2Q8QVWUXFWXUHG8QFHUWDLQW\$QDO\VLVLQ
$FWXDWRU'\QDPLFVRIWKH7KUHHORRS/DWHUDO
0LVVLOH$XWRSLORW
%LUDM*XKD
Department of Electrical Engineering Techno India, Salt Lake, West Bengal, India
$EVWUDFW$QDO\VLVRIXQVWUXFWXUHGXQFHUWDLQW\LQKLJKHURUGHUDFWXDWRUG\QDPLFVRIWKHWKUHHORRSODWHUDODXWRSLORWRI WDLO FRQWUROOHG VXUIDFH WR VXUIDFH PLVVLOH KDV EHHQ SUHVHQWHG LQ WKH SDSHU 7KH PLVVLOH DXWRSLORW V\VWHP KDV EHHQ FKDUDFWHUL]HGE\WKHG\QDPLFVLQYROYLQJQRQPLQLPXPSKDVH]HUR7KHXQVWUXFWXUHGXQFHUWDLQW\DULVHVW\SLFDOO\IURP WUXQFDWLQJDFRPSOH[PRGHOE\UHWDLQLQJRQO\VRPHRIWKHGRPLQDQWPRGHVZKLFKXVXDOO\OLHLQWKHORZIUHTXHQF\UDQJH 7KHIUHTXHQF\GRPDLQDQDO\VLVRIWKHXQVWUXFWXUHGXQFHUWDLQW\LQDFWXDWRUG\QDPLFVKDVEHHQFDUULHGRXWE\GHOWD65 PHWKRG
.H\ZRUGV$XWRSLORWQRQPLQLPXPSKDVHXQVWUXFWXUHGXQFHUWDLQW\DFWXDWRUPLVVLOH
Parameters identification
.E$LUIUDPHDHURG\QDPLFJDLQVHF0S3HDNRYHUVKRRW
.S/DWHUDODXWRSLORWFRQWUROJDLQRXWHUORRS40LVVLOHERG\UDWHLQSLWFKUDGVHF
TG0LVVLOHERG\UDWHGHPDQGHGLQSLWFKUDGVHF.T)LQVHUYRJDLQVHF
7D,QFLGHQFHODJVRIDLUIUDPHVHFȟD'DPSLQJUDWLRRIDFWXDWRU
T0LVVLOHERG\UDWHLQSLWFKUDGVHFK(OHYDWRUGHIOHFWLRQUDG
ȦE:HDWKHUFRFNIUHTXHQF\UDGVHF
JJG)OLJKWSDWKDQJOHUDGDQGIOLJKWSDWKUDWHGHPDQGHGUDGVHFUHVSHFWLYHO\
ȦD1DWXUDOIUHTXHQF\RIRVFLOODWLRQRI$FWXDWRUUDGVHF
*&)*DLQFURVVRYHUIUHTXHQF\
6HSDUDWLRQIDFWRUUDWLREHWZHHQLQQHUORRS*&)DQGDFWXDWRUIUHTXHQF\ȦD
PȘ0RPHQWGHULYDWLYHGXHWRHOHYDWRUGHIOHFWLRQVHF±6HPLQRQGLPHQVLRQDOIRUP
ı$TXDQWLW\ZKRVHLQYHUVHGHWHUPLQHVWKHORFDWLRQRIQRQPLQLPXPSKDVH]HURLQVSODQH
ȦL/DWHUDODXWRSLORWFRQWUROJDLQLQWHUPHGLDWHORRS
%56SHFLILHGPLVVLOHERG\WDUHUDGVHF
,,1752'8&7,21
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ȦDDQGGDPSLQJUDWLRȟDDUH
JLYHQDQGWKHDLUIUDPHHQYLURQPHQWSDUDPHWHUVDUHUHSUHVHQWHGE\WKHDHURG\QDPLFSDUDPHWHUV7DPȘȦEı7DEOH
,,,DQGWKHSHUIRUPDQFHDFKLHYHGIRUVXFKRSHUDWLQJSRLQWVKDYHEHHQLOOXVWUDWHGLQ>@ZLWKQXPHULFDOH[DPSOHV 7KHPHWKRGRORJ\DVVXUHVDGHTXDWHVWDELOLW\PDUJLQVDWWKHVHRSHUDWLQJSRLQWVIRUFKRVHQVHWVRIQRPLQDOYDOXHVRI DHURG\QDPLFDQGDFWXDWRUSDUDPHWHUV7KHRXWHUORRSRIWKHWKUHHORRSPLVVLOHDXWRSLORWFRQILJXUDWLRQLVNQRZQDV IOLJKW SDWK UDWH ORRS ZKHUHDV WKH LQWHUPHGLDWH ORRS LV ERG\ UDWH ORRS 7KH LQQHU ORRS FRQVLVWV RI WKH SLWFK UDWH IHHGEDFNDQGWKHVHUYRJDLQ.TDVPHQWLRQHGLQ>@
DWWHPSWWRGHYHORSDVLPSOHPHWKRGRORJ\WRDFHUWDLQVWDELOLW\UREXVWQHVVSURSHUW\RIWKHWZRORRSDXWRSLORWLQVSLWH RIPRGHOLQJHUURUVGXHWRKLJKIUHTXHQF\XQPRGHOOHGG\QDPLFVDQGSODQWSDUDPHWHUYDULDWLRQV
7KH UHVW RI WKH SDSHU LV RUJDQL]HG DV IROORZV 7KH SHUIRUPDQFH FKDUDFWHULVWLFV RI WKH WKUHH ORRS ODWHUDO PLVVLOH DXWRSLORWLQSLWFKSODQHKDYHEHHQH[SODLQHGLQVHFWLRQ,,/LWHUDWXUHUHYLHZLVJLYHQLQVHFWLRQ,,,ZKHUHDVWKHHIIHFW RIXQPRGHOOHGDFWXDWRUG\QDPLFVDQGDXWRSLORWUREXVWQHVVKDVEHHQSUHVHQWHGLQVHFWLRQ,9&RQFOXVLRQLVJLYHQLQ VHFWLRQ9
,, 7+(3(5)250$1&(&+$5$&7(5,67,&62)7+(7+5((/223/$7(5$/0,66,/($8723,/27,13,7&+3/$1(
7KHWKUHHORRSODWHUDOPLVVLOHDXWRSLORWFRQILJXUDWLRQDVGHYHORSHGLQ>@KDVEHHQVKRZQLQ)LJ$DQGLVXWLOL]HG LQWKHSUHVHQWZRUN7KHWLPHUHVSRQVHFXUYHFRUUHVSRQGLQJWRXQLWVWHSLQSXWKDVEHHQVKRZQLQ)LJ%DQGWKH WLPHGRPDLQFKDUDFWHULVWLFVKDYHEHHQSURYLGHGLQ7DEOH,
)LJXUH$7KUHHORRSODWHUDODXWRSLORWRIWDLOFRQWUROOHGPLVVLOHLQSLWFKSODQH
6WHS5HVSRQVH
7LPHVHFRQGV
$
P
SOLWX
GH
)LJXUH%6WHSUHVSRQVHRIPLVVLOHDXWRSLORW
,QWKHILJXUH$*UHSUHVHQWVVHFRQGRUGHUDFWXDWRUG\QDPLFVZKHUHDV*DQG*DUHWKHDHURG\QDPLFWUDQVIHU IXQFWLRQV
7DEOH,6WHSUHVSRQVHRI3,FRQWUROOHGWZRORRSDXWRSLORW
5HILQSXW 0S 5LVH7LPH 3HDN7LPH 6HWWOLQJ7LPH 6WHDG\VWDWHHUURU
8QLWVWHS VHF VHF VHF
,,, /,7(5$785(5(9,(:
FRQVWDQWGDPSLQJDQGWKHRSHQORRSFURVVRYHUIUHTXHQF\EUHDNLQJLQWHUPRVWORRSDWDFWXDWRURXWSXWDUHVSHFLILHG WKHFRQWUROJDLQVFDQEHFRPSXWHGDOJHEUDLFDOO\
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
$V\VWHPDWLFPHWKRGRORJ\IRUWKHGHVLJQRIDWKUHHORRSODWHUDODXWRSLORWIRUDFODVVRIKRPLQJPLVVLOHVKDVEHHQ GHYHORSHGLQ>@DQGWKHGHVLJQSUREOHPVDUHDVIROORZV
L &ULWLFDOJDLQPDUJLQDVSHFLILHGYDOXHRIJDLQPDUJLQ LL &ULWLFDOSKDVHPDUJLQDVSHFLILHGYDOXHRISKDVHPDUJLQ LLL 0LVVLOHERG\UDWHDVSHFLILHGYDOXHRIERG\UDWH
7KHFRQWUROJDLQVNSȦLNTKDYHEHHQHYDOXDWHGZLWKWKHDERYHPHQWLRQHGGHVLJQSUREOHPV,QWKHZRUNFDUULHGRXW
LQ>@WKHHIIHFWRIXQFHUWDLQW\RQWKHSHUIRUPDQFHRIWKHFORVHGORRSDXWRSLORWV\VWHPKDVQRWEHHQGHDOWZLWK7KH SUHVHQWZRUNLQFOXGHVDVWXG\RQSODQWXQFHUWDLQWLHV7KHHIIHFWVRIXQVWUXFWXUHGXQFHUWDLQW\RQWKHKLJKHURUGHUWK
RUGHUDFWXDWRUG\QDPLFVDQGWKHV\VWHPUREXVWQHVVKDYHEHHQFDUULHGRXWLQWKHSUHVHQWZRUN7KHSUHVHQWZRUN FRQFHQWUDWHV RQO\ RQ WKH XQVWUXFWXUHG XQFHUWDLQW\ ,W LV TXLWH MXVWLILHG WR DQDO\]H WKH HIIHFW RI XQPRGHOOHG KLJK IUHTXHQF\G\QDPLFVLQDFRQWUROORRSVXEV\VWHPOLNHDQDFWXDWRUV\VWHP
,9 ())(&72)8102'(//('$&78$725'<1$0,&6$1'7+($8723,/2752%8671(66 A. Autopilot performance limitations due to plant uncertainty
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ȟD DQG QDWXUDO IUHTXHQF\ ȦD 7KH VWDELOLW\ UREXVWQHVV RI WKH WKUHH ORRS DXWRSLORW LQ
SUHVHQFHRIXQVWUXFWXUHGXQFHUWDLQW\KDVEHHQIRFXVHGLQWKHSUHVHQWZRUNWKDWLQFRUSRUDWHVKLJKHURUGHUG\QDPLF PRGHOVL[WKRUGHUPRGHOIRUWKHDFWXDWRUV\VWHPLQVWHDGRIWKHVHFRQGRUGHUPRGHOZLWKVSHFLILHGȟDDQGȦQXVHGLQ
>@7KHUREXVWQHVVSHUIRUPDQFHKDVEHHQFDUULHGRXWE\GHOWD65 PHWKRGLQRUGHUWRLQYHVWLJDWHWKHDXWRSLORW SHUIRUPDQFHOLPLWDWLRQVXVLQJWKHGHVLJQSDUDPHWHUVIRUDW\SLFDORSHUDWLQJSRLQW7DEOH,,,RIWKHIOLJKWSDWKDWWKH DHURG\QDPLFFRQWUROSKDVH
B. Methodology used for robustness analysis
7KHXQVWUXFWXUHGXQFHUWDLQW\FDQEHUHSUHVHQWHGLQWKHIRUPRIDQDGGLWLYHRUDPXOWLSOLFDWLYHSHUWXUEDWLRQ )RUWKHPXOWLSOLFDWLYHSHUWXUEDWLRQWKHWUXHWUDQVIHUIXQFWLRQLV
*V Vș>lV@««««$
:KHUH VșLVDSDUDPHWHUL]HGPRGHORIWKHSODQWZLWKWKHVWUXFWXUHGXQFHUWDLQW\șZKLFKUHSUHVHQWVWKHSODQW SDUDPHWHUYDULDWLRQV VșLVDNQRZQIXQFWLRQEXWWKHYDOXHVRIWKHSDUDPHWHUșDUHXQFHUWDLQ7KHIXQFWLRQlV LVDQXQVWUXFWXUHGXQFHUWDLQW\DQGLWLVHQWLUHO\XQNQRZQH[FHSWWKDWLWLVOLPLWHGLQPDJQLWXGHWR_lMȦ_ lȦDQG
lȦLVDNQRZQUHDOVFDODUIXQFWLRQ7KHERXQGFDQEHYLHZHGDVDIUHTXHQF\GHSHQGHQW³UDGLXV´RIXQFHUWDLQW\RI
WKHWUXHSODQWWUDQVIHUIXQFWLRQV*VDERXWVRPHPRGHO VșIRUDJLYHQș)LJ$VKRZVKRZVXFKDERXQGFDQ EHFDOFXODWHGH[SHULPHQWDOO\E\VLPSO\FRPSDULQJWKHDFWXDOSODQWZLWKWKHPRGHO
$VVXPLQJWKDWDOOWKHVWUXFWXUHGDQGXQVWUXFWXUHGXQFHUWDLQWLHVDUHOXPSHGLQWRDVWDEOHPXOWLSOLFDWLYHSHUWXUEDWLRQ WKHQ
:KHUH V UHSUHVHQWV WKH QRPLQDO SODQW WUDQVIHU IXQFWLRQ VHFRQG RUGHU DFWXDWRU G\QDPLFV DQG IXQFWLRQlV LV WKH XQVWUXFWXUHGXQFHUWDLQW\ZKLFKLVHQWLUHO\XQNQRZQDQG*VLVWKHKLJKHURUGHUDFWXDWRUG\QDPLFV6L[WKRUGHU
)LJXUH$)UHTXHQF\GHSHQGHQWXQFHUWDLQW\ERXQG)LJXUH)LJXUH%&RPSHQVDWHGIHHGEDFNV\VWHP
%\3XWWLQJV MȦLQHT%WKHIROORZLQJH[SUHVVLRQLVREWDLQHG
*MȦ MȦUMȦ«««««
ZKHUHUMȦ MȦlMȦ
,QJHQHUDODJRRGPRGHOZLOOEHZHOONQRZQDWORZIUHTXHQFLHVZKLFKUHVXOWLQVPDOOYDOXHVRIlȦDQGOHVVZHOONQRZQ DWKLJKIUHTXHQFLHVZKHUHWKHYDOXHRIlȦLVODUJH7KHV\VWHP*VDORQJZLWKFRPSHQVDWLRQ'VLVVKRZQLQ)LJ %7KHV\VWHP*VWHQGVWRJHWXQVWDEOHLQSUHVHQFHRIWKHXQFHUWDLQW\lV$FRPSHQVDWRU'VLQLQVHUWHGLQWRWKH V\VWHPIRUPDNLQJWKHFORVHGORRSV\VWHPVWDEOH$W\SLFDOQ\TXLVWSORWRIWKHFRPSHQVDWHGV\VWHPLVVKRZQ)LJ
)LJXUH1\TXLVWGLDJUDPPRGLILHGE\PRGHOXQFHUWDLQW\
$V VLVSHUWXUEHGWKHQ\TXLVWSORWPRYHVDURXQGZLWKDQHQYHORSHDVVKRZQLQWKH)LJWKHV\VWHPUHPDLQVVWDEOH DVORQJDVWKHQXPEHURIHQFLUFOHPHQWVRIUHPDLQVXQFKDQJHGZKLFKZLOOEHWUXHIRUDOOlLI
_'MȦ*MȦ_ ««««
$VORQJDVWKHSHUWXUEHGQ\TXLVWGLDJUDPGRHVQRWSDVVWKURXJKWKHSRLQWWKHV\VWHPUHPDLQVVWDEOH7KHVWDELOLW\ FRQGLWLRQRIHTFDQEHUHZULWWHQDV
_'MȦ*MȦİl_ IRU ««««
+HUHİLVDFRQVWDQWDQGLWVYDOXHLVZKHQSHUWXUEDWLRQLVPD[LPXP:KHQİHTXDOVWRSHUWXUEDWLRQLVPLQLPXPWKDW LQGLFDWHVWKHUHLVQRXQFHUWDLQW\LQWKHV\VWHPDQG(TLVWUXHLIDQGRQO\LI
_'*Ǧİl_ DQG_'*_ «««
,WLVUHTXLUHGWRH[SUHVVWKHUHTXLUHPHQWLQWHUPVRIWKH3,FRQWUROOHUJDLQVRIWKHQRPLQDOV\VWHP'*7KLVFDQEHGRQH
_'*Ǧİl_ _'*Ǧ__l_ 2U_'*Ǧ_ _l_««« 7KHV\VWHPLVJXDUDQWHHGWREHVWDEOHDVORQJDVHTLVVDWLVILHG7KHUHIRUHVWDELOLW\UREXVWQHVVLVGHILQHGDV
_' Ǧ_««««
$VORQJDVWKHPRGHOXQFHUWDLQW\UHPDLQVEHORZ_ _IRUDOOIUHTXHQFLHVWKHV\VWHPLVJXDUDQWHHGWRUHPDLQVWDEOHLQ VSLWHRIWKHSHUWXUEDWLRQVlV'HOWD65 LVVLPSO\WKHLQYHUVHRIWKHFORVHGORRSPDJQLWXGHIUHTXHQF\UHVSRQVHLH WKHLQYHUVHRIWKHFRPSOHPHQWDU\VHQVLWLYLW\IXQFWLRQ7V7KXVLQWHUPVRIWKHFRPSOHPHQWDU\VHQVLWLYLW\IXQFWLRQ
_7VǦ_ _l_«««
7KLVPHDQVWKDWPRGHOXQFHUWDLQW\GLFWDWHVDQXSSHUERXQGRQWKHPDJQLWXGHRI7V7KHTXDOLW\lGHILQHVWKHPLQLPXP GLVWDQFHIURPWKHSRLQWWRWKHLQYHUVHQ\TXLVWSORW
C. Stability Robustness of Autopilot with second Order and Sixth order Actuator Model
6WHSUHVSRQVHDQGIUHTXHQF\UHVSRQVHERGHSORWRIWKHVHFRQGRUGHUDQGVL[WKRUGHUDFWXDWRUG\QDPLFVKDYHEHHQ SUHVHQWHGLQ)LJ$ %DQGWKHUHVXOWLVIRUPXODWHGLQ7DEOH,,IRUILQGLQJRXWZKHWKHUWKHKLJKHURUGHUPRGHO FDQEHWDNHQDVWKHHTXLYDOHQFHRIVHFRQGRUGHUPRGHO
6WHSUHVSRQVHRIQGRUGHUDQGWKRUGHUDFWXDWRUG\QDPLFV
7LPHVHFRQGV
$P
SO
LWX
GH
6HFRQGRUGHUDFWXDWRU 6L[WKRUGHUDFWXDWRU
)LJXUH$6WHSUHVSRQVHRIDFWXDWRU
3K
DV
H
G
HJ
)UHTXHQF\UHVSRQVHRIQGRUGHUDQGWKRUGHUDFWXDWRUG\QDPLFV
)UHTXHQF\UDGV
6\VWHP6L[WKRUGHUDFWXDWRU )UHTXHQF\UDGV 0DJQLWXGHG%
0
DJQ
LWXGH
G%
6HFRQGRUGHUDFWXDWRU 6L[WKRUGHUDFWXDWRU
7KHDXWRSLORWGHVLJQFDUULHGRXWLQ>@XVHGDVHFRQGRUGHUDFWXDWRUPRGHOIRUȟD DQGȦD UDGVHFIRUDQ
RSHUDWLQJSRLQW7DEOH,,,ZLWKDWUDQVIHUIXQFWLRQ
*V
««««$7KHSROHVRIWKHDFWXDWRUDUH M7KHSUHVHQWDQDO\VLVLVIROORZLQJWKHPHWKRGRORJ\GHVFULEHGLQ SUHYLRXVVHFWLRQDQGXVLQJDQHTXLYDOHQWVL[WKRUGHUDFWXDWRUPRGHOZLWKWZRGRPLQDQWSROHVDW MDQGWZR SDLU RI FRPSOH[ FRQMXJDWH SROHV DW M DQG M 7KLV PRGHO UHIOHFWV WKH SUHVHQFH RI KLJKHU IUHTXHQF\PRGHVLQDQDFWXDWRUZKLFKLVQRWH[SOLFLWLQWKHVHFRQGRUGHUPRGHO7KHWUDQVIHUIXQFWLRQRIVL[WKRUGHU DFWXDWRUPRGHOLV
*V
«««%,WLVREVHUYHGWKDWWKHUHLVDYHU\FORVHPDWFKLQJLQWKHJDLQVRIWKHWZRPRGHOVXSWRDIUHTXHQF\RIDERXW UDGVHF)LJ%,WKDVDOVREHHQQRWLFHGWKDWWKHWLPHUHVSRQVHFKDUDFWHULVWLFVRIWKHVL[WKRUGHUDFWXDWRUPRGHO FORVHO\PDWFKZLWKWKDWRIWKHWLPHUHVSRQVHFKDUDFWHULVWLFVRIVHFRQGRUGHUDFWXDWRUPRGHO7KXVWKHVHFRQGRUGHU PRGHOPD\EHUHJDUGHGWRVDPHDVHTXLYDOHQWORZHURUGHUDSSUR[LPDWLRQRIWKLVVL[WKRUGHUPRGHO
7DEOH,,6WHSUHVSRQVHFKDUDFWHULVWLFVRIVHFRQGRUGHUDQGVL[WKRUGHUDFWXDWRUPRGHOGHVLJQ
QGRUGHUDFWXDWRU WKRUGHUDFWXDWRU
3HDNRYHUVKRRW
6HWWOLQJWLPHVHF
5LVHWLPHVHF VHF
6WHDG\VWDWH
,Q WKH PHWKRGRORJ\ SUHVHQWHG LQ >@ WKH XQVWUXFWXUHG XQFHUWDLQW\ ERXQGlV FRXOG EH IRXQG H[SHULPHQWDOO\ DV PHQWLRQHGLQWKHVHFWLRQHG,,%,QRUGHUWRDVFHUWDLQZKHWKHUWKHV\VWHPUHPDLQVVWDEOHLQVSLWHRISHUWXUEDWLRQV lVWKHERGHSORWDQDO\VLVIRU_ _DQG_lV_KDYHEHHQHYDOXDWHGWRJHWKHUDVIXQFWLRQVRIIUHTXHQF\DQGUHSUHVHQWHG LQ)LJ
0
DJ
QL
WX
GH
G%
%RGH'LDJUDP
)UHTXHQF\UDGV
8QVWUXFWXUHGXQFHUWDLQW\/V 'HOWD65
)LJ6WDELOLW\UREXVWQHVV
7KHH[SUHVVLRQIRUWKHVWDELOLW\UREXVWQHVVPHDVXUH DVREWDLQHGLQHTE\SXWWLQJ' ZKLFKLVWKHODWHUDO DXWRSLORWFRQWUROJDLQDVHYDOXDWHGLQ>@LVJLYHQLQHT$
«««$ 7KHXQVWUXFWXUHGXQFHUWDLQW\lVLVFDOFXODWHGIURPHT%DQGWKHFRUUHVSRQGLQJWUDQVIHUIXQFWLRQLVSUHVHQWHGLQ HT%
lV
«««%
,WLVREVHUYHGWKDWWKHV\VWHPVWDELOLW\LVJXDUDQWHHGIRUWKHSHUWXUEDWLRQFRQVLGHUHGVLQFHWKHPRGHOXQFHUWDLQW\ UHPDLQV EHORZ DV VKRZQ LQ )LJ IRU DOO IUHTXHQFLHV IUHTXHQF\ UDQJH UDGVHF 7KH QRPLQDO YDOXHV RI DXWRSLORWV\VWHPSDUDPHWHUVIRUDQRSHUDWLQJSRLQWDVREWDLQHGIURP>@KDYHEHHQSUHVHQWHGLQWDEOH,,,
7DEOH,,,$XWRSLORWV\VWHPGHVLJQSDUDPHWHUV
7D6HF ȦEUDGVHF ı PȘVHF ȦDUDGVHF ȟD .EVHF NS ȦL NT
9 &21&/86,21
7KHUREXVWQHVVVWXG\KDVEHHQFDUULHGRXWIRURQHW\SLFDORSHUDWLQJSRLQWRQO\XWLOL]LQJWKHGHVLJQHGFRQWUROJDLQV DQG DQGDKLJKHURUGHUVL[WKRUGHUG\QDPLFVIRUDFWXDWRUV\VWHP7KHDFWXDODFWXDWRUV\VWHPXVHGLQDUHDO DXWRSLORW PXVW KDYH VWLOO KLJKHU RUGHU G\QDPLFV 6LQFH VXFK KLJKHU RUGHU UHDOLVWLF PRGHO ZDV QRW DYDLODEOH WKH UREXVWQHVVRIWKHGHYHORSHGGHVLJQPHWKRGRORJ\KDVEHHQLQYHVWLJDWHGZLWKDFKRVHQVL[WKRUGHUPRGHOZLWKVRPH QRQGRPLQDQWKLJKIUHTXHQF\PRGH7KHDQDO\VLVFDUULHGRXWLQIUHTXHQF\GRPDLQLQGLFDWHVWKDWWKHWZRSORWVIRU _ _DQG_lV_GRQRWLQWHUVHFWDWDQ\IUHTXHQF\ZLWKLQ UDGVHFDQGWKHPDUJLQDYRLGDQFHLQGELVTXLWHODUJH ERWKDWORZIUHTXHQF\DQGYHU\KLJKIUHTXHQF\UDQJHV+RZHYHUWKHWZRFXUYHVEHFRPHFORVHWRHDFKRWKHUDWD IUHTXHQF\RIUDGVHFDQGWKHGEPDUJLQEHWZHHQWKHPDWWKDWSRLQWLVDERXWG%WKHV\VWHPVWDELOLW\LVWKXV JXDUDQWHHGIRUWKHDVVXPHGSHUWXUEDWLRQ7KHXQFHUWDLQW\ERXQGXVHGLQWKHSUHVHQWVWXG\LVG% GE,QFDVHRIDV\VWHPZKHUHWKHUHLVDQLQWHUVHFWLRQEHWZHHQWKHFXUYHV_ _DQG_lV_LQGLFDWLQJDSHUIRUPDQFH OLPLWDWLRQWRTXDOLI\DV\VWHPWREHUREXVWIRUDFRQVLGHUHGSHUWXUEDWLRQERXQGlV,WLVIHOWWKDWDSURSHUO\GHVLJQHG ³1RWFK ILOWHU´ FRXOG EH LPSOHPHQWHG LQ WKH FRQWURO ORRS LQQHU ORRS WR LPSURYH WKH PDUJLQ DYRLGDQFH LQ GE EHWZHHQWKHFXUYHVDWDSDUWLFXODUIUHTXHQF\ZKHUHWKHFXUYHVLQWHUVHFW$OOWKHSURJUDPVKDYHEHHQZRUNHGRXWLQ 0DWODE$
5()(5(1&(6
>@ *'DV.'DWWD7.*KRVKDO6.*RVZDPLµ6WUXFWXUHG/LQHDU'HVLJQ0HWKRGRORJ\IRU7KUHHORRS/DWHUDO0LVVLOH$XWRSLORW¶-RXUQDORI WKH,QVWLWXWLRQRI(QJLQHHUV,QGLDYRO0DUFK
>@ 3=DUFKDQµ7DFWLFDODQG6WUDWHJLF0LVVLOH*XLGDQFH¶7KLUG(GLWLRQ$,$$OQF
>@ * 'DV .'DWWD 7.*KRVKDO 6 .*RVZDPL µ6WUXFWXUHG 'HVLJQ 0HWKRGRORJ\ RI 0LVVLOH $XWRSLORW,,¶ -RXUQDO RI WKH ,QVWLWXWLRQ RI (QJLQHHUV,QGLDYRO0D\
>@ ):1HVWOLQHDQG1&1DEEHIHOGµ'HVLJQRI'LJLWDO$XWRSLORWVIRUKRPLQJ0LVVLOHV8¶SDSHUSUHVHQWHGDWWKH)OLJKW0HFKDQLFV3DQHO 6\PSRVLXPRQ0LVVLOH6\VWHPV)OLJKW0HFKDQLFV+HOGDW/RQGRQ0D\
>@ 3*DUQHOODQG'-(DVWµ*XLGHG:HDSRQ&RQWURO6\VWHPV¶3HUJDPRQ3UHVV3ULQWHGLQ*UHDW%ULWDLQ)LUVWHGLWLRQ
>@ * 'DV .'DWWD 7.*KRVKDO 6 .*RVZDPL µ6WUXFWXUHG 'HVLJQ 0HWKRGRORJ\ RI 0LVVLOH $XWRSLORW¶ -RXUQDO RI WKH ,QVWLWXWLRQ RI (QJLQHHUV,QGLDYRO0DUFK
>@ *HQH ))UDQNOLQ - 'DYLG 3DUHOO $EEDV (PDQL1DOLQL µ)HHGEDFN&RQWURO RI '\QDPLF 6\VWHPV¶ $GGLVRQ:HVOH\ SXEOLVKLQJ FRPSDQ\ -XQH
>@ .2JDWDµ0RGHUQ&RQWURO(QJLQHHULQJ¶)RXUWKHGLWLRQ3UHQWLFH+DOO
>@ .XR%HQMDPLQµ$XWRPDWLF&RQWURO6\VWHPV¶3UHQWLFH+DOORI,QGLD6HYHQWKHGLWLRQ
>@-RKQ'R\OH%UXFH)UDQFLV$OOHQ7DQQHQEDXPµ)HHGEDFN&RQWURO7KHRU\¶0DFPLOODQ3XEOLVKLQJ&R
>@'HIHQFH5HVHDUFK 'HYHORSPHQW2UJDQL]DWLRQµ*XLGHG0LVVLOHV¶3RSXODU6FLHQFHDQG7HFKQRORJ\6HULHV3XEOLVKHGLQ
>@-+&KRXDQG:+/LDR³6WDELOLW\UREXVWQHVVRIFRQWLQXRXVWLPHSHUWXUEHGGHVFULSWRUV\VWHPV´IEEE Trans. on Circuits and Syst. - I:
Fundamental Theory and Appl.YROSS±