODQW JLYHQ E\
UV
V V
)LQG WKH UREXVWO\ VWDELOL]LQJ FRPSHQVDWRU
V
&+$37(5 52%867 &21752/
6WHS m
^ &RPSXWH
m
DQG
UP V Sa V m
DQG
7KHUHIRUH
%V % V
/RRNLQJ DW WKH XQVWDEOH SROHV DUH
FDQ EH ZULWWHQ
t % V
*LYHQ
%V S a V
UV
6WHS RI
S V
V
FDQ EH ZULWWHQ
SaV
6LQFH
u Vb
V V V
UP V
LV D PLQLPXP SKDVH SURSHU WUDQVIHU IXQFWLRQ
^ )LQG DQ 6%5 IXQFWLRQ
XV
V
VXFK WKDW
XmL
RI WKH PXOWLSOLFLW\ WKH nUVW WZR GHULYDWLYHV RI
XV
UP mL Sa mL
nL
LQ WKH 5+3 6ROYH WKH 1HYDQOLQQD3LFN SUREOHP
UV ZKHUH
)LUVW FDOFXODWH
PXVW DOVR PDWFK
mL
DUH WKH SROHV
XmL
%HFDXVH
7KHVH LQWHUSRODWLRQ
FRQGLWLRQV DUH PHW ZKHQ WKH PRGLnHG )HQ\YHV $UUD\ LV FRQVWUXFWHG XVLQJ
7KH
)HQ\YHV $UUD\ LV VKRZQ LQ )LJXUH 8VLQJ WKH FDOFXODWLRQV UHTXLUHG WR FRQVWUXFW
WKH )HQ\YHV DUUD\ DUH RXWOLQHG EHORZ
Xm
mL mL
X mL
X
mL
X
X
mL
X
b
b mL
8VLQJ
X m
m x
m
b MXm M t
X m
b M M
X m
u
2QFH DJDLQ DSSO\LQJ \LHOGV
X m
m x
m
b MXm M
X m
&+$37(5 52%867 &21752/ +RZHYHU
X mL
PXVW EH H[SUHVVHG LQ WHUPV RI
X mL
7KLV LV REWDLQHG E\ GLmHUHQWLDWLQJ
WKH PDSSLQJ ZKLFK \LHOGV
t u XV
Vm x
V m x
x b MXm M m m n n X V X m X V m m x n n n Vm V m x x
b MX m M
X
V
V mL
6XEVWLWXWLQJ
V
m
LQWR \LHOGV
X m
8VLQJ WKH LQYHUVH PDSSLQJ DQG DUELWUDULO\ FKRRVLQJ
IRU
XV
JLYHV WKH IROORZLQJ VROXWLRQ
XV
X V
6WHS
^ &RPSXWH
^ &RPSXWH
V
V
V
TV
TV
6WHS
V
%V XV UP V
V
V
V
V V V V V
FV
FV
TV
b S V TV
t u
V
V
V V
7KH SROHV RI WKH FORVHGORRS V\VWHP ZLWK WKH QRPLQDO SODQW
b h M
b
S V
DUH ORFDWHG DW
b
DQG
$OWKRXJK WKLV DSSURDFK FDQ EH DSSOLHG IRU FDVHV RI KLJKHU PXOWLSOLFLW\
WKH DOJHEUD UHTXLUHG WR GHWHUPLQH WKH WHUPV RI WKH )HQ\YHV $UUD\ EHFRPHV UDWKHU WHGLRXV
IRU
P!
&+$37(5 52%867 &21752/
m X
m
m
X V
X
X V
X
X
X V
X
X V
)LJXUH )HQ\YHV $UUD\ IRU ([DPSOH
6XPPDU\ DQG &RQFOXVLRQ 7KLV FKDSWHU KDV UHYLHZHG WKH EDVLF WKHRU\ RI UREXVW FRQWURO XVLQJ LQWHUSRODWLRQ IRU SODQWV
ZLWK DGGLWLYH XQVWUXFWXUHG SHUWXUEDWLRQV
3ODQWV ZLWK SROHV RQ WKH
MZ
7KHUH DUH OLPLWDWLRQV WR WKH FXUUHQW WKHRU\
D[LV DQG XQVWDEOH SROHV ZLWK PXOWLSOLFLW\ JUHDWHU WKDQ FDQQRW
EH KDQGOHG ZLWK WKH H[FHSWLRQ RI D VLQJOH SROH DW WKH RULJLQ
7KLV FKDSWHU H[WHQGHG WKH
WKHRU\ E\ DOORZLQJ WKH DSSURDFK WR LQFOXGH SODQWV ZLWK SROHV RQ WKH
MZ
D[LV DV ZHOO DV SODQWV
ZLWK D PXOWLSOLFLW\ RI XQVWDEOH SROHV
3ROHV RQ WKH
MZ
D[LV DUH KDQGOHG E\ XVLQJ D VOLJKWO\ PRGLnHG PDSSLQJ
7KH FODVVLFDO
1HYDQOLQQD3LFN DOJRULWKP UHOLHV RQ D PDSSLQJ ZKLFK SURGXFHV 6%5 IXQFWLRQV DQDO\WLF LQ
WKH ULJKWKDOISODQH %HFDXVH WKH
MZ
D[LV OLHV RQ WKH ERXQGDU\ RI WKH DQDO\WLF UHJLRQ WKH
PDSSLQJ FDQQRW EH XVHG ZLWK SROHV RQ WKH
MZ
D[LV 7KH PDSSLQJ LQWURGXFHG LQ WKLV FKDSWHU
PRGLnHV WKH DQDO\WLF UHJLRQ RI WKH PDSSLQJ WR LQFOXGH VRPH RI WKH OHIWKDOISODQH ZKLFK
DOORZV LQWHUSRODWLRQ RQ WKH
MZ
D[LV
7KH FDVH RI XQVWDEOH SROHV ZLWK PXOWLSOLFLW\ LV KDQGOHG E\ XVLQJ D PRGLnHG )HQ\YHV
DUUD\ ,QWHUSRODWLRQ DW SROHV ZLWK PXOWLSOLFLW\ SODFHV FRQVWUDLQWV RQ WKH GHULYDWLYHV RI
XV
7KHVH DUH LQFRUSRUDWHG LQ WKH PRGLnHG )HQ\YHV DUUD\ 2QFH WKH PRGLnHG )HQ\YHV DUUD\ LV
&+$37(5 52%867 &21752/ FRQVWUXFWHG WKH IXQFWLRQ
XV
LV REWDLQHG LQ WKH XVXDO PDQQHU
,Q VXPPDU\ WKLV FKDSWHU KDV SUHVHQWHG WKH FXUUHQW WKHRU\ IRU UREXVW FRQWURO RI V\VWHPV
ZLWK DGGLWLYH XQVWUXFWXUHG SHUWXUEDWLRQV DQG H[WHQGHG WKH WKHRU\ WR LQFOXGH SODQWV ZLWK
D PXOWLSOLFLW\ RI XQVWDEOH SROHV DQG SROHV RQ WKH
WHFKQLTXHV WR WKH ODWHUDO FRQWURO SUREOHP
MZ
D[LV 7KH QH[W FKDSWHU DSSOLHV WKHVH
&KDSWHU 7KH /DWHUDO &RQWURO 3UREOHP 7KLV FKDSWHU DSSOLHV WKH UREXVW FRQWURO WHFKQLTXHV GHYHORSHG LQ WKH SUHYLRXV FKDSWHU WR
WKH ODWHUDO FRQWURO RI KLJKZD\ YHKLFOHV
$ ERXQG RQ WKH SODQW XQFHUWDLQW\ LV REWDLQHG E\
VLPXODWLQJ WKH FDU PRGHO DV WKH YHORFLW\ DQG FRUQHULQJ VWLmQHVV DUH YDULHG
7KH '2)
OLQHDUL]HG ELF\FOH PRGHO LV XVHG WR UHSUHVHQW WKH ODWHUDO G\QDPLFV RI WKH WHVW YHKLFOH D
*0& 6 %OD]HU
)URP &KDSWHU WKH OLQHDUL]HG PRGHO KDV D UHODWLYH GHJUHH RI ZLWK
WZR SROHV DW WKH RULJLQ 7KH WZR SROHV DW WKH RULJLQ PD\ EH KDQGOHG XVLQJ WKH LQWHUSRODWLRQ
WHFKQLTXHV GHYHORSHG LQ WKH SUHYLRXV FKDSWHU +RZHYHU WKH UHODWLYH GHJUHH RI WKH SODQW ZLOO
UHTXLUH WZR LQWHUSRODWLRQ FRQGLWLRQV DW
$Q DSSURDFK IRU KDQGOLQJ WKH WZR LQWHUSRODWLRQ
SRLQWV DW LQnQLW\ LV RXWOLQHG LQ WKLV FKDSWHU 7KH QH[W VHFWLRQ GHVFULEHV WKH SURFHVV XVHG WR
GHWHUPLQH WKH ERXQG RQ WKH SODQW XQFHUWDLQW\
&+$37(5 7+( /$7(5$/ &21752/ 352%/(0
3DUDPHWHU 1RPLQDO 9DOXH P
9[
P V
O O &U &I
NJ
,]
OA
5DQJH FRQVWDQW
NPSK
P P
b P V b NPSK
FRQVWDQW
.Q UDG
WR
NJ c P
FRQVWDQW
P
FRQVWDQW
7DEOH (VWLPDWHG 3DUDPHWHUV IRU 6 %OD]HU
9HKLFOH 0RGHOLQJ DQG 8QFHUWDLQW\ 7KH WZR GHJUHHRIIUHHGRP OLQHDUL]HG ELF\FOH PRGHO IRU D YHKLFOH V ODWHUDO G\QDPLFV SUHVHQWHG
LQ &KDSWHU ZLOO EH XVHG LQ WKLV VHFWLRQ WR PRGHO WKH WHVW YHKLFOH D *0& 6 %OD]HU 7KH
HVWLPDWHG QRPLQDO SDUDPHWHUV IRU WKH %OD]HU DQG WKH H[SHFWHG UDQJH RI YDOXHV DUH OLVWHG
LQ 7DEOH
7KH QRPLQDO VSHHG RI
VSHHGV FRUUHVSRQG WR
NPSK
DQG
P V
NPSK
FRUUHVSRQGV WR
NPSK
ZKLOH WKH H[WUHPH
UHVSHFWLYHO\ 7KHVH YDOXHV ZHUH FKRVHQ EHFDXVH
WKH LQLWLDO nHOG WHVWLQJ ZLOO EH FRQGXFWHG DW UHODWLYHO\ ORZ VSHHGV
6LPXODWLRQ UHVXOWV IRU
KLJKZD\ VSHHGV DSSHDU LQ >@
8VLQJ WKH YDOXHV LQ 7DEOH WKH QRPLQDO FDU PRGHO LV JLYHQ E\ HTXDWLRQ
(I V pI V $
0DWODE
R
V
VV
V
V
SURJUDP VHH $SSHQGL[ % ZDV ZULWWHQ WR GHWHUPLQH WKH ERXQG RQ WKH
IUHTXHQF\GRPDLQ XQFHUWDLQW\ RI WKH QRPLQDO SODQW DV WKH YHORFLW\ DQG FRUQHULQJ VWLmQHVV
&+$37(5 7+( /$7(5$/ &21752/ 352%/(0
Plant Uncertainty 0.6
Ratio of Uncertainty to Po(jw)
0.5
0.4
0.3
0.2
-1
10
0
1
10
2
10
10
Frequency (rads/sec)
)LJXUH 6LPXODWLRQ RI 3ODQW 8QFHUWDLQW\
YDU\ RYHU WKH UDQJHV LQ 7DEOH 7KH SURJUDP nQGV WKH PDJQLWXGH RI
MpSMZ M
ZKHUH
S V
MS MZ b SMZ M
LV WKH WUDQVIHU IXQFWLRQ RI WKH QRPLQDO SODQW DQG
RI WKH DFWXDO SODQW DV WKH SDUDPHWHUV DUH YDULHG
SV
LV WKH WUDQVIHU IXQFWLRQ
7KH UHVXOWV RI WKH FRPSXWHU VLPXODWLRQ
DUH VKRZQ LQ )LJXUH 7KH UHVXOWV DUH SORWWHG DV WKH UDWLR
SUHVHQWDWLRQ ZDV FKRVHQ EHFDXVH LW IDFLOLWDWHV WKH FKRLFH RI
MZ M pS S MZ M
UV
7KLV IRUPDW RI GDWD
DV D IXQFWLRQ RI
S V
7KLV
VLPSOLnHV WKH FDOFXODWLRQV UHTXLUHG WR DUULYH DW WKH UREXVW FRQWUROOHU LQ WKH QH[W VHFWLRQ
&+$37(5 7+( /$7(5$/ &21752/ 352%/(0
&RQWUROOHU 'HVLJQ 8VLQJ WKH GDWD LQ )LJXUH D FRQVHUYDWLYH ERXQG RQ WKH SODQW XQFHUWDLQW\ FDQ EH H[SUHVVHG
DV
UV
S V
:LWK WKLV ERXQG D UREXVWO\ VWDELOL]LQJ FRQWUROOHU FDQ EH GHVLJQHG LI WKHUH H[LVWV DQ 6%5
VROXWLRQ WR WKH LQWHUSRODWLRQ SUREOHP ,W VKRXOG EH QRWHG WKDW WKLV FKRLFH RI XQFHUWDLQW\ LV
HTXLYDOHQW WR WKH XQFHUWDLQ JDLQ SUREOHP ZKRVH VROXWLRQ LV GHVFULEHG LQ > @ +RZHYHU
D OHVV FRQVHUYDWLYH JDLQ FRXOG EH FKRVHQ ZKLFK ZRXOG UHTXLUH WKH XVH RI WKH WHFKQLTXHV
GHVFULEHG LQ &KDSWHU
7KH QRPLQDO SODQW GHVFULEHG E\ HTXDWLRQ KDV WZR SROHV DW WKH RULJLQ DQG D UHODWLYH
GHJUHH RI
7KHUHIRUH WKH XQFHUWDLQW\ ERXQG DOVR KDV D UHODWLYH GHJUHH RI
7KH WZR
SROHV DW WKH RULJLQ FDQ EH KDQGOHG E\ XVLQJ WKH WHFKQLTXHV RXWOLQHG LQ &KDSWHU
7KH
WZR LQWHUSRODWLRQ SRLQWV DW LQnQLW\ PXVW EH KDQGOHG GLmHUHQWO\ 2QH LQWHUSRODWLRQ SRLQW DW
LQnQLW\ ZLOO EH KDQGOHG XVLQJ WKH DSSURDFK GHVFULEHG LQ &KDSWHU 7KH VHFRQG LQWHUSRODWLRQ
SRLQW DW LQnQLW\ ZLOO EH DGGHG XVLQJ HTXDWLRQ
$Q DOWHUQDWH PHWKRG WR KDQGOH WKH
PXOWLSOH LQWHUSRODWLRQ SRLQWV DW LQnQLW\ ZRXOG EH WR PDS WKH SUREOHP WR WKH
]HURV DW LQnQLW\ DUH UHSUHVHQWHG DV
]
] GRPDLQ ZKHUH
XA V
XV lV
%\ SURSHUO\ FKRRVLQJ lV WKH VHFRQG LQWHUSRODWLRQ SRLQW DW LQnQLW\ FDQ EH DFKLHYHG ZKLOH
VWLOO NHHSLQJ
XA V
6%5
&+$37(5 7+( /$7(5$/ &21752/ 352%/(0
6WHS
^ &RPSXWH
UP V S a V
%V
DQG
'HnQH
Sa V
S V
V
8VLQJ HTXDWLRQ S a V PD\ EH ZULWWHQ
SaV
V V
V
V
6LPLODUO\ GHnQH
A V UP
UV
V
ZKHUH
A UP V
% V
EHFDXVH WKH QRPLQDO SODQW KDV QR SROHV LQ WKH RSHQ ULJKWKDOISODQH
6WHS RI
S a V
SV
^ )LQG DQ 6%5 IXQFWLRQ
XV
VXFK WKDW
XmL
nL
A UP mL Sa mL
ZKHUH
mL
DUH WKH SROHV
LQ WKH FORVHG 5+3 6ROYH WKH 1HYDQOLQQD3LFN LQWHUSRODWLRQ SUREOHP
)RU WKH FDU SUREOHP WKHUH DUH QR LQWHUSRODWLRQ SRLQWV LQ WKH RSHQ 5+3 EHFDXVH WKH
SODQW KDV QR SROHV LQ WKH 5+3 +RZHYHU WKHUH DUH WZR LQWHUSRODWLRQ SRLQWV RQ WKH
m
DQG
m
MZ
D[LV
7KHUH LV DOVR RQH LQWHUSRODWLRQ SRLQW DW LQnQLW\ WKH RWKHU RQH ZLOO EH
KDQGOHG ODWHU %HFDXVH RI WKH FKRLFH RI
XmL
A Xm UP L
LV D FRQVWDQW VKRZQ LQ HTXDWLRQ
X mL
8VLQJ WKH UHVXOWV IURP WKH SUHYLRXV FKDSWHU WKH PRGLnHG )HQ\YHV DUUD\ IRU WKH FDU SUREOHP
LV VKRZQ LQ )LJXUH
1RWH WKDW IRU WKLV SDUWLFXODU FDVH WKH HOHPHQWV RI WKH 0RGLnHG )HQ\YHV DUUD\ DUH QRW D
IXQFWLRQ RI
q
$ VXLWDEOH \HW DUELWUDU\ FKRLFH IRU
X V
X V
b
LV JLYHQ LQ HTXDWLRQ
&+$37(5 7+( /$7(5$/ &21752/ 352%/(0
m
m
m
XV
b
XV
b
XV
)LJXUH 0RGLnHG )HQ\YHV $UUD\ IRU &DU 3UREOHP
8VLQJ WKH PRGLnHG PDSSLQJ IURP &KDSWHU
X V
)LQDOO\
XV
b
LV VKRZQ LQ HTXDWLRQ
V
V q
LV JLYHQ LQ HTXDWLRQ
qV q
X V
1RWH WKDW
X V
XV
V qV q
KDV D UHODWLYH GHJUHH RI DV H[SHFWHG
,Q RUGHU WR REWDLQ WKH VHFRQG
LQWHUSRODWLRQ SRLQW DW LQnQLW\ WKH lV LQ HTXDWLRQ ZLOO EH FKRVHQ RI WKH IRUP
lV
7KH FRHpFLHQWV
D E
DQG
F
V V
D
E V F
PXVW EH FKRVHQ WR HQVXUH WKDW
XAV
LV 6%5 DQG WKDW WKH
LQWHUSRODWLRQ FRQGLWLRQV DW WKH RULJLQ DUH VWLOO PHW 2QH SRVVLEOH FKRLFH RI lV LV VKRZQ LQ
HTXDWLRQ
lV
7KLV \LHOGV WKH IROORZLQJ
V V
XA V XAV
qV q V V qV q V
&+$37(5 7+( /$7(5$/ &21752/ 352%/(0 7KH FKRLFH RI
V\VWHP
q LQ HTXDWLRQ DmHFWV WKH
7KHUHIRUH
6XEVWLWXWLQJ
q
q
^ &RPSXWH
^ &RPSXWH
FV
TV TV
FV
V V
XA V
V V V
FDQ EH IRXQG XVLQJ HTXDWLRQ
% V XAV
V V
UV
V V V S V
7KH FRPSHQVDWRU LV VKRZQ LQ HTXDWLRQ
V
V V
V
V V V V
7KH SROHV RI WKH QRPLQDOFORVHG ORRS V\VWHP DUH
SROHV RI
RI WKH FORVHGORRS QRPLQDO
LQ HTXDWLRQ \LHOGV HTXDWLRQ
TV
6WHS
Z
UHVXOWV LQ D QDWXUDO IUHTXHQF\ RI DSSUR[LPDWHO\ UDGVHF
XA V
6WHS
QDWXUDO IUHTXHQF\
b b
DQG
b
7KHVH DUH WKH
7KH VWHS UHVSRQVH RI WKH FORVHGORRS V\VWHP LV VKRZQ LQ )LJXUH
7KH ODQH FKDQJH WUDMHFWRU\ VKRZQ LQ )LJXUH ZDV XVHG WR VLPXODWH WKH IDPLO\ RI
SODQWV DV WKH FRUQHULQJ VWLmQHVV DQG YHORFLW\ ZHUH YDULHG 7KH ODQH FKDQJH SHUIRUPDQFH RI
WKH IDPLO\ RI SODQWV LV VKRZQ LI )LJXUH 7KH ODQH FKDQJH UHVSRQVH IRU WKH IDPLO\ RI SODQWV
YDULHV DV WKH PRGHO FKDQJHV EXW DOO UHVSRQVHV DUH VWDEOH DQG VOLJKWO\ XQGHUGDPSHG
7KH
PD[LPXP SHUFHQW RYHUVKRRW LV DSSUR[LPDWHO\ SHUFHQW 0RGLnFDWLRQV LQ WKH UHVSRQVH RI
WKH V\VWHP PD\ EH PDGH E\ FKRRVLQJ D GLmHUHQW
XV
DQG E\ FKRRVLQJ D GLmHUHQW
q
6XPPDU\ DQG &RQFOXVLRQV 7KLV FKDSWHU KDV SUHVHQWHG WKH GHVLJQ RI D UREXVW ODWHUDO FRQWURO V\VWHP ZKLFK JXDUDQWHHV
VWDELOLW\ DV WKH FRUQHULQJ VWLmQHVV DQG YHORFLW\ YDU\ RYHU D SUHVFULEHG UDQJH 7KH FDU ODWHUDO
&+$37(5 7+( /$7(5$/ &21752/ 352%/(0
Closed-Loop Step Response for Nominal Plant 1.2
1
Amplitude
0.8
0.6
0.4
0.2
0 0
2
4
6 8 Time (secs)
10
12
14
)LJXUH 6WHS 5HVSRQVH RI &ORVHG/RRS 6\VWHP ZLWK WKH 1RPLQDO 3ODQW
&+$37(5 7+( /$7(5$/ &21752/ 352%/(0
Lane Change Trajectory 3
Lateral Position - Meters
2.5
2
1.5
1
0.5
0 0
2
4
6
8
10 12 Time - Secs
14
)LJXUH /DQH &KDQJH 7UDMHFWRU\
16
18
20
&+$37(5 7+( /$7(5$/ &21752/ 352%/(0
Lane Change Response for Family of Plants 4
3.5
Lateral Position (meters)
3
2.5
2
1.5
1
0.5
0 0
2
4
6
8
10 12 Time (secs)
14
16
)LJXUH /DQH &KDQJH 5HVSRQVH )DPLO\ RI 3ODQWV
18
20
&+$37(5 7+( /$7(5$/ &21752/ 352%/(0
FRQWURO SUREOHP EHFRPHV DQ LQWHUSRODWLRQ SUREOHP ZLWK WZR LQWHUSRODWLRQ SRLQWV DW WKH
RULJLQ DQG WZR LQWHUSRODWLRQ SRLQWV DW LQnQLW\ 7KH WHFKQLTXHV GHYHORSHG LQ &KDSWHU DUH
XVHG WR KDQGOH WKH WZR LQWHUSRODWLRQ SRLQWV DW WKH RULJLQ DQG RQH LQWHUSRODWLRQ SRLQW DW
LQnQLW\ 7KH VHFRQG LQWHUSRODWLRQ SRLQW DW LQnQLW\ LV DFKLHYHG E\ PXOWLSO\LQJ WKH IXQFWLRQ
XV
E\ DQRWKHU IXQFWLRQ lV ZKLFK UHVXOWV LQ WKH FRUUHFW UHODWLYH GHJUHH
6LPXODWLRQ UHVXOWV DUH SUHVHQWHG IRU WKH IDPLO\ RI SODQWV DV WKH FRUQHULQJ VWLmQHVV DQG
YHORFLW\ DUH YDULHG 7KH SHUIRUPDQFH RI WKH FORVHGORRS V\VWHP YDULHV DV WKH SODQW SDUDPH
WHUV FKDQJH EXW DOO RI WKH UHVSRQVHV DUH VWDEOH IRU WKH n[HG FRQWUROOHU 3HUIRUPDQFH RI WKH
FORVHGORRS V\VWHP PD\ EH PRGLnHG E\ FKDQJLQJ WKH SROHV RI
XV
RU E\ YDU\LQJ
q
QH[W FKDSWHU GLVFXVVHV WKH LPSOHPHQWDWLRQ RI WKLV FRQWURO DOJRULWKP RQ D WHVW YHKLFOH
7KH
&KDSWHU 6\VWHP ,PSOHPHQWDWLRQ DQG ([SHULPHQWDO 5HVXOWV 7KLV FKDSWHU SUHVHQWV H[SHULPHQWDO UHVXOWV IURP WKH nHOG WHVWLQJ RI WKH UREXVW ODWHUDO FRQWURO
DOJRULWKP GHVLJQHG LQ WKH SUHYLRXV FKDSWHU $Q RYHUYLHZ RI WKH WHVW YHKLFOH D *0&
-LPP\ [ LV DOVR SURYLGHG 7KH PRWLYDWLRQ IRU LPSOHPHQWLQJ WKH UREXVW FRQWUROOHU ZDV WR
GHWHUPLQH WKH SHUIRUPDQFH RI WKH FRQWUROOHU RQ WKH DFWXDO V\VWHP DQG GHWHUPLQH GHnFLHQFLHV
RI WKLV UREXVW FRQWURO DSSURDFK ZKLFK PLJKW UHTXLUH IXUWKHU UHVHDUFK 7KH FRQWLQXRXVWLPH
UREXVW FRQWUROOHU ZDV GLVFUHWL]HG XVLQJ WKH ELOLQHDU WUDQVIRUPDWLRQ IRU FRPSXWHU LPSOHPHQWD
WLRQ $ SURSRUWLRQDOLQWHJUDOGHULYDWLYH 3,' ZDV DOVR WHVWHG IRU FRPSDULVRQ WR WKH UREXVW
FRQWUROOHU 7KH QH[W VHFWLRQ SURYLGHV DQ RYHUYLHZ RI WKH WHVWEHG YHKLFOH
&+$37(5 6 ] > b ] > ] > > ] > b ] > ] > b ]
DUH UDGLDQV ZKLOH WKH XQLWV RI
(I ]
DUH PHWHUV 7KH FRPSXWHU LPSOH
PHQWDWLRQ UHTXLUHV D VFDOH IDFWRU WR FKDQJHV WKH XQLWV WR $' DQG '$ FRXQWV
7KLV LV
FDOFXODWHG EHORZ
t
UDGLDQV
ut
PHWHUV
GHJ
ut
FRXQWV
UDG
PHWHU YROWV
GHJ
t
ut
'$ FRXQWV
ut
YROW
u
FRXQWV
u
$' FRXQWV
8VLQJ HTXDWLRQ WKH UREXVW FRQWUROOHU H[SUHVVHG LQ WHUPV RI '$ DQG $' FRXQWV LV
JLYHQ E\
pI ] (I ]
b ] > ] > b ] > ] > > ] > b ] > ] > b ]
:ULWLQJ HTXDWLRQ DV D GLmHUHQFH HTXDWLRQ \LHOGV
pI N
p I N
b b pI N b pI N b b
&+$37(5 6
']
]
>
b ( ]
3 ] , ] ']
7KH SHUIRUPDQFH RI WKH 3,' DOJRULWKP DW WKH VDPH WKUHH VSHHGV LV VKRZQ LQ )LJXUHV
$ VXPPDU\ RI WKH
UPV
HUURU IRU HDFK WHVW UXQ DSSHDUV LQ 7DEOH
&+$37(5 6@
5DWKHU WKDQ GHVFULELQJ WKH SODQW XQFHUWDLQW\ LQ WKH
IUHTXHQF\ GRPDLQ WKLV WHFKQLTXH DSSOLHV .KDULWRQRY V 7KHRUHP WR DQDO\]H VWDELOLW\ DV
WKH FRHpFLHQWV RI WKH WUDQVIHU IXQFWLRQ PRGHO DUH YDULHG 7KH VHFRQG DSSURDFK GHVFULEHG
LQYROYHV PLQLPL]LQJ WKH VHQVLWLYLW\ IXQFWLRQ
5V
6 V
DQG WKH GHULYDWLYH RI WKH FRQWURO VHQVLWLYLW\
LQ RUGHU WR LPSURYH WKH SHUIRUPDQFH RI WKH ODWHUDO FRQWURO V\VWHP
LPSURYHV WKH GLVWXUEDQFH UHMHFWLRQ ZKLOH PLQLPL]LQJ WKH GHULYDWLYH RI
IUHTXHQF\ FRQWHQW RI WKH VWHHULQJ FRPPDQGV IURP WKH FRQWURO V\VWHP
0LQLPL]LQJ
5V
6 V
PLQLPL]HV WKH
&+$37(5 6,08/7$1(286 67$%,/,=$7,21 6(16,7,9,7< 0,1,0,=$7,21
6LPXOWDQHRXV 6WDELOL]DWLRQ *LYHQ WKH IDPLO\ RI SODQWV GHVFULEHG E\ HTXDWLRQ VLPXOWDQHRXV VWDELOL]DWLRQ FDQ EH
JXDUDQWHHG ZKHQ WKH IROORZLQJ DVVXPSWLRQV DUH PHW >@
P T ; L
3 V T
EL T VPT >L
Q; T VQT DL T VQT >L L
1S V T
'SV T
$VVXPSWLRQV
)RU HDFK n[HG
T
4 3 V T
LV VWULFWO\ SURSHU
7KHUH H[LVWV VRPH SRVLWLYH LQWHJHU
QPD[
)RU DOO DOORZDEOH YDOXHV RI WKH VXEVFULSW
4
PT QT
VXFK WKDW
L DL T
DQG
QT
EL T
QPD[
IRU DOO
T
DUH FRQWLQXRXV RYHU
4 4
3
LV D FRPSDFW VXEVHW RI ,5
/HW
PPD[
QPD[
PD[T 4
PT
DQG
QPD[
PD[T 4
QT
7KHQ IRU HDFK
N PPD[ O
WKH VHW
IT 4 PT
4NO
)RU HDFK n[HG
T
4 3 V T
N QT
OJ
LV PLQLPXP SKDVH
7KH VLJQ RI WKH KLJK IUHTXHQF\ JDLQ
ET
LV LQYDULDQW RYHU
4
7KH FRHpFLHQWV RI WKH WUDQVIHU IXQFWLRQ PRGHO RI D FDU V ODWHUDO G\QDPLFV PD\ EH GH
VFULEHG E\
(I V pI V
T V
V T V
T V T
T V T
&+$37(5 6,08/7$1(286 67$%,/,=$7,21 6(16,7,9,7< 0,1,0,=$7,21
PD[
PLQ
T
T
T
T
T
T
FRHpFLHQW
7DEOH 6XPPDU\ RI &RHpFLHQW &KDQJHV
(TXDWLRQ PHHWV DOO RI WKH DVVXPSWLRQV UHTXLUHG IRU VLPXOWDQHRXV VWDELOL]DWLRQ RI WKH
IDPLO\ RI SODQWV DV WKH SDUDPHWHUV YDU\
$
0DWODE
SURJUDP ZDV ZULWWHQ WR GHWHUPLQH WKH PLQLPXP DQG PD[LPXP YDOXHV RI
WKH FRHpFLHQWV LQ WKH WUDQVIHU IXQFWLRQ PRGHO DV WKH YHORFLW\ DQG FRUQHULQJ VWLmQHVV YDU\
7KH YDOXHV LQ 7DEOH GHVFULELQJ WKH SDUDPHWHUV IRU WKH *0& %OD]HU ZHUH XVHG LQ WKH
VLPXODWLRQV 7KH
0DWODE
SURJUDP DSSHDUV LQ $SSHQGL[ % 7KH UHVXOWV RI WKH VLPXODWLRQ
DUH VXPPDUL]HG LQ 7DEOH
8VLQJ WKH UHVXOWV GHVFULEHG LQ >@ D FRPSHQVDWRU RI WKH IRUP
& V
p V p
q V
qV q
p !
FDQ EH FRQVWUXFWHG WR VWDELOL]H WKH IDPLO\ RI SODQWV DV WKH SDUDPHWHUV YDU\
HQVXUH WKDW
1F V
LV +XUZLW] ZH ZLOO FKRRVH
p
p
7KLV \LHOGV
,Q RUGHU WR
&+$37(5 6,08/7$1(286 67$%,/,=$7,21 6(16,7,9,7< 0,1,0,=$7,21
1F V
V
7KH QH[W VWHS LQ FRQVWUXFWLQJ WKH FRPSHQVDWRU WR VWDELOL]H WKH IDPLO\ RI SODQWV LV WR FRQVWUXFW
V T
1F V 1S V T
(TXDWLRQ PXVW DOZD\V EH +XUZLW] IRU D VLPXOWDQHRXVO\ VWDELOL]LQJ FRQWUROOHU WR
H[LVW
7KH FRHpFLHQWV
T
b T
DUH DOZD\V SRVLWLYH HQVXULQJ WKDW
LV DOZD\V VWDEOH
,Q
RUGHU WR GHWHUPLQH WKH FRHpFLHQWV RI WKH VLPXOWDQHRXVO\ VWDELOL]LQJ FRQWUROOHU WKH IROORZLQJ
HTXDWLRQV PXVW EH LWHUDWLYHO\ VROYHG PDNLQJ VXUH WKDW HDFK LV DOZD\V +XUZLW] IRU WKH
H[SHFWHG SDUDPHWHU FKDQJHV ,Q >@ WKH H[LVWHQFH RI D VWDEOH
L V T
LV JXDUDQWHHG
V T
V T q'S V T
V T
V T qV'S V T
V T
V T qV'S V T
2QH ZD\ RI SURYLQJ WKDW D +XUZLW] VROXWLRQ WR HTXDWLRQV H[LVWV LV WR ZULWH WKH
HTXDWLRQV LQ WKH IROORZLQJ IRUP
L V T /HW
qL
.L
L V T qL VL 'S V T
7KHQ HTXDWLRQ FDQ EH ZULWWHQ
.L LV T VL 'S V T
7DNLQJ WKH OLPLW DV
.L
DSSURDFKHV
ZKLFK LV VWDEOH E\ FRQVWUXFWLRQ
L V T .L L V 'SV
WKH ]HURV RI LV T DSSURDFK WKH ]HURV RI L V T 2QH ]HUR RI
LV T
DSSURDFKHV
b
ZKLFK LV DOVR
&+$37(5 6,08/7$1(286 67$%,/,=$7,21 6(16,7,9,7< 0,1,0,=$7,21
VWDEOH EHFDXVH WKH UHODWLYH GHJUHH RI
D +XUZLW]
L
L VT V L ' S V
LV HTXDO WR 7KHUHIRUH DV
qL
DSSURDFKHV ]HUR
LV DOZD\V JXDUDQWHHG WR H[LVW
7KH WDVN RI HQVXULQJ WKDW HTXDWLRQV DUH +XUZLW] LV JUHDWO\ VLPSOLnHG E\ DSSO\
LQJ .KDULWRQRY V 7KHRUHP > @ .KDULWRQRY V 7KHRUHP LV VWDWHG EHORZ
7KHRUHP
>@ 7KH SRO\QRPLDO IDPLO\
3 V $
ISV D
D
DV DQ VQ MD
$J DQ !
LV VWDEOH LI DQG RQO\ LI WKH IROORZLQJ SRO\QRPLDOV DUH VWDEOH
S> V
D
> D> V D V D V D V
S V
D
> > D V D V D V D V
S> V
D>
> > D V D V D V D V
S>> V
D>
> D> V D V D V D V
7KH SRO\QRPLDOV DUH FDOOHG .KDULWRQRY SRO\QRPLDOV
7KH VXSHUVFULSWV RQ
D
LQGLFDWH WKH XSSHU DQG ORZHU ERXQGV RQ WKH FRHpFLHQWV
$
0DWODE
SURJUDP ZDV ZULWWHQ WR YHULI\ .KDULWRQRY VWDELOLW\ DV WKH FRQWUROOHU ZDV
FRQVWUXFWHG LWHUDWLYHO\ XVLQJ HTXDWLRQV 7KH IROORZLQJ YDOXHV IRU
q q
q
ZDV VHOHFWHG WR DUULYH DW D GF JDLQ RI
q
q
DQG
qL
ZHUH FKRVHQ
q
ZHUH FKRVHQ WR JXDUDQWHH .KDULWRQRY
VWDELOLW\ 7KH VLPXOWDQHRXVO\ VWDELOL]LQJ FRQWUROOHU LV VKRZQ LQ HTXDWLRQ
FV
V V V
&+$37(5 6,08/7$1(286 67$%,/,=$7,21 6(16,7,9,7< 0,1,0,=$7,21
Gain dB
40
20
0 -1 10
0
10
1
10
2
10 Frequency (rad/sec)
3
10
4
10
5
10
Phase deg
90
0
-90 -1
10
0
10
1
10
2
10 Frequency (rad/sec)
3
10
4
10
5
10
)LJXUH %RGH 3ORW RI 6LPXOWDQHRXVO\ 6WDELOL]LQJ &RQWUROOHU
$ %RGH SORW RI WKH VLPXOWDQHRXVO\ VWDELOL]LQJ FRQWUROOHU DSSHDUV LQ )LJXUH 7KH UREXVW
FRQWUROOHU LV EDVLFDOO\ D OHDG FRPSHQVDWRU LJQRULQJ WKH KLJKHU IUHTXHQF\ UROORm 7KH ODQH
FKDQJH UHVSRQVH IRU WKH IDPLO\ RI SODQWV ZLWK WKLV UREXVW FRQWUROOHU LQ VKRZQ LQ )LJXUH
1RWH WKDW WKH ODQH FKDQJH UHVSRQVH IRU WKH IDPLO\ RI SODQWV LV VLJQLnFDQWO\ EHWWHU WKDQ
IRU WKH UREXVW FRQWUROOHU GHVLJQHG LQ &KDSWHU
7KHUH LV DQ LQWHUHVWLQJ V\QHUJ\ EHWZHHQ
WKH VLPXOWDQHRXV VWDELOL]DWLRQ DSSURDFK DQG FODVVLFDO IUHTXHQF\ GRPDLQ PHWKRGV
,W LV
SRVVLEOH WR GHVLJQ D OHDG FRPSHQVDWRU XVLQJ FODVVLFDO PHWKRGV WDNLQJ LQWR DFFRXQW WKH
SHUIRUPDQFH RI WKH QRPLQDO FORVHGORRS V\VWHP ZKLOH VWLOO JXDUDQWHHLQJ VWDELOLW\ IRU WKH
IDPLO\ RI SODQWV 7KLV ZRXOG EH DQ LWHUDWLYH WULDO DQG HUURU SURFHVV WKRXJK LQYROYLQJ WKH
GHVLJQ RI WKH OHDG FRPSHQVDWRU IRU QRPLQDO SODQW SHUIRUPDQFH DQG WKHQ WKH FRQVWUXFWLRQ
RI D VLPLODU FRPSHQVDWRU XVLQJ WKH VLPXOWDQHRXV VWDELOL]DWLRQ DSSURDFK
&+$37(5 6,08/7$1(286 67$%,/,=$7,21 6(16,7,9,7< 0,1,0,=$7,21
Lane Change Response for Family of Plants 3.5
3
Lateral Position (meters)
2.5
2
1.5
1
0.5
0 0
2
4
6
8
10 12 Time (secs)
14
16
)LJXUH /DQH &KDQJH 5HVSRQVH IRU )DPLO\ RI 3ODQWV
18
20
&+$37(5 6,08/7$1(286 67$%,/,=$7,21 6(16,7,9,7< 0,1,0,=$7,21
]
]
]
: V
: V
Y
< 9 ; :H b
: V G
< 9 ; :
& V
X
3 V
\
< 9 ; :
]
Q
)LJXUH )HHGEDFN 6\VWHP ZLWK :HLJKWLQJ
6HQVLWLYLW\ 0LQLPL]DWLRQ 7KLV VHFWLRQ H[SORUHV WKH DSSOLFDWLRQ RI PXOWLREMHFWLYH GHVLJQ WR WKH ODWHUDO FRQWURO SUREOHP
*LYHQ WKH IHHGEDFN V\VWHP ZLWK ZHLJKWLQJV
:
b :
VKRZQ LQ )LJXUH LW LV SRVVLEOH WR
GHVLJQ D VWDELOL]LQJ FRPSHQVDWRU ZKLFK DOVR PLQLPL]HV WKH IROORZLQJ
o o o : V 6 V o o o o o : V 5V o o o o o : V 7 V
o o o o o o o o o o o o o
+
QRUP
&+$37(5 6,08/7$1(286 67$%,/,=$7,21 6(16,7,9,7< 0,1,0,=$7,21
ZKHUH
6 V 5V 7 V
7KH ZHLJKWLQJ IXQFWLRQ
& V 3 V
& V 3 V
& V & V 3 V
: V
3 V & V
6HQVLWLYLW\
&RQWURO 6HQVLWLYLW\
&RPSOHPHQWDU\ 6HQVLWLYLW\
6 V
LV D PLUURU LPDJH RI WKH GHVLUHG VHQVLWLYLW\ IXQFWLRQ
,W LV GHVLUDEOH WR KDYH WKH PDJQLWXGH RI
6 V
VPDOO DW ORZ IUHTXHQFLHV DQG ODUJH DW KLJK
IUHTXHQFLHV WR REWDLQ JRRG GLVWXUEDQFH UHMHFWLRQ >@
WR SHQDOL]H DFWXDWRU VLJQDOV $Q DSSURSULDWH
: V
7KH DFWXDWRU ZHLJKW
:V
LV XVHG
VKRXOG KDYH D VPDOO PDJQLWXGH DW ORZ
IUHTXHQFLHV DQG D ODUJH PDJQLWXGH DW KLJK IUHTXHQFLHV WR FRVW IRU VDWXUDWLRQ >@
:V
PD\
DOVR FRQWDLQ D FRQVWDQW FRPSRQHQW WR UHoHFW WKH FRVWV RI FRQVWDQW DFWXDWLRQ ,W LV GHVLUDEOH
WR SHQDOL]H WKH FRPSOHPHQWDU\ VHQVLWLYLW\ DW KLJK IUHTXHQFLHV WR PLQLPL]H WKH LQoXHQFH RI
KLJK IUHTXHQF\ PHDVXUHPHQW QRLVH
7KLV \LHOGV D KLJK SDVV nOWHU VKDSH IRU
FORVHGORRS EDQGZLGWK FDQ DOVR EH OLPLWHG E\
: V
:V
VLQFH WKH FXWRm IUHTXHQF\ RI
7KH
:V
OLPLWV WKH V\VWHP EDQGZLGWK >@
$ VROXWLRQ WR WKH UREXVW PLQLPL]DWLRQ SUREOHP GHVFULEHG E\ HTXDWLRQ FDQ EH
REWDLQHG E\ XVLQJ DQ DXJPHQWHG SODQW VKRZQ LQ )LJXUHV DQG VROYLQJ WZR 5LFFDWL
HTXDWLRQV >@ 7KH HTXDWLRQV GHVFULELQJ WKH DXJPHQWHG V\VWHP DUH JLYHQ E\
[B
$[ % X X
\
& [ ' X ' X
\
& [ ' X ' X
&+$37(5 6,08/7$1(286 67$%,/,=$7,21 6(16,7,9,7< 0,1,0,=$7,21
X
\
3DXJ V X
\
) V
]
)LJXUH $XJPHQWHG 0RGHO
ZKHUH WKH DXJPHQWHG SODQW
3DXJ V
LV
3DXJ V
: b: 3 : :3 , b3
ZLWK WKH VWDWHVSDFH UHDOL]DWLRQ
3 V
$ % % & ' '
&
7KH
0DWODE
FRPPDQG
KLQI
'
'
ZDV XVHG WR VROYH WKH PXOWLREMHFWLYH PLQLPL]DWLRQ SUREOHP
ZLWK WKH IROORZLQJ ZHLJKWLQJ PDWULFHV 2QFH DJDLQ WKH QRPLQDO FDU PRGHO GHVFULEHG E\ WKH
&+$37(5 6,08/7$1(286 67$%,/,=$7,21 6(16,7,9,7< 0,1,0,=$7,21
Step Response of Nominal Plant 0.9 0.8 0.7
Amplitude
0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.1 Time, (secs)
0.2
)LJXUH 1RPLQDO 3ODQW 6WHS 5HVSRQVH
SDUDPHWHUV LQ 7DEOH ZDV XVHG
V V
: V
: V
: V
V V
V V
7KH VLPXODWLRQ UHVXOWV IRU WKH UREXVWO\ VWDELOL]LQJ FRQWUROOHU DSSHDU LQ )LJXUH
7KH
SHUIRUPDQFH RI WKH FRQWUROOHU LV DFFHSWDEOH EXW WKH FRQWUROOHU KDV WZR ]HURV YHU\ FORVH WR
WKH RULJLQ ZKLFK PLJKW FDXVH SUREOHPV LQ DQ DFWXDO LPSOHPHQWDWLRQ
&+$37(5 6,08/7$1(286 67$%,/,=$7,21 6(16,7,9,7< 0,1,0,=$7,21
6XPPDU\ DQG &RQFOXVLRQV 7KLV FKDSWHU KDV H[SORUHG WZR DGGLWLRQDO UREXVW FRQWURO WHFKQLTXHV ZKLFK DUH DSSOLFDEOH
WR WKH ODWHUDO FRQWURO SUREOHP
7KH nUVW DSSURDFK VLPXOWDQHRXV VWDELOL]DWLRQ RI D IDPLO\
RI SODQWV LV SRVVLEOH EHFDXVH WKH V\VWHP PRGHO PHHWV WKH PLQLPXP SKDVH UHTXLUHPHQW
7KLV DSSURDFK LV SRWHQWLDOO\ YHU\ XVHIXO EHFDXVH WKH VWUXFWXUH RI WKH FRQWUROOHU LV NQRZQ LQ
DGYDQFH 7KLV DOORZV WZHDNLQJ WKH FRQWUROOHU ZLWK IUHTXHQF\GRPDLQ WULDODQGHUURU PHWKRGV
WR REWDLQ WKH GHVLUHG SHUIRUPDQFH RI WKH QRPLQDO SODQW DV ZHOO DV VWDELOLW\ IRU WKH IDPLO\
RI SODQWV
7KH VHFRQG DSSURDFK GHVFULEHG LQ WKLV FKDSWHU LV D PXOWLREMHFWLYH GHVLJQ ZKHUH WKH
VHQVLWLYLW\
6 V
DQG WKH FRQWURO VHQVLWLYLW\
5V
DUH PLQLPL]HG 0LQLPL]LQJ WKH VHQVLWLYLW\
UHGXFHV WKH DmHFWV RI GLVWXUEDQFHV ZKLOH PLQLPL]LQJ WKH GHULYDWLYH RI WKH FRQWURO VHQVLWLYLW\
UHGXFHV WKH IUHTXHQF\ FRQWHQW RI WKH FRQWURO HmRUW
7KH VLPXODWHG VWHS UHVSRQVH IRU WKH
QRPLQDO SODQW ZLWK WKH UREXVW FRQWUROOHU ZDV VDWLVIDFWRU\ +RZHYHU WKH FRQWUROOHU REWDLQHG
E\ VROYLQJ 5LFFDWL HTXDWLRQV FRQWDLQV WZR ]HURV YHU\ FORVH WR WKH RULJLQ
FDXVH GLpFXOWLHV LQ D SUDFWLFDO LPSOHPHQWDWLRQ
7KHVH PLJKW
&KDSWHU 6XPPDU\ DQG &RQFOXVLRQV 7KLV FKDSWHU SURYLGHV D VXPPDU\ DQG UHFRPPHQGDWLRQV IRU IXWXUH UHVHDUFK
6XPPDU\ 7KH PDLQ IRFXV RI WKLV GLVVHUWDWLRQ KDV EHHQ WKH DXWRPDWLF ODWHUDO FRQWURO RI KLJKZD\ YHKL
FOHV DQG WKH DSSOLFDWLRQ RI UREXVW FRQWURO WHFKQLTXHV WR WKLV SUREOHP ,Q &KDSWHU D UHYLHZ
RI ODWHUDO FRQWURO UHVHDUFK ZDV SUHVHQWHG 0DQ\ RI WKH FRQWURO WHFKQLTXHV EHLQJ DSSOLHG WR
WKH ODWHUDO FRQWURO SUREOHP WRGD\ OLNH RSWLPDO FRQWURO DQG JDLQVFKHGXOLQJ KDYH WKHLU RUL
JLQV LQ WKH HDUO\ UHVHDUFK 7KH ODUJHVW DXWRPDWHG KLJKZD\ UHVHDUFK HmRUW LV FXUUHQWO\ EHLQJ
FRQGXFWHG DW 3$7+ 5HFHQW UHVXOWV KDYH LQFOXGHG nHOG WHVWLQJ RI IUHTXHQF\VKDSHGOLQHDU
TXDGUDWLF RSWLPDO FRQWUROOHUV 3,' FRQWUROOHUV DQG IX]]\ ORJLF FRQWUROOHUV 7HVW VSHHGV DUH
UHODWLYHO\ VORZ UDQJLQJ IURP
NPSK
WR
NPSK
3DUDPHWULF UREXVW FRQWURO WHFKQLTXHV
KDYH DOVR EHHQ SURSRVHG E\ - $FNHUPDQQ LQ VHYHUDO UHFHQW SXEOLFDWLRQV
7KH UREXVW FRQWURO DSSURDFK XVHG LQ WKLV GLVVHUWDWLRQ PRGHOV WKH SODQW XQFHUWDLQW\ DV
&+$37(5 6800$5< $1' &21&/86,216
XQVWUXFWXUHG DGGLWLYH SHUWXUEDWLRQV LQ WKH IUHTXHQF\GRPDLQ &KDSWHU FRQWDLQV D UHYLHZ
RI UREXVW FRQWURO LQ WKH IDFH RI DGGLWLYH XQVWUXFWXUHG SHUWXUEDWLRQV LQ WKH IUHTXHQF\GRPDLQ
7KHUH DUH VHYHUDO OLPLWDWLRQV WR WKH FXUUHQW WKHRU\ 7KHVH LQFOXGH SUREOHPV ZLWK KDQGOLQJ
SROHV RQ WKH
MZ
D[LV DQG XQVWDEOH SROHV ZLWK D PXOWLSOLFLW\ JUHDWHU WKDQ 7KH PRGHO IRU
WKH ODWHUDO G\QDPLFV RI DQ DXWRPRELOH FRQWDLQV SROHV ORFDWHG DW WKH RULJLQ ,Q &KDSWHU
WKH FXUUHQW WKHRU\ ZDV H[WHQGHG WR DOORZ GHDOLQJ ZLWK SROHV RQ WKH
MZ
D[LV DQG XQVWDEOH
SROHV ZLWK D PXOWLSOLFLW\ JUHDWHU WKDQ
8VLQJ WKH LQWHUSRODWLRQ WHFKQLTXHV GHYHORSHG LQ &KDSWHU D UREXVW ODWHUDO FRQWUROOHU
ZDV GHVLJQHG LQ &KDSWHU 7KH XQFHUWDLQW\ ZDV FKDUDFWHUL]HG E\ VLPXODWLQJ D OLQHDUL]HG
ELF\FOH PRGHO RI WKH ODWHUDO G\QDPLFV DV WKH YHORFLW\ DQG FRUQHULQJ VWLmQHVV ZHUH YDULHG
7KH XQFHUWDLQW\ ZDV WKHQ H[SUHVVHG DV D IUDFWLRQ RI WKH QRPLQDO SODQW WUDQVIHU IXQFWLRQ
7KH UREXVW ODWHUDO FRQWUROOHU GHVLJQHG LQ &KDSWHU ZDV LPSOHPHQWHG RQ D WHVW YHKLFOH
DQG WKH WHVW UHVXOWV DUH VXPPDUL]HG LQ &KDSWHU
$ 3,' FRQWUROOHU ZDV DOVR WHVWHG IRU
FRPSDULVRQ SXUSRVHV %RWK FRQWUROOHUV SHUIRUPHG VDWLVIDFWRULO\ EXW VHYHUDO GLpFXOWLHV ZHUH
IRXQG ZLWK WKH UREXVW FRQWURO DSSURDFK HPSOR\HG 7KH WHVW UHVXOWV ZHUH YHU\ FRPSDUDEOH
WR WKH UHVXOWV EHLQJ REWDLQHG DW 3$7+ >@
7KH UREXVW FRQWUROOHU KDG GLpFXOW\ ]HURLQJ RXW VWHDG\ VWDWHHUURU EHFDXVH RI D ODFN RI
LQWHJUDWLRQ DFWLRQ
6WHDG\VWDWH HUURUV ZHUH FDXVHG E\ FHQWHU VWHHULQJ RmVHWV EDFNODVK LQ
WKH VWHHULQJ DFWXDWRU DQG URDG GLVWXUEDQFHV 7KHVH W\SHV RI XQFHUWDLQWLHV ZHUH QRW LQFOXGHG
LQ WKH UREXVW FRQWUROOHU GHVLJQ VR WKHUHIRUH LW LV UHDVRQDEOH WKDW WKH FRQWUROOHU ZRXOG KDYH
GLpFXOW\ KDQGOLQJ WKHP ,Q DGGLWLRQ WKH XQFHUWDLQW\ ERXQG XVHG IRU WKH UREXVW FRQWUROOHU
GHVLJQ ZDV UDWKHU FRQVHUYDWLYH
7KLV FRQVHUYDWLYH PRGHOLQJ RI SDUDPHWHU XQFHUWDLQWLHV
YHORFLW\ DQG FRUQHULQJ VWLmQHVV UHGXFHG WKH JDLQ RI WKH UREXVW FRQWUROOHU ZKLFK OHG WR WKH
&+$37(5 6800$5< $1' &21&/86,216
GLpFXOW\ LQ KDQGOLQJ RWKHU W\SHV RI XQFHUWDLQWLHV QRQOLQHDULWLHV DQG GLVWXUEDQFHV
,Q &KDSWHU WZR RWKHU UREXVW FRQWURO WHFKQLTXHV ZHUH DSSOLHG WR WKH ODWHUDO FRQWURO
SUREOHP 7KH nUVW VLPXOWDQHRXV VWDELOL]DWLRQ RI D IDPLO\ RI SODQWV XVHG .KDULWRQRY V 7KHR
UHP WR KHOS FRQVWUXFW D VWDELOL]LQJ FRPSHQVDWRU 7KLV DSSURDFK \LHOGHG D OHDG FRPSHQVDWRU
ZKLFK FRXOG EH WZHDNHG XVLQJ FODVVLFDO IUHTXHQF\GRPDLQ WHFKQLTXHV
7KH VLPXODWHG SHU
IRUPDQFH RI WKH VLPXOWDQHRXVO\ VWDELOL]LQJ FRQWUROOHU ZDV EHWWHU WKDQ WKH UREXVW FRQWUROOHU
GHVFULEHG LQ &KDSWHU 7KH VHFRQG FRQWUROOHU GHVLJQHG LQ &KDSWHU LQYROYHG D PXOWLREMHF
WLYH GHVLJQ 7KH VHQVLWLYLW\ IXQFWLRQ
6 V
ZDV PLQLPL]HG WR LPSURYH GLVWXUEDQFH UHMHFWLRQ
ZKLOH WKH GHULYDWLYH RI WKH FRQWURO VHQVLWLYLW\
FRQWHQW RI WKH VWHHULQJ DFWXDWRU
5V
ZDV PLQLPL]HG WR UHGXFH WKH IUHTXHQF\
$OWKRXJK WKLV DSSURDFK XVHG D FRQVHUYDWLYH ERXQG WKH
VLPXODWLRQ UHVXOWV ZHUH DOVR DFFHSWDEOH
7KH FRQWULEXWLRQV RI WKLV GLVVHUWDWLRQ DUH PDGH LQ WZR DUHDV
)LUVW .LPXUD V UREXVW
FRQWURO DSSURDFK IRU V\VWHPV ZLWK DGGLWLYH XQVWUXFWXUHG SHUWXUEDWLRQV LQ WKH IUHTXHQF\
GRPDLQ ZDV H[WHQGHG WR LQFOXGH XQVWDEOH SROHV ZLWK PXOWLSOLFLW\ DQG SROHV RQ WKH
MZ
D[LV $ PRGLnHG PDSSLQJ IRU WKH 1HYDQOLQQD3LFN LQWHUSRODWLRQ DOJRULWKP ZDV GHYHORSHG WR
KDQGOH SROHV RQ WKH
MZ
ZDV DOVR SUHVHQWHG
D[LV $ WHFKQLTXH IRU KDQGOLQJ LQWHUSRODWLRQ SRLQWV ZLWK PXOWLSOLFLW\
7KHVH QHZ LQWHUSRODWLRQ WHFKQLTXHV DUH DSSOLFDEOH WR RWKHU UREXVW
FRQWURO DSSURDFKHV LQYROYLQJ LQWHUSRODWLRQ 7KH VHFRQG FRQWULEXWLRQ RI WKLV GLVVHUWDWLRQ LV
WKH H[SORUDWLRQ RI LPSOHPHQWDWLRQ LVVXHV ZLWK WKLV UREXVW FRQWURO DSSURDFK DSSOLHG WR WKH
ODWHUDO FRQWURO RI KLJKZD\ YHKLFOHV
7KH QH[W VHFWLRQ PDNHV UHFRPPHQGDWLRQV IRU IXWXUH UHVHDUFK
&+$37(5 6800$5< $1' &21&/86,216
5HFRPPHQGDWLRQV IRU )XWXUH 5HVHDUFK 7KH PRWLYDWLRQ IRU DSSO\LQJ UREXVW FRQWURO WHFKQLTXHV WR WKH ODWHUDO FRQWURO SUREOHP ZDV
WKH QDWXUH RI WKH FRQWURO SUREOHP 3DUDPHWHUV ZHUH VXEMHFW WR FKDQJH DQG WKHUH ZDV VRPH
XQFHUWDLQW\ WR WKH SDUDPHWHU FKDQJHV ,Q DGGLWLRQ XVLQJ D OLQHDUL]HG PRGHO IRU WKH ODWHUDO
G\QDPLFV DGGHG PRUH XQFHUWDLQW\ WR WKH V\VWHP PRGHOLQJ )URP SUHYLRXV H[SHULHQFH ZLWK
DGDSWLYH FRQWUROOHUV >@ WKHUH ZDV DOVR VRPH FRQFHUQ DERXW WKH PDJQLWXGH RI WKH VWHHULQJ
FRPPDQG FDXVLQJ VDWXUDWLRQ DV ZHOO DV GULYHU GLVFRPIRUW 7KHVH FRQFHUQV DUH QRW LVRODWHG
WR WKH ODWHUDO FRQWURO RI KLJKZD\ YHKLFOHV 0RGHOLQJ XQFHUWDLQW\ QRQOLQHDULWLHV SDUDPHWHU
FKDQJHV DQG VDWXUDWLRQ DSSHDU ZKHQ DOPRVW HYHU\ WKHRUHWLFDO DOJRULWKP LV XVHG RQ D SK\VLFDO
V\VWHP
7KUHH %DVLF 5XOHV RI 5REXVW
6RPH RI WKHVH GLpFXOWLHV DUH HPERGLHG LQ $FNHUPDQQ V ?
&RQWURO
VKRZQ EHORZ >@
q
5XOH
5HTXLUH UREXVWQHVV RI D FRQWURO V\VWHP RQO\ IRU SK\VLFDOO\ PRWLYDWHG SDUDP
HWHU YDOXHV DQG QRW ZLWK UHVSHFW WR DUELWUDULO\ DVVXPHG XQFHUWDLQWLHV RI WKH PDWKH
PDWLFDO PRGHO
q
5XOH
:KHQ \RX FORVH D ORRS ZLWK DFWXDWRU FRQVWUDLQWV OHDYH D VORZ V\VWHP VORZ
DQG OHDYH D IDVW V\VWHP IDVW
q
5XOH
%H SHVVLPLVWLF LQ DQDO\VLV WKHQ \RX FDQ DmRUG WR EH DQ RSWLPLVW LQ WKH
GHVLJQ
0RGHOLQJ WKH V\VWHP XQFHUWDLQW\ LQ WKH IUHTXHQF\GRPDLQ DV XQVWUXFWXUHG DGGLWLYH SHU
WXUEDWLRQV DV WKH YHORFLW\ DQG FRUQHULQJ VWLmQHVV YDULHG REH\HG 5XOHV DQG 7KH UREXVW
&+$37(5 6800$5< $1' &21&/86,216
QHVV ZDV PRWLYDWHG E\ SK\VLFDO SDUDPHWHU FKDQJHV WKH YHORFLW\ RI D FDU FKDQJHV DV GRHV
WKH FRUQHULQJ VWLmQHVV
7KH XQFHUWDLQW\ ERXQG FKRVHQ ZDV DOVR YHU\ FRQVHUYDWLYH
5XOH
ZDV DOVR IROORZHG LQ WKDW ZH NHSW D VORZ V\VWHP VORZ WKHUHIRUH DYRLGLQJ DQ\ DFWXDWRU
VDWXUDWLRQ SUREOHPV
(YHQ WKRXJK $FNHUPDQQ V %DVLF 5XOHV RI 5REXVW FRQWURO ZHUH QRW
YLRODWHG WKH SHUIRUPDQFH RI WKH UREXVW FRQWUROOHU VWLOO OHIW VRPH URRP IRU LPSURYHPHQW
ZKHQ LPSOHPHQWHG RQ WKH SK\VLFDO V\VWHP 7KH SUREOHPV ZLWK WKH UREXVW FRQWUROOHU DURVH
IURP DFWXDWRU EDFNODVK D QRQOLQHDULW\ FHQWHU VWHHULQJ RmVHWV D PRGHOLQJ HUURU DQG URDG
GLVWXUEDQFHV
)RU WKH PRVW SDUW QRQOLQHDULWLHV OLNH EDFNODVK DUH QRW D IUHTXHQF\GRPDLQ
SKHQRPHQRQ 7KHUHIRUH RQH DUHD UHTXLULQJ PRUH UHVHDUFK LV KRZ WR LQFRUSRUDWH QRQOLQHDUL
WLHV OLNH EDFNODVK LQWR D IUHTXHQF\GRPDLQ GHVLJQ 2QH PHWKRG IRU KDQGOLQJ QRQOLQHDULWLHV LV
WR XVH 4XDQWLWDWLYH )HHGEDFN 7KHRU\ 4)7 EXW WKLV DSSURDFK UHOLHV RQ nQGLQJ DQ ?HTXLY
DOHQW OLQHDU WLPHLQYDULDQW SODQW VHW ZKRVH UHVSRQVHV IROORZ WKH QRQOLQHDU V\VWHP >@
)RU WKH ODWHUDO FRQWURO SUREOHP URDG GLVWXUEDQFHV FHQWHU VWHHULQJ RmVHWV DQG DFWXDWRU
EDFNODVK DUH VWUXFWXUHG XQFHUWDLQW\ QRZ WKDW WKH\ KDYH EHHQ LGHQWLnHG DV SUREOHPDWLF
7KHVH GLVWXUEDQFHV DUH VKRZQ LQ )LJXUH
7KH SHUIRUPDQFH GHnFLHQFLHV RI WKH UREXVW
FRQWUROOHU GHVLJQHG LQ &KDSWHU FDQ SUREDEO\ EH HOLPLQDWHG E\ XVLQJ D OHVV FRQVHUYDWLYH
GHVFULSWLRQ RI WKH SODQW XQFHUWDLQW\ LQFRUSRUDWLQJ VRPH NQRZOHGJH RI WKH VWUXFWXUH RI WKH
XQFHUWDLQW\ LQWR WKH GHVLJQ 7KLV LV DQRWKHU DUHD UHTXLULQJ IXUWKHU UHVHDUFK
7KH VLPXOWDQHRXV VWDELOL]DWLRQ WHFKQLTXH XVHG LQ &KDSWHU FRXOG EH GHYHORSHG LQWR
D SRZHUIXO GHVLJQ WRRO IRU D OLPLWHG FODVV RI PLQLPXP SKDVH V\VWHPV
7KH VWUXFWXUH RI
WKH FRQWUROOHU LV NQRZQ DW WKH VWDUW RI WKH GHVLJQ VR LW LV SRVVLEOH WR LQFRUSRUDWH RWKHU
GHVLJQ FULWHULD LQWR WKH FRQWUROOHU GHVLJQ )RU H[DPSOH WKH OHDG FRPSHQVDWRU GHVLJQHG IRU
WKH ODWHUDO FRQWURO SUREOHP FRXOG EH WZHDNHG XVLQJ IUHTXHQF\GRPDLQ WHFKQLTXHV ORRNLQJ DW
&+$37(5 6800$5< $1' &21&/86,216
G
U
< 9 ; :H
b
< 9 ; :
FV
X
SV
\
G
< 9 ; :
]
ZKHUH
G
Q
UHSUHVHQWV FHQWHU VWHHULQJ RmVHWV DFWXDWRU EDFNODVK DQG PHDVXUHPHQW QRLVH
G
UHSUHVHQWV URDG GLVWXUEDQFHV DQG
Q
UHSUHVHQWV PHDVXUHPHQW QRLVH
)LJXUH /DWHUDO &RQWURO 6\VWHP 0RGHO
&+$37(5 6800$5< $1' &21&/86,216
WKH SKDVH PDUJLQ RI WKH QRPLQDO SODQW ZKLOH VWLOO JXDUDQWHHLQJ VWDELOLW\ IRU WKH IDPLO\ RI
SODQWV $OWKRXJK WKLV ZRXOG EH DQ LWHUDWLYH WULDO DQG HUURU SURFHVV PDQ\ FRQWURO HQJLQHHUV
DUH DOUHDG\ IDPLOLDU ZLWK SHUIRUPDQFH FRQVWUDLQWV UHODWHG WR IUHTXHQF\GRPDLQ LQIRUPDWLRQ
%\ LQFRUSRUDWLQJ WKH VLPXOWDQHRXV VWDELOL]DWLRQ DSSURDFK LQWR WKH GHVLJQ PRUH UREXVWQHVV
SURSHUWLHV RI WKH FRQWURO V\VWHP FRXOG EH LQFRUSRUDWHG RU NQRZQ LQ DGYDQFH
2QH WRSLF WKDW ZDV KLJKOLJKWHG ZKLOH SUHSDULQJ WKLV GLVVHUWDWLRQ LV WKH GLmHUHQFH EH
WZHHQ DQDO\WLF IHHGEDFN GHVLJQ DSSURDFKHV LH LQWHUSRODWLRQ DQG WULDODQGHUURU GHVLJQ
DSSURDFKHV LH 1\TXLVW VWDELOLW\ FULWHULRQ $QDO\WLF GHVLJQ WHFKQLTXHV DUH DWWUDFWLYH EH
FDXVH WKH\ LQFOXGH WKH IROORZLQJ WZR HOHPHQWV FRQGLWLRQV IRU H[LVWHQFH RI D VROXWLRQ DQG
DQ DOJRULWKP ZKLFK LV JXDUDQWHHG WR nQG WKH VROXWLRQ ZKHQ LW H[LVWV >@ +RZHYHU ZKHQ
LPSOHPHQWLQJ D FRQWURO DOJRULWKP RQ D SK\VLFDO V\VWHP RU HYHQ LQ VLPXODWLRQ WKH nUVW FXW
DW D FRQWUROOHU UDUHO\ PHHWV DOO RI WKH GHVLJQ UHTXLUHPHQWV
RU WZHDNLQJ LV UHTXLUHG
7KHUHIRUH VRPH PRGLnFDWLRQ
)RU WULDODQGHUURU PHWKRGV WKLV LV UHODWLYHO\ HDV\ EHFDXVH WKH
RULJLQDO GHVLJQ ZDV UHDFKHG E\ WULDODQGHUURU )RU VRPH DQDO\WLF GHVLJQV WKRXJK LW VRPH
WLPHV LV QRW LQWXLWLYHO\ REYLRXV ZKDW WR FKDQJH WR WU\ DQG LPSURYH WKH SHUIRUPDQFH 7KLV
LV HVSHFLDOO\ WUXH IRU LQWHUSRODWLRQ WHFKQLTXHV 2Q WKH RWKHU KDQG OLQHDUTXDGUDWLF WKHRU\
LV DQ H[DPSOH RI DQ DQDO\WLF DSSURDFK ZKHUH LV LW UHODWLYHO\ VWUDLJKWIRUZDUG DQG LQWXLWLYH
WR WZHDN WKH FRQWUROOHU E\ FKDQJLQJ WKH ZHLJKWLQJ PDWULFHV
7KHUHIRUH PRUH UHVHDUFK LV
QHHGHG RQ WKH ?ZKDW WR GR QH[W VWHS LQ WZHDNLQJ DQDO\WLF GHVLJQ PHWKRGV HVSHFLDOO\ WKRVH
LQYROYLQJ LQWHUSRODWLRQ WR LPSURYH V\VWHP SHUIRUPDQFH
%DVHG RQ WKH UHVXOWV RI WKLV UHVHDUFK VHYHUDO UHFRPPHQGDWLRQV IRU IXUWKHU VWXG\ RI WKH
ODWHUDO FRQWURO SUREOHP DUH RXWOLQHG EHORZ
q
'HYHORS EHWWHU DQDO\WLFDO PHWKRGV WR LQFOXGH ERWK SHUIRUPDQFH DQG UREXVWQHVV LQ WKH
&+$37(5 6800$5< $1' &21&/86,216
FRQWUROOHU GHVLJQ
q
,QFOXGH QRQOLQHDULWLHV OLNH VWHHULQJ DFWXDWRU EDFNODVK LQ WKH GHVLJQ WR LPSURYH UREXVW
QHVV
q
8VH PRUH NQRZOHGJH RI WKH SODQW XQFHUWDLQW\ LQ WKH FRQWUROOHU GHVLJQ WR LPSURYH V\VWHP
SHUIRUPDQFH
q
$OWKRXJK D n[HG FRQWUROOHU IRU DOO YHORFLWLHV DQG RSHUDWLQJ FRQGLWLRQV LV SUREDEO\
LPSRVVLEOH WKH XVH RI VHYHUDO n[HG FRQWUROOHUV IRU WKH YDULRXV RSHUDWLQJ FRQGLWLRQV
PLJKW EH SUHIHUDEOH WR JDLQVFKHGXOLQJ DV D IXQFWLRQ RI PDQ\ SDUDPHWHUV 7KLV ZRXOG
UHGXFH WKH VHQVRU UHTXLUHPHQWV IRU WKH JDLQVFKHGXOLQJ
q
0RUH UHVHDUFK LV QHHGHG WR LQYHVWLJDWH WKH WUDGHRmV EHWZHHQ LQFUHDVHG V\VWHP FRP
SOH[LW\ LH PRUH VHQVRUV IRU LPSURYHG SHUIRUPDQFH DQG WKH LQFUHDVHG FKDQFHV RI
IDLOXUH IURP JUHDWHU V\VWHP FRPSOH[LW\
$SSHQGL[ $ +DUGZDUH 'RFXPHQWDWLRQ
$33(1',; $ +$5':$5( '2&80(17$7,21
$SSHQGL[ % 0$7/$% 3URJUDPV
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
[ ORRS L ORRS
$33(1',; % 0$7/$% 352*5$06 KROG RII
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
$33(1',; % 0$7/$% 352*5$06 URRWVGSS URRWVGPS URRWVGPP
$SSHQGL[ & 9HKLFOH 6RIWZDUH
$33(1',; & 9(+,&/( 62)7:$5(
-,00< GDWD DFTXLVLVWLRQFRQWURO SURJUDP VWDUWHG
ODVW PRGLILHG
ZULWWHQ E\ 5D\ %\UQH
,1&/8'(6
LQFOXGH VWGLRK! LQFOXGH FRQLRK! LQFOXGH GRVK! LQFOXGH LRK!
'(),1(6
0$75,; $' %2$5' GHILQH $'B&+B6(/(&7 [)(% GHILQH $'B'$7$ [)(& 57& GHILQHV GHILQH 0$,1B67$786 [)'& GHILQH ,17(55837B [)'& GHILQH 3HULRGLFB)ODJ [)'& FRQWURO GHILQHV GHILQH YDOYHBPD[BS GHILQH YDOYHBPD[BQ
*/2%$/ 9$5,$%/(6
),/( GDWDBILOH XQVLJQHG FKDU )ODJ GXPP\ XQVLJQHG LQW L FRXQW FRXQW GDWD UDZBVHQVRU SUHYBVHQVRU SUHYBSUHYBVHQVRU UDZBMR\VWLFN UDZBSUHVVXUH SUHYBMR\VWLFN UDZBVWHHULQJ SUHYBVWHHULQJ FHQWHUBVWHHU SUHYBVWHHULQJ LQW VWHHUBHUURU GRZQFRXQW VHQVRU MR\VWLFN FRPPBVWHHULQJ VWHHULQJ URDGBHUURU HUURUBKLVW>@ YDOYHBRXW ORQJ LQW VWHHUBLQWHJUDO IORDW YDOYHBRXWBIS FRPPBVWHHULQJBIS URDGBSURS URDGBGHULY URDGBLQWHJUDO VHQVRUBKLVW>@ RXWSXWBKLVW>@ ILOWBVHQVRU>@ DUUD\ RI ILOWHUHG VHQVRU GDWD
)81&7,21 352727@ URDGBLQWHJUDO URDGBLQWHJUDO URDGBHUURU GRZQFRXQW LIGRZQFRXQW ! ^ HUURUBKLVW>@ HUURUBKLVW>@
$33(1',; & 9(+,&/( 62)7:$5( HUURUBKLVW>@ HUURUBKLVW>@ HUURUBKLVW>@ HUURUBKLVW>@ RXWSXWBKLVW>@ RXWSXWBKLVW>@ RXWSXWBKLVW>@ RXWSXWBKLVW>@
HUURUBKLVW>@ HUURUBKLVW>@ HUURUBKLVW>@ URDGBHUURU RXWSXWBKLVW>@ RXWSXWBKLVW>@ RXWSXWBKLVW>@ RXWSXWBKLVW>@
RXWSXWBKLVW>@ RXWSXWBKLVW>@ RXWSXWBKLVW>@ RXWSXWBKLVW>@ RXWSXWBKLVW>@ HUURUBKLVW>@ HUURUBKLVW>@ HUURUBKLVW>@ HUURUBKLVW>@ HUURUBKLVW>@ GRZQFRXQW ` HQG RI VHF ORRS FRPPBVWHHULQJ
RXWSXWBKLVW>@ URDGBLQWHJUDO
VWHHUBHUURU UDZBVWHHULQJ FRPPBVWHHULQJ VWHHUBLQWHJUDO VWHHUBLQWHJUDO VWHHUBHUURU YDOYHBRXWBIS VWHHUBHUURU VWHHUBLQWHJUDO YDOYHBRXWBIS YDOYHBRXW YDOYHBPD[BS OLPLW VSHHG LI YDOYHBRXW ! YDOYHBPD[BS YDOYHBRXW LI YDOYHBRXW YDOYHBPD[BQ YDOYHBRXW YDOYHBPD[BQ RI VWHHULQJ RXWSRUWE [IH YDOYHBRXW [II RXWSRUWE [IH YDOYHBRXW !! RXWSRUWE [I [II RXWSRUWE [I [ WRJJOH ZDWFKGRJ SUHYBVWHHULQJ UDZBVWHHULQJ RXWSRUWE [ [ QRQVSHFLILF (2, UHWXUQ ` HQG RI LQWHUUXSW VHUYLFH URXWLQH YRLG ,QLWB57& YRLG ^ RXWSRUWE 0$,1B67$786 [ GXPP\ LQSRUWE 3HULRGLFB)ODJ RXWSRUWE 0$,1B67$786 [ RXWSRUWE ,17(55837B [ UHWXUQ ` HQG RI ,QLWB57&
VHW ELW ELW UHDG FOHDUV IODJ UHJLVWHU VHW ELW ELW JHQHUDWH LQWHUUXSW # VHF
YRLG FUHDWHBILOHV YRLG ^ GDWDBILOH IRSHQUGDWDP D UHWXUQ ` HQG RI FUHDWHBILOHV YRLG FORVHBILOHV YRLG ^ IFORVH GDWDBILOH UHWXUQ ` HQG RI FORVHBILOHV
0$,1 352*5$0
$33(1',; & 9(+,&/( 62)7:$5( YRLG PDLQ ^ FUHDWHBILOHV ,QLWB57& LQLWLDOL]H UHDO WLPH FORFN LQLW9HFWRUV LQLWLDOL]H ,65 DQG ,5 PDVN IRU L LL ILOWBVHQVRU>L@ LQLW ILOWHU IRU L LL HUURUBKLVW>L@ IRU L LL RXWSXWBKLVW>L@ RXWSRUWE $'B&+B6(/(&7 [ VHOHFW &+ GR ^ FHQWHUBVWHHU LQSRUW $'B'$7$ ` ZKLOH FHQWHUBVWHHU ! [ ZKLOH NEKLW ^ LI )ODJ ^ FRXQW )ODJ IRUL LL ^ ILOWBVHQVRU>L@ ILOWBVHQVRU>L@ ` HQG RI IRU ORRS ILOWBVHQVRU>@ H UDZBVHQVRU SUHYBVHQVRU SUHYBSUHYBVHQVRU ILOWBVHQVRU>@ ILOWBVHQVRU>@ SUHYBSUHYBVHQVRU SUHYBVHQVRU SUHYBVHQVRU UDZBVHQVRU ISULQWIGDWDBILOHG G G I I ?Q UDZBVHQVRU URDGBHUURU UDZBVWHHULQJ RXWSXWBKLVW>@ ILOWBVHQVRU>@ ` HQG RI LI VWDWHPHQW ` HQG RI ZKLOH ORRS ),1,6+ UHVWRUH9HFWRUV FORVHBILOHV `
HQG RI PDLQ
%LEOLRJUDSK\ >@ - $FNHUPDQQ
5REXVW FDU VWHHULQJ E\ \DZ UDWH FRQWURO
,Q
3URF RI WKH &'&
SDJHV ^ +RQROXOX
>@ - $FNHUPDQQ
5REXVW FDU VWHHULQJ E\ \DZ UDWH IHHGEDFN
,Q
&RQWURO RI 8QFHUWDLQ
'\QDPLF 6\VWHPV
SDJHV ^ &5& 3UHVV %RFD 5DWRQ
>@ - $FNHUPDQQ
9HORFLW\LQGHSHQGHQW \DZ HLJHQYDOXHV RI IRXU ZKHHOVWHHULQJ DXWRPR
ELOHV ,Q 0 0DQVRXU 6 %DOHPL DQG : 7UXRO HGLWRUV
5REXVWQHVV RI '\QDPLF 6\VWHPV
ZLWK 3DUDPHWHU 8QFHUWDLQWLHV
SDJHV ^ %LUNKDXVHU 9HUODJ %DVHO
>@ - $FNHUPDQQ $ %DUWOHWW ' .DHVEDXHU : 6LHQHO DQG 5 6WHLQKDXVHU
5REXVW
&RQWURO 6\VWHPV ZLWK 8QFHUWDLQ 3K\VLFDO 3DUDPHWHUV
6SULQJHU 9HUODJ /RQGRQ
>@ - $FNHUPDQQ - *XOGQHU DQG 9 , 8WNLQ
DXWRPDWLF SDWK WUDFNLQJ RI D FDU ,Q
$ UREXVW QRQOLQHDU FRQWURO DSSURDFK WR
3URF RI WKH ,QWHUQDWLRQDO &RQIHUHQFH RQ &RQWURO
SDJHV ^ &RYHQWU\ (QJODQG
>@ - $FNHUPDQQ DQG : 6LHQHO 5REXVW FRQWURO IRU DXWRPDWLF VWHHULQJ ,Q
3URF RI WKH
$&&
SDJHV ^ 6DQ 'LHJR
>@ 1 , $NKLH]HU
7KH &ODVVLFDO 0RPHQW 3UREOHP
2OLYHU DQG %R\G /RQGRQ
%,%/,2*5$3+
@ $ + $ + $OL
$ 6XUYH\ RI :HLJKWLQJ )XQFWLRQV IRU
+
&RQWURO
7HFKQLFDO 5H
SRUW &RQWURO 6\VWHP &HQWUH 80,67 0DQFKHVWHU 8. 0D\
>@ ) 3 $QGUHVHQ DQG / 6 'DYLV
9LVXDO 3RVLWLRQ 'HWHUPLQDWLRQ IRU $XWRQRPRXV /DQG
9HKLFOH 1DYLJDWLRQ
7HFKQLFDO 5HSRUW &$575 8QLYHUVLW\ RI 0DU\ODQG &ROOHJH
3DUN 0'
>@ ' $XEHUW DQG & ( 7KRUSH
&RORU ,PDJH 3URFHVVLQJ IRU 1DYLJDWLRQ7ZR 5RDG 7UDFN
HUV
7HFKQLFDO 5HSRUW &085,75 &DUQHJLH 0HOORQ 8QLYHUVLW\ 3LWWVEXUJ
>@ % 5 %DUPLVK DQG . + :HL 6LPXOWDQHRXV VWDELOL]DELOLW\ RI VLQJOH LQSXWVLQJOH RXWSXW
V\VWHPV ,Q
3URF RI WKH WK ,QWO 6\PSRVLXP RQ 0DWKHPDWLFDO 7KHRU\ RI 1HWZRUNV DQG
6\VWHPV
SDJHV ^ 6WRFNKROP
>@ ' ( %DUULFN
$XWRPDWLF 6WHHULQJ 7HFKQLTXHV
7HFKQLFDO 5HSRUW ((6 $ 2KLR
6WDWH 8QLYHUVLW\ (QJU ([S 6WDWLRQ &ROXPEXV 2+ 'HF
>@ / 6 %RQGHUVRQ 2SWLPXP ODWHUDO FRQWURO IRU GXDOPRGH YHKLFOHV ,Q
3URF RI WKH ,QW
&RQI RQ 'XDO0RGH 7UDQVSRUWDWLRQ
SDJH
>@ 5 + %\UQH DQG & 7 $EGDOODK 'HVLJQ RI D PRGHO UHIHUHQFH DGDSWLYH FRQWUROOHU IRU
YHKLFOH URDG IROORZLQJ $FFHSWHG LQ 1HWZRUN &RQWURO &RPPXQLFDWLRQ DQG &RPSXWLQJ
7HFKQRORJLHV IRU ,QWHOOLJHQW 9HKLFOH +LJKZD\ 6\VWHPV
>@ 5 + %\UQH DQG & 7 $EGDOODK 5REXVW ODWHUDO FRQWURO RI KLJKZD\ YHKLFOHV 7R DSSHDU
LQ WKH 3URF RI WKH ,QWHOOLJHQW 9HKLFOHV 6\PSRVLXP
%,%/,2*5$3+
@ . + ) &DUGHZ
7KH $XWRPDWLF 6WHHULQJ RI 9HKLFOHV $Q ([SHULPHQWDO 6\VWHP )LWWHG
WR D '6 &LWURJHQ &DU
7HFKQLFDO 5HSRUW /5 5RDG 5HVHDUFK /DE *UHDW %ULWDLQ
>@ + &KULVW : 'DUHQEHUJ ) 3DQLN DQG : :HLGHPDQQ $XWRPDWLF WUDFN FRQWURO RI
YHKLFOHV WKHRU\ DQG H[SHULPHQW ,Q
3URF RI WKH WK 96' QG ,87$0 6\PSRVLXP
SDJHV ^ 9LHQQD
>@ : + &RUPLHU DQG 5 ( )HQWRQ 2Q WKH VWHHULQJ RI DXWRPDWHG YHKLFOHV D YHORFLW\
DGDSWLYH FRQWUROOHU
,((( 7UDQV RQ 9HK 7HFK
^ 1RY
>@ : 'DUHQEHUJ ) 3DQLN DQG : :HLGHPDQQ
FRQWUROOHUV
,Q
'HVLJQ RI DXWRPDWLF ODWHUDO YHKLFOH
3URF RI WKH WK ,)$& :RUOG &RQJUHVV
SDJHV ^ +HOVLQNL
>@ / 6 'DYLV DQG 7 5 .XVKQHU
QDYLJDWLRQ ,Q
5RDG ERXQGDU\ GHWHFWLRQ IRU DXWRQRPRXV YHKLFOH
,QWHOOLJHQW 5RERWV DQG &RPSXWHU 9LVLRQ
SDJHV ^
>@ / 6 'DYLV 7 5 .XVKQHU - / /H0RLJQH DQG $ 0 :D[PDQ
GHWHFWLRQ IRU DXWRQRPRXV YHKLFOH QDYLJDWLRQ
5RDG ERXQGDU\
2SWLFDO (QJLQHHULQJ
^
>@ / 6 'DYLV DQG - / /H0RLJQH 9LVXDO QDYLJDWLRQ RI URDGZD\V ,Q
3URF RI WKH ,QWO
&RQI RQ ,QWHOOLJHQW 6\VWHPV
SDJHV ^ $PVWHUGDP
>@ 3 + 'HOVDUWH @ 3 'RUDWR
$QDO\WLF )HHGEDFN 6\VWHP 'HVLJQ $Q ,QWHUSRODWLRQ $SSURDFK
7HFKQLFDO
5HSRUW 8QLYHUVLW\ RI 1HZ 0H[LFR
>@ 3 'RUDWR / )RUWXQD DQG * 0XVFDWR
5REXVW &RQWURO IRU 8QVWUXFWXUHG 3HUWXUEDWLRQV
$Q ,QWURGXFWLRQ
6SULQJHU 9HUODJ 1HZ @ 3 'RUDWR DQG @ - & 'R\OH . *ORYHU 3 3 .KDUJRQHNDU DQG % $ )UDQFLV 6WDWHVSDFH VROXWLRQV WR
VWDQGDUG
+
DQG
+
FRQWURO SUREOHPV
,((( 7UDQV $XWRPDW &RQWU
$&^
>@ - & 'R\OH DQG * 6WHLQ 0XOWLYDULDEOH IHHGEDFN GHVLJQ FRQFHSWV IRU FODVVLFDOPRGHUQ
V\QWKHVLV
,((( 7UDQV $XWRPDW &RQWU
$&^
>@ 5 )HQWRQ DQG , 6HOLP 2Q WKH RSWLPDO GHVLJQ RI DQ DXWRPDWLF ODWHUDO FRQWUROOHU
,(((
7UDQV RQ 9HK 7HFK
^
>@ 5 ( )HQWRQ ,9+6$+6 GULYLQJ LQWR WKH IXWXUH
,((( &RQWURO 6\VWHPV 0DJD]LQH
^ 'HFHPEHU
>@ 5 ( )HQWRQ 5 / &RVJULm . : 2OVRQ DQG / 0 %ODFNZHOO
KLJKZD\ DXWRPDWLRQ
3URF RI WKH ,(((
^
2QH DSSURDFK WR
%,%/,2*5$3+
@ 5 ( )HQWRQ DQG 5 - 0D\KDQ $XWRPDWHG KLJKZD\ VWXGLHV DW WKH RKLR VWDWH XQLYHUVLW\
DQ RYHUYLHZ
,((( 7UDQV RQ 9HK 7HFK
^
>@ 5 ( )HQWRQ 5 - 0D\KDQ * 0 7DNDVDNL DQG - *OLPP
)XQGDPHQWDO 6WXGLHV LQ
$XWRPDWLF 9HKLFOH &RQWURO
7HFKQLFDO 5HSRUW 2KLR 6WDWH 8QLYHUVLW\ &ROXP
EXV 2+ 0D\
>@ 5 ( )HQWRQ * & 0HORFLN DQG . : 2OVRQ 2Q WKH VWHHULQJ RI DXWRPDWHG YHKLFOHV
WKHRU\ DQG H[SHULPHQW
,((( 7UDQV $XWRPDW &RQWU
$&^
>@ 5 ( )HQWRQ DQG 6 6 0XUSK\ $ PLFURSURFHVVRUEDVHG YHKLFOH ODWHUDO FRQWUROOHU ,Q
3URF RI WKH VW 9HK 7HFK 6RF &RQI
SDJHV ^ :DVKLQJWRQ '&
>@ ) 5 *DQWPDFKHU
>@ . *DUGHOV
7KH 7KHRU\ RI 0DWULFHV
9ROXPH &KHOVHD 1HZ @ 1 . *XSWD
)UHTXHQF\VKDSHG FRVW
JDXVVLDQ GHVLJQ PHWKRGV
IXQFWLRQDOV
H[WHQVLRQ RI OLQHDUTXDGUDWLF
- *XLGDQFH DQG &RQWURO
>@ . +D\DIXQH DQG + @ - . +HGULFN 0 7RPL]XND DQG 3 9DUDL\D
V\VWHPV
,((( &RQWURO 6\VWHPV 0DJD]LQH
&RQWURO LVVXHV LQ DXWRPDWHG KLJKZD\
^ 'HFHPEHU
%,%/,2*5$3+
@ 7 +HVVEXUJ DQG 0 7RPL]XND )X]]\ ORJLF FRQWURO IRU ODWHUDO YHKLFOH JXLGDQFH
,(((
&RQWURO 6\VWHPV 0DJD]LQH
^ $XJXVW
>@ , +RURZLW] 4XDQWLWDWLYH IHHGEDFN WKHRU\
,(( 3URF
^
>@ 7 ,WR 0 )XUXPDWD ) +DUDVKLPD + ,QDED DQG 6 0DWVXPRWR
GULYLQJ V\VWHP RI DXWRPRELOHV E\ JXLGDQFH FDEOHV
,Q
$Q DXWRPDWLF
3URF RI WKH ,QW $XWRPRWLYH
(QJLQHHULQJ &RQIHUHQFH
'HWURLW
>@ + .LPXUD 5REXVW VWDELOLW\ IRU D FODVV RI WUDQVIHU IXQFWLRQV
,((( 7UDQV $XWRPDW
&RQWU
$& ^
>@ 1 $ /HKWRPDNL 1 5 6DQGHOO DQG 0 $WKDQV
5REXVWQHVV UHVXOWV LQ WKH OLQHDU
TXDGUDWLF JDXVVLDQ EDVHG PXOWLYDULDEOH FRQWURO GHVLJQV
,((( 7UDQV $XWRPDW &RQWU
$& ^
>@ @ 5 - 0D\KDQ DQG 5 $ %LVKHO $ WZR IUHTXHQF\ UDGDU IRU YHKLFOH DXWRPDWLF ODWHUDO
FRQWURO
,((( 7UDQV RQ 9HK 7HFK
97 ^ )HE
%,%/,2*5$3+
@ ' 0RUJHQWKDOHU 6 - +HQQHVV\ DQG ' 'H0HQWKRQ 5DQJHYLGHR IXVLRQ DQG FRPSDU
LVRQ RI LQYHUVH SHUVSHFWLYH DOJRULWKPV LQ VWDWLF LPDJHV
,((( 7UDQV RQ 6\VWHPV 0DQ
DQG &\EHUQHWLFV
^
>@ 6 6 0XUSK\
$ 0LFURSURFHVVRU%DVHG /DWHUDO &RQWUROOHU IRU DQ $XWRPDWHG 9HKLFOH
0DVWHU V WKHVLV 2KLR 6WDWH 8QLYHUVLW\ &ROXPEXV 2+
>@ 5 1HYDQOLQQD 8EHU EHVFKUDQNWH IXQNWLRQHQ GLH LQ JHJHEHQ SXQNWHQ YRUJHVFKULHGHQH
ZHUWH DQQHKPHQ
$QQ $FDG 6FL )HQQ
^
>@ . : 2OVRQ ( 5 6DSS DQG 7 / )ODLJ $ V\VWHP IRU DXWRPDWLF YHKLFOH JXLGDQFH
,Q
+LJKZD\ 5HVHDUFK 5HFRUG 3URF RI WKH WK $QQXDO 0HHWLQJ
SDJHV ^
>@ 5 ( 3DUVRQV DQG : % =KDQJ
ODWHUDO JXLGDQFHFRQWURO
,Q
3URJUDP RQ DGYDQFHG WHFKQRORJ\ IRU WKH KLJKZD\
3URF RI WKH VW ,QW O &RQI $SSOLFDWLRQV RI $GYDQFHG
7HFKQRORJ\ LQ 7UDQVSRUWDWLRQ (QJLQHHULQJ
SDJHV ^ 6DQ 'LHJR &$
>@ 6 3DVWHUQDFN
0RGHUQ &RQWURO $VSHFWV RI $XWRPDWLFDOO\ 6WHHUHG 9HKLFOHV
7HFKQLFDO
5HSRUW '2776&267 7UDQVSRUWDWLRQ 6\VWHPV &HQWHU &DPEULGJH 0$ 'H
FHPEHU
>@ 5 - 3DWWRQ DQG - &KHQ
VWUXFWXUH DVVLJQPHQW
5REXVW IDXOW GHWHFWLRQ RI MHW HQJLQH VHQVRUV XVLQJ HLJHQ
$,$$ -RXUQDO RI *XLGDQFH &RQWURO DQG '\QDPLFV
^
>@ 6 3DWZDUGKDQ DQG 0 7RPL]XND 5REXVW IDLOXUH GHWHFWLRQ LQ ODWHUDO FRQWURO IRU ,9+6
,Q
3URF RI WKH $&&
SDJHV ^ &KLFDJR
%,%/,2*5$3+
@ * 3LFN 8EHU GLH EHVFKUDQNXQJHQ DQDO\WLVFKHU IXQNWLRQHQ ZHOFKH GXUFK YRUJHJHEHQHQ
ZHUWH DQQHKPHQ
0DWK $QQ
>@ ' $ 3RPPHUOHDX
GULYLQJ
,Q
^
3URJUHVV LQ QHXUDO QHWZRUNEDVHG YLVLRQ IRU DXWRQRPRXV URERW
3URF RI WKH ,QWHOOLJHQW 9HKLFOHV 6\PSRVLXP
SDJHV ^ 'HWURLW
>@ + 3XHQJ 7 +HVVEXUJ 0 7RPL]XND : % =KDQJ @ ( % 6Dm DQG $ ' 6QLGHU
)XQGDPHQWDOV RI &RPSOH[ $QDO\VLV IRU 0DWKHPDWLFV DQG
6FLHQFH
3UHQWLFH +DOO (QJOHZRRG &OLmV 1-
>@ 6 6HLGD
$/9 FORVHXS
nQGLQJ WKH URDG ZKHQ RmURDG
3URFHHGLQJV RI WKH 63,(
^
>@ 6 6KHLNKROHVODP DQG & $ 'HVRHU
SODWRRQ RI YHKLFOHV ,Q
&RPELQHG ORQJLWXGLQDO DQG ODWHUDO FRQWURO RI D
3URF RI WKH $&&
SDJHV ^ &KLFDJR
$QDO\VLV DQG 'HVLJQ RI 6WHHULQJ
>@ 6 6KODGRYHU 5 )LVK + 5LFKDUGVRQ DQG ' :RUPOH\
&RQWUROOHUV IRU $XWRPDWHG *XLGHZD\ 7UDQVLW 9HKLFOHV
7HFKQLFDO 5HSRUW 807$5'
0$ 0DVVDFKXVHWV ,QVWLWXWH RI 7HFKQRORJ\ &DPEULGJH 0$ 6HSW
>@ 6 ( 6KODGRYHU & $ 'HVRHU - . +HGULFN 0 7RPL]XND - :DOUDQG : % =KDQJ
' + 0F+DKRQ + 3XHQJ 6 6KHLNKROHVODP DQG 1 0F.HRZQ
$XWRPDWLF YHKLFOH
%,%/,2*5$3+
@ 6 ( 6KODGRYHU ' 1 :RUPOH\ + + 5LFKDUGVRQ DQG 5 )LVK
GHVLJQ IRU DXWRPDWHG JXLGHZD\ WUDQVLW YHKLFOH
6WHHULQJ FRQWUROOHU
-RXUQDO RI '\QDPLF 6\VWHPV 0HDVXUH
PHQW DQG &RQWURO
^ 0DUFK
>@ / , 6PLOHQ ,QWHUSRODWLRQ RQ WKH UHDO IUHTXHQF\ D[LV
,((( ,QWHUQDW &RQY 5HFRUG
^
>@ + 6XVVPDQQ ( 6RQWDJ DQG @ - @ : =KDQJ 5 ( 3DUVRQV DQG 7 :HVW $Q LQWHOOLJHQW URDGZD\ UHIHUHQFH V\VWHP IRU
YHKLFOH ODWHUDO JXLGDQFHFRQWURO ,Q
3URF RI WKH $&&
SDJHV ^ 6DQ 'LHJR
%,%/,2*5$3+
@ 9 . =ZRU\NLQ DQG / )ORU\ (OHFWURQLF FRQWURO RI PRWRU YHKLFOHV RQ WKH KLJKZD\ ,Q
3URF RI WKH WK $QQXDO 0HHWLQJ RI WKH +LJKZD\ 5HVHDUFK %RDUG