Kim B.J.Design of fuzzy PID controller for tracking control

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

,QWURGXFWLRQ

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

$IWHU 0DPGDQL DSSOLHG WKH IX]]\ ORJLF WR FRQWURO V\VWHP IRU WKH ILUVW WLPH > @ WKH IX]]\ FRQWUROOHU LV ZLGHO\ XVHG WR FRQWURO YDJXH V\VWHP RU QRQOLQHDU V\VWHP 7KH UHVHDUFK RQ WKH IX]]\ FRQWUROOHU KDV EHHQ IRFXVHG RQ WKH WZR LQSXW IX]]\ V\VWHP > @ <LQJ DQDO\]HG JHQHUDO VWUXFWXUH RI WKH WZR LQSXW IX]]\ FRQWUROOHU WKDW XVHV µHUURU¶ DQG µFKDQJH LQ HUURU¶ DV WKH LQSXW YDULDEOHV > @> @ 7KHUH KDYH EHHQ PDQ\ DSSOLFDWLRQV RI WKH WZR LQSXW IX]]\ FRQWUROOHU VLQFH %DVLFDOO\ WKHUH DUH WZR W\SHV LQ WZR LQSXW IX]]\ FRQWUROOHUV 2QH LV D 3' W\SH IX]]\ FRQWUROOHU ,W JHQHUDWHV FRQWURO VLJQDO IURP µHUURU¶ DQG µFKDQJH

&RUUHVSRQGLQJ $XWKRU7KLV ZRUN ZDV VXSSRUWHG E\ SURMHFW IRU VXSSRUWLQJ OHDGLQJ WULDO VFKRROV LQ ,7 IURP WKH 0LQLVWU\ RI ,QIRUPDWLRQ DQG &RPPXQLFDWLRQ 0,&

LQ HUURU¶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µWZR LQSXW IX]]\ FRQWUROOHU¶ RU SDUWLDOO\ IX]]\ PRGLILHG OLQHDU 3,' FRQWUROOHUV DUH HPHUJLQJ 0LVLU GHVLJQHG D GLJLWDO W\SH 3,' FRQWUROOHU ZKLFK XVHV WZR µWZR LQSXW IX]]\ V\VWHP¶ EDVHG RQ WKH <LQJ¶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

,Q WKLV SDSHU SURSRUWLRQDO VLJQDO DQG GHULYDWLRQ VLJQDO RI WKH FRQYHQWLRQDO 3,' FRQWUROOHU LV PRGLILHG ZLWK 3' W\SH WZR LQSXW IX]]\ FRQWUROOHU WR LQFOXGH WKH YDU\LQJ JDLQV 7KH SURSRUWLRQDO VLJQDO DQG WKH GHULYDWLYH VLJQDO DUH GRPLQDQW WR GHFLGH WKH WUDQVLHQW UHVSRQVH %XW WKH LQWHJUDO VLJQDO ZKRVH PDMRU UROO LV WR HOLPLQDWH WKH VWHDG\ VWDWH HUURU KDV IL[HG JDLQ 1DPHO\ SURSRVHG IX]]\ 3,' FRQWUROOHU LV µIX]]\ 3' OLQHDU ,¶ W\SH 7R H[DPLQH WKH SHUIRUPDQFH RI WKH IX]]\ 3,' FRQWUROOHU D FRPSDULVRQ EHWZHHQ WKH IX]]\ 3,' DQG WKH OLQHDU 3,' LV SHUIRUPHG XQGHU VDPH WXQLQJ )RU WKH GLUHFW FRPSDULVRQ RI WKH SHUIRUPDQFH D OLQHDU LQIHUHQFH PHWKRG

SURSRVHG E\ 0L]XPRWR LV XVHG LQVWHDG RI PLQ PD[ JUDYLW\ PHWKRG RU RWKHU JHQHUDOL]HG LQIHUHQFH PHWKRGV > @> @ 7KH GHVLJQ SURFHGXUH SURSRVHG LQ WKLV SDSHU LV DGGLQJ GHVLUHG QRQOLQHDULWLHV XVLQJ PHPEHUVKLS IXQFWLRQV DQG FRQWURO UXOHV DIWHU LPSOHPHQWLQJ VDPH RXWSXW VXUIDFH DV OLQHDU 3,' XVLQJ OLQHDU LQIHUHQFH PHWKRG ,I FRQYHQWLRQDO QRQOLQHDU LQIHUHQFH PHWKRG LV XVHG XQGHVLUHG QRQOLQHDULWLHV DUH JHQHUDWHG RQ WKH RXWSXW VXUIDFH RI WKH IX]]\ V\VWHP %XW WKH

SURGXFW VXP JUDYLW\ PHWKRG RU WKH VLPSOLILHG UHDVRQLQJ PHWKRG VLPSOLILHG YHUVLRQ RI WKH SURGXFW VXP JUDYLW\ PHWKRG LV XVHG 7KH QRQOLQHDULWLHV DGGHG WR HQKDQFH WKH WUDFNLQJ SHUIRUPDQFH FDQ EH JHQHUDWHG RQ WKH RXWSXW VXUIDFH ,Q WKLV ZD\ WKH HIIHFWV RI WKH DGGHG QRQOLQHDULWLHV RQ WKH WUDFNLQJ SHUIRUPDQFH FDQ EH XQGHUVWRRG LQWXLWLYHO\ 7KH GHJUHHV RI WKH QRQOLQHDULWLHV DGGHG WR WKH SURSRUWLRQDO SDUW DQG GHULYDWLYH SDUW FDQ EH DGMXVWHG UHVSHFWLYHO\

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

6WUXFWXUH RI IX]]\ 3,' FRQWUROOHU

)LJ %ORFN GLDJUDP RI IX]]\ 3,' FRQWUROOHU

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µIX]]\ 3' OLQHDU ,¶ VWUXFWXUH ,Q WKLV VWUXFWXUH WKH IX]]\ V\VWHP LV DSSOLHG RQO\ WR WKH SURSRUWLRQDO DQG GHULYDWLYH VLJQDO RI WKH OLQHDU 3,' FRQWUROOHU 7KH LQWHJUDO VLJQDO XVHV FRQYHQWLRQDO OLQHDU PHWKRG 7KH PDMRU UROO RI WKH LQWHJUDO VLJQDO LV WR HOLPLQDWH WKH VWHDG\ VWDWH HUURU 7KH WUDQVLHQW UHVSRQVH LV DIIHFWHG PRVWO\ E\ WKH SURSRUWLRQDO VLJQDO DQG WKH GHULYDWLYH VLJQDO )RU WKH HQKDQFHPHQW RI WKH WUDQVLHQW UHVSRQVH WKH YDU\LQJ JDLQV DUH LPSOHPHQWHG RQ WKH SURSRUWLRQDO DQG GHULYDWLYH SDUWV XVLQJ WZR LQSXW IX]]\ V\VWHP 7KH QRQOLQHDULWLHV WKDW PDNH WKH YDU\LQJ JDLQV SRVVLEOH DUH DGGHG E\ WKH IX]]\ FRQWURO UXOHV DQG WKH PHPEHUVKLS IXQFWLRQV 7KH QRQOLQHDULWLHV HPSKDVL]H WKH SURSRUWLRQDO JDLQ ZKHQ WKH WUDFNLQJ HUURU LV UHODWLYHO\ ODUJH DQG DFFHOHUDWHV GHFUHDVLQJ VSHHG RI WKH WUDFNLQJ HUURU 7KH

QRQOLQHDULWLHV LQ WKH GHULYDWLYH JDLQ VXSSUHVV RYHUVKRRW DQG LQFUHDVH GDPSLQJ IURP WKH EHJLQQLQJ RI WKH VHWWOLQJ ,Q WKH SURSRVHG VWUXFWXUH WKH IX]]\ V\VWHP LV QRUPDOL]HG ZLWK UHVSHFW WR WKH PD[LPXP UDQJH RI WKH VLJQDO ,I WKH IX]]\ V\VWHP EORFN LV UHSODFHG ZLWK VLPSOH VXPPLQJ EORFN WKLV VWUXFWXUH LV VDPH DV FRQYHQWLRQDO OLQHDU 3,' VWUXFWXUH 8VLQJ WKLV FKDUDFWHULVWLF WKH H[SHULPHQW LQ FKDSWHU VKRZV WKH FRPSDULVRQ EHWZHHQ WKH IX]]\ 3,' DQG WKH OLQHDU 3,' XQGHU VDPH WXQLQJ

'HVLJQ RI IX]]\ 3' FRQWUROOHU

2XWSXW VXUIDFH RI WKH OLQHDU 3' FRQWUROOHU

*HQHUDOO\ WKH OLQHDU 3' FRQWUROOHU LV JLYHQ DV

X = aH + bDH

ZKHUH a DQG b DUH WKH SURSRUWLRQDO JDLQ DQG GHULYDWLYH JDLQ UHVSHFWLYHO\ H LV WUDFNLQJ HUURU DH LV FKDQJH LQ HUURU 7KH RXWSXW VXUIDFH RI WKH 3' FRQWUROOHU LV D SODQH DV VKRZQ LQ )LJ

)LJ 2XWSXW VXUIDFH RI WKH OLQHDU 3' FRQWUROOHU

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

'HVLJQ RI PHPEHUVKLS IXQFWLRQV

2QH WULDQJXODU PHPEHUVKLS IXQFWLRQ ZKLFK PHDQV µ]HUR¶ DQG WZR WUDSH]RLGDO PHPEHUVKLS IXQFWLRQV ZKLFK PHDQ µSRVLWLYH¶ DQG µQHJDWLYH¶ FRPSRVH WKH LQSXW PHPEHUVKLS IXQFWLRQV IRU SURSRUWLRQDO VLJQDO DV )LJ 7KH GHJUHH RI PHPEHUVKLS LV ZLWKLQ WR %\ XVLQJ WKUHH PHPEHUVKLS IXQFWLRQV DV VKRZQ LQ )LJ D WKH IX]]\ FRQWURO UXOHV ZKLFK DFWLYDWHV ZKHQ WKH WUDFNLQJ HUURU LV VPDOO FDQ GLIIHU ZLWK WKH

UXOHV WKDW DFWLYDWHV ZKHQ WKH WUDFNLQJ HUURU LV ODUJH )RU WKH GHULYDWLYH VLJQDO ZH QHHG RQO\ WZR WUDSH]RLG PHPEHUVKLS IXQFWLRQV WKDW RYHUODS ZLWK HDFK RWKHU

D E

)LJ D 3URSRUWLRQDO LQSXW PHPEHUVKLS IXQFWLRQ E GHULYDWLYH LQSXW PHPEHUVKLS IXQFWLRQ

)LJ 2XWSXW PHPEHUVKLS IXQFWLRQ

7KH RXWSXW PHPEHUVKLS IXQFWLRQV DUH FRPSRVHG RI VL[ WULDQJXODU PHPEHUVKLS IXQFWLRQV DV VKRZQ LQ )LJ 7KH OHQJWK RI WKH EDVH RI HDFK PHPEHUVKLS IXQFWLRQ LV KHQFH KDOI RI HDFK WULDQJOH LV RYHUODSSHG ZKHQ XQLIRUPO\ GLVWULEXWHG WKDW KDSSHQV ZKHQ F F 7KH KHLJKW RI HDFK WULDQJOH LV 7KH PHPEHUVKLS IXQFWLRQV DUH V\PPHWULF ZLWK UHVSHFW WR FHQWHU D[LV 7KH GLVWDQFH RI WKH µSVPDOO¶ DQG µQVPDOO¶ IURP WKH FHQWHU D[LV LV µF ¶ DQG WKH GLVWDQFH RI WKH µSPLG¶ DQG µQPLG¶ IURP WKH FHQWHU D[LV LV µ F ¶ 7KH PHPEHUVKLS IXQFWLRQ µSELJ¶ DQG µQELJ¶ KDV IL[HG ORFDWLRQ 7KH ORFDWLRQ LV DQG ± DSDUW IURP WKH FHQWHU D[LV UHVSHFWLYHO\

DQG DUH WKH PD[LPXP DQG PLQLPXP RXWSXW YDOXH RI WKH QRUPDOL]HG IX]]\ V\VWHP ,Q WKLV VWUXFWXUH WKH GHVLJQ RI WKH IX]]\ V\VWHP LV FRPSOHWHG ZLWK WXQLQJ RI WKH GHVLJQ YDULDEOHV µF ¶ DQG µF ¶ 7KHVH GHVLJQ YDULDEOHV GHFLGH WKH GHJUHH RI WKH QRQOLQHDULW\ LQ WKH IX]]\ V\VWHP )ROORZLQJ VHFWLRQV GHVFULEHV KRZ WR GHVLJQ µF ¶ DQG µF ¶

'HVLJQ RI WKH IX]]\ FRQWURO UXOHV

7KH LQSXW YDULDEOH H KDV WKUHH PHPEHUVKLS IXQFWLRQV DQG DH KDV WZR PHPEHUVKLS IXQFWLRQV LQ )LJ $QG ZLWK WKH FRPELQDWLRQ RI WKH LQSXW PHPEHUVKLS IXQFWLRQV WRWDO VL[ IX]]\ FRQWURO UXOHV FDQ EH JHQHUDWHG

5 ,I H LV QHJ DQG DH LV QHJ WKHQ RXW LV QELJ

5 ,I H LV SRV DQG DH LV SRV WKHQ RXW LV SELJ

5 ,I H LV QHJ DQG DH LV SRV WKHQ RXW LV QVPDOO

5 ,I H LV SRV DQG DH LV QHJ WKHQ RXW LV SVPDOO

5 ,I H LV ]HUR DQG DH LV SRV WKHQ RXW LV SPLG

5 ,I H LV ]HUR DQG DH LV QHJ WKHQ RXW LV QPLG

5 DQG 5 UHVXOWV ODUJH FRQWURO VLJQDO WKDW SXOOV V\VWHP RXWSXW WR D VHW SRLQW ZKHQ WKH V\VWHP RXWSXW LV PRYHG DZD\ IURP WKH

%\ H[SUHVVLQJ WKH PHPEHUVKLS IXQFWLRQ DV

LQIHUHQFH UHVXOW LV JLYHQ DV

m& ] = m$ [ ¼m % \ ¼m& ]

ZKHUH \ LV WKH LQSXW YDULDEOHV DQG ¼ VWDQGV IRU

DOJHEUDLF SURGXFW 7KH ILQDO LQIHUHQFH UHVXOW & LV DJJUHJDWHG E\ WDNLQJ WKH VXP RI HDFK IX]]\ UXOH¶V UHVXOW & & L &Q

1DPHO\

&HQWHU RI JUDYLW\ PHWKRG LV XVHG DV GHIX]]LILFDWLRQ PHWKRG +HQFH WKH RXWSXW YDOXH RI WKH IX]]\ V\VWHP ] LV JLYHQ DV

3URGXFW VXP JUDYLW\ PHWKRG LV RQO\ XVHG LQ FRPSXWHU VLPXODWLRQ %XW WKH LPSOHPHQWHG GLJLWDO IX]]\ V\VWHP IRU WUDFNLQJ H[SHULPHQW LV XVLQJ VLPSOLILHG UHDVRQLQJ PHWKRG WKDW LV D PRGLILHG IRUP RI SURGXFW VXP JUDYLW\ PHWKRG 7KH VLPSOLILHG UHDVRQLQJ PHWKRG JLYHV H[DFWO\ WKH VDPH UHVXOW DV WKH SURGXFW VXP JUDYLW\ PHWKRG %XW LWV FRPSXWDWLRQ WLPH LV VKRUWHU WKDQ WKDW RI SURGXFW VXP JUDYLW\ PHWKRG 7KH LQIHUHQFH SURFHVV RI WKH VLPSOLILHG UHDVRQLQJ PHWKRG LV VKRZQ LQ )LJ

)LJ 6LPSOLILHG UHDVRQLQJ PHWKRG

'HJUHH RI ILWQHVV RI WKH µL¶WK IX]]\ FRQWURO UXOH LV FRPSXWHG DV

KL = m$ [ ¼ m% \

'HIX]]LILFDWLRQ UHVXOW LV REWDLQHG DV WKH ZHLJKWHG DYHUDJH RI ]L E\ WKH GHJUHH KL 1DPHO\

6LPSOLILHG UHDVRQLQJ PHWKRG XVHV VLQJOHWRQ W\SH PHPEHUVKLS IXQFWLRQV DV VKRZQ LQ )LJ LQVWHDG RI WULDQJXODU PHPEHUVKLS IXQFWLRQV $V IRUPHUO\ F DQG F DUH XVHG DV WKH GHVLJQ YDULDEOHV RI WKH IX]]\ V\VWHP $QG WKH IXQFWLRQ RI HDFK YDULDEOH F DQG F GRHV QRW FKDQJH

)LJ 0RGLILHG RXWSXW PHPEHUVKLS IXQFWLRQ IRU VLPSOLILHG UHDVRQLQJ PHWKRG

2XWSXW VXUIDFH RI WKH IX]]\ FRQWUROOHU

$ FRPSDULVRQ EHWZHHQ WKH GHVLJQHG RXWSXW VXUIDFH DQG RXWSXW VXUIDFH JHQHUDWHG E\ PLQ PD[ JUDYLW\ PHWKRG FDQ KHOS XV WR SUHGLFW WKH FKDQJH LQ WUDFNLQJ SHUIRUPDQFH DQG VKRZ XV KRZ WKH GHVLJQ YDULDEOH F DQG F KDYH HIIHFWV RQ WKH RXWSXW VXUIDFH )LJ VKRZV WKH RXWSXW VXUIDFH RI WKH IX]]\ 3' FRQWUROOHU LPSOHPHQWHG E\ XVLQJ PLQ PD[ JUDYLW\ PHWKRG

7KH RXWSXW VXUIDFH VKRZQ LQ )LJ LV QRW H[DFWO\ SODQH GXH WR WKH QRQOLQHDULW\ LQ WKH LQIHUHQFH PHWKRG +HQFH LI FRQYHQWLRQDO OLQHDU 3' FRQWUROOHU LV UHSODFHG E\ WKLV IX]]\ 3' FRQWUROOHU WKH VDPH SHUIRUPDQFH LV QRW JXDUDQWHHG DQG WKH SHUIRUPDQFH LV LUUHJXODU ZLWK UHVSHFW WR LQSXW VLJQDO OHYHO DQG DSSOLHG UHJLRQ

)LJ 2XWSXW VXUIDFH RI WKH IX]]\ 3' FRQWUROOHU XVLQJ PLQ PD[ JUDYLW\ PHWKRG

)LJ 2XWSXW VXUIDFH RI WKH IX]]\ 3' FRQWUROOHU XVLQJ SURG VXP JUDYLW\ PHWKRG RU VLPSOLILHG PHWKRG F F

)LJ 2XWSXW VXUIDFH RI WKH IX]]\ 3' FRQWUROOHU XVLQJ SURG VXP JUDYLW\ PHWKRG RU VLPSOLILHG PHWKRG F F

)LJ VKRZV WKH RXWSXW VXUIDFH RI WKH IX]]\ 3' FRQWUROOHU XVLQJ SURGXFW VXP JUDYLW\ PHWKRG RU VLPSOLILHG UHDVRQLQJ PHWKRG ,Q WKLV FDVH ERWK F DQG F DUH ]HURV 7KH RXWSXW VXUIDFH VKRZQ LQ )LJ LV FRPSOHWHO\ D SODQH $QG WKLV VXUIDFH KDV WKH VDPH SHUIRUPDQFH DV OLQHDU 3' FRQWUROOHU )LJ

VKRZV WKH RXWSXW VXUIDFH RI WKH IX]]\ 3' FRQWUROOHU XVLQJ SURGXFW VXP JUDYLW\ PHWKRG RU VLPSOLILHG UHDVRQLQJ PHWKRG ZLWK QRQ]HUR GHVLJQ YDULDEOH YDOXHV ,Q WKLV FDVH F LV

DQG F LV 'XH WR WKH QRQ]HUR F YDOXH WKLV RXWSXW VXUIDFH KDV D WLOW WR WKH OHIW DQG WKLV FDXVHV DFFHOHUDWLRQ HIIHFW WRZDUG WKH VHW SRLQW $QG WKH VORSH DORQJ bDH D[LV YDULHV ZLWK WKH YDOXH RI HUURU 7KLV PHDQV YDU\LQJ GHULYDWLYH JDLQ GHSHQGV XSRQ WKH YDOXH RI WKH HUURU 7KH VPDOOHU HUURU PDNHV WKH ODUJHU GHULYDWLYH JDLQ DQG ODUJHU HUURU PDNHV UHODWLYHO\ VPDOO GHULYDWLYH JDLQ 7KHVH HIIHFWV DUH LQFUHDVH ZLWK WKH YDOXHV RI F DQG F UHVSHFWLYHO\ 1DPHO\ F PDLQO\ DIIHFWV WKH ULVH WLPH DQG F DIIHFWV WKH YDULDWLRQ RI GDPSLQJ

6WUXFWXUH RI WKH IX]]\ 3' /LQHDU , FRQWUROOHU

7R H[DPLQH WKH GHVLJQHG IX]]\ FRQWUROOHU FRPSXWHU VLPXODWLRQ DQG WUDFNLQJ H[SHULPHQW DUH SHUIRUPHG XVLQJ YRLFH FRLO PRWRU V\VWHP )LJ VKRZV EORFN GLDJUDP RI WKH 3,' FRQWURO V\VWHP )LJ VKRZV WKH 3,' FRQWURO V\VWHP RI WKH YRLFH FRLO PRWRU

)RU WKH FRPSDULVRQ EHWZHHQ OLQHDU 3,' DQG IX]]\ 3,' D VZLWFK WKDW WRJJOHV IX]]\ 3,' DQG OLQHDU 3,' LV LQFOXGHG ,Q WKLV VWUXFWXUH GHULYDWLYH RI RXWSXW VLJQDO LV XVHG DV GHULYDWLYH VLJQDO LQVWHDG RI WKH FKDQJH RI HUURU %XW WKH GHVLJQHG IX]]\ 3,' FRQWUROOHU FDQ EH XVHG ZLWKRXW DQ\ PRGLILFDWLRQ )RU WKH H[SHULPHQW DQDORJ 3,' FLUFXLW LV LPSOHPHQWHG DQG IX]]\ 3' FRQWUROOHU SDUW LV LPSOHPHQWHG XVLQJ ELW WZR FKDQQHO $' '$ ERDUG DQG 706 & '63 DV VKRZQ LQ )LJ 7KH IX]]\ DOJRULWKP LV LPSOHPHQWHG XVLQJ VLPSOLILHG UHDVRQLQJ PHWKRG ZLWK & ODQJXDJH N+] VDPSOH UDWH LV XVHG IRU WKLV H[SHULPHQW

)LJ EORFN GLDJUDP RI DQDORJ 3,' FRQWURO V\VWHP LQFOXGLQJ IX]]\ 3' FRQWUROOHU

)LJ 3,' FRQWURO V\VWHP RI YRLFH FRLO PRWRU IRU IX]]\ 3,' H[SHULPHQW

)LJ ([SHULPHQWDO VHW XS IRU WKH FRPSDULVRQ EHWZHHQ IX]]\ 3,' FRQWUROOHU DQG OLQHDU 3,' FRQWUROOHU

6LPXODWLRQ UHVXOW

7KH FRPSXWHU VLPXODWLRQ LV SHUIRUPHG ZLWK 0DWODE DQG 6LPXOLQN 7KH VLPXODWLRQ VWDUWV ZLWK EHVW WXQHG FRQWURO JDLQV.S .L .G :KHQ WKH 3,' JDLQV DUH EHVW WXQHG WKH IX]]\ 3,' VKRZV DOPRVW VDPH SHUIRUPDQFH DV WKH OLQHDU 3,' %XW IX]]\ 3,' VKRZV HQKDQFHG SHUIRUPDQFH ZKHQ WKH 3,' JDLQV KDYH RIIVHW 7KH WUDFNLQJ SHUIRUPDQFH LV WHVWHG ZLWK WKH YDULRXV 3,' JDLQV )LJ VKRZV WKH VWHS UHVSRQVH ZLWK YDULRXV LQWHJUDO JDLQV )X]]\ FRQWUROOHU¶V GHVLJQ YDULDEOHV VHW DV F F 'DVKHG OLQHV DUH WKH UHVXOWV RI WKH OLQHDU 3,' FRQWUROOHU 6ROLG OLQHV DUH WKH UHVXOW RI WKH IX]]\ 3,' FRQWUROOHU 7KH RYHUVKRRW GXH WR ODUJH .L LV GHFUHDVHG E\ XVLQJ WKH IX]]\ 3,' FRQWUROOHU 7UDFNLQJ HUURU FDXVHG E\ VPDOO

.L LV DOVR GHFUHDVHG E\ WKH IX]]\ 3,' FRQWUROOHU )X]]\ 3,' FRQWUROOHU PDNHV IDVWHU ULVH WLPH WKHQ WKH OLQHDU 3,' FRQWURO 7KXV ZH REVHUYHG WKDW WKH IX]]\ 3,' FRQWURO LV OHVV VHQVLWLYH WR YDULDWLRQ RI WKH LQWHJUDO JDLQ .L

)LJ 6WHS UHVSRQVHV RI WKH OLQHDU 3,' DQG IX]]\ 3,' ZLWK YDU\LQJ LQWHJUDO JDLQ

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

OLQHDU 3,' FRQWURO $QG WKH IX]]\ 3,' FRQWUROOHU LV DOVR OHVV VHQVLWLYH WR YDULDWLRQ RI WKH WRUTXH FRQVWDQW UHODWLYHO\ WR OLQHDU 3,' FRQWUROOHU

)LJ 6WHS UHVSRQVH RI WKH OLQHDU 3,' DQG IX]]\ 3,' ZLWK YDU\LQJ SURSRUWLRQDO JDLQ

UHVSRQVH KDV ODUJH RYHUVKRRW DQG WKH WUDFNLQJ HUURU WR WKH WUDSH]RLG LQSXW LV LUUHJXODU

7KH WUDFNLQJ SHUIRUPDQFH E\ WKH IX]]\ 3,' FRQWURO LV VKRZQ LQ WKH )LJ E DQG G 7KH RYHUVKRRW LQ WKH VWHS UHVSRQVH LV GHFUHDVHG DQG WKH WUDFNLQJ HUURU WR WKH WUDSH]RLG LQSXW LV PRUH UHJXODU WKDQ WKH OLQHDU 3,' FRQWURO 7KH WUDFNLQJ HUURU LQ WKH XSSHU KRUL]RQWDO OLQH DQG WKH ERWWRP KRUL]RQWDO OLQH RI WKH WUDSH]RLG DUH DOVR GHFUHDVHG WKDQ WKH OLQHDU 3,' FRQWURO

)LJ 6WHS UHVSRQVH RI WKH OLQHDU 3,' DQG IX]]\ 3,' ZLWK YDU\LQJ GHULYDWLYH JDLQ

)LJ 6WHS UHVSRQVH RI WKH OLQHDU 3,' DQG IX]]\ 3,' ZLWK YDU\LQJ WRUTXH FRQVWDQW

([SHULPHQW UHVXOW

)RU WKH WUDFNLQJ H[SHULPHQW D IXQFWLRQ JHQHUDWRU VLJQDO LV XVHG DV UHIHUHQFH LQSXW DQG WKH SRVLWLRQ VHQVRU VLJQDO RI PRWRU LV XVHG DV D IHHGEDFN VLJQDO 3URSRUWLRQDO VLJQDO DQG GHULYDWLYH VLJQDO LV VDPSOHG E\ WZR FKDQQHO ELW $' '$ ERDUG ZLWK N+] VDPSOH UDWH 7KHQ IX]]\ 3' DOJRULWKP LV DSSOLHG ZLWK WKH '63 ERDUG 7KLV IX]]\ 3' FRQWURO VLJQDO LV VXPPHG ZLWK WKH DQDORJ LQWHJUDO VLJQDO WR JHQHUDWH IX]]\ 3,' FRQWURO VLJQDO

)LJ LV D FRPSDULVRQ EHWZHHQ OLQHDU 3,' FRQWURO DQG IX]]\ 3,' FRQWURO ZKLFK DUH URXJKO\ WXQHG ZKHUH 3,' JDLQV DUH VDPH )LJ D DQG F DUH VWHS UHVSRQVH DQG WUDSH]RLG UHVSRQVH RI WKH OLQHDU 3,' FRQWURO UHVSHFWLYHO\ 7KH VWHS

D 6WHS UHVSRQVH OLQHDU E 6WHS UHVSRQVH IX]]\

F WUDSH]RLGDO OLQHDU G WUDSH]RLGDO IX]]\ )LJ &RPSDULVRQ EHWZHHQ OLQHDU 3,' FRQWURO DQG IX]]\ 3,' FRQWURO ZKLFK DUH URXJKO\ WXQHG ZKHUH 3,' JDLQV DUH VDPHF F

)LJ VKRZV WKH VWHS UHVSRQVH XQGHU YDULRXV WRUTXH FRQVWDQW %\ FKDQJLQJ FRQWURO VLJQDO JDLQ WKH VDPH HIIHFW DV FKDQJLQJ WRUTXH FRQVWDQW LV DFKLHYHG )LJ F DQG G

VKRZV WKH VWHS UHVSRQVHV RI WKH WZR FRQWUROOHUV ZKHQ QRUPDO

.W LV XVHG ,Q WKH ILJXUH ZH FDQ VHH WKDW WKHUH LV QR GLIIHUHQFH EHWZHHQ WKH WZR FRQWUROOHUV )LJ D DQG E VKRZ WKH VWHS UHVSRQVH XQGHU GHFUHDVHG WRUTXH FRQVWDQW ,Q WKLV FDVH ULVH WLPH LV VORZHU WKDQ WKH UHVSRQVH ZLWK QRUPDO WRUTXH FRQVWDQW DQG RYHUVKRRW LV JHQHUDWHG %XW RYHUVKRRW VXSSUHVVLRQ HIIHFW RI WKH IX]]\ 3,' FRQWURO LV VWLOO DFWLQJ )LJ

H DQG I VKRZ WKH VWHS UHVSRQVH XQGHU LQFUHDVHG WRUTXH FRQVWDQW ,Q WKLV FDVH WKH SHUIRUPDQFH RI WKH IX]]\ 3,' FRQWURO LV QRW EHWWHU WKDQ WKH OLQHDU 3,' FRQWURO %XW WKH UHVSRQVHV VKRZ WKH FKDUDFWHULVWLF RI WKH IX]]\ 3,' FRQWURO )LJ

I VKRZV IDVWHU ULVH DQG LQFUHDVHG GDPSLQJ WKDQ WKH )LJ

H

&RQFOXVLRQ

,Q WKLV UHVHDUFK D µIX]]\ 3' OLQHDU ,¶ W\SH IX]]\ 3,' FRQWUROOHU ZKLFK EULQJV HQKDQFHPHQW RI WKH WUDFNLQJ SHUIRUPDQFH LV GHVLJQHG DQG LPSOHPHQWHG 7KH SURSRUWLRQDO

DQG GHULYDWLYH SDUW RI WKH FRQYHQWLRQDO 3,' FRQWUROOHU LV PRGLILHG XVLQJ µWZR LQSXW RQH RXWSXW IX]]\ V\VWHP¶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

5HIHUHQFH

> @ + <LQJ : 6LOHU DQG - - %XFNOH\ )X]]\ FRQWURO WKHRU\ $ QRQOLQHDU FDVH $XWRPDWLFD YRO SS

> @ 0 0L]XPRWR 5HDOL]DWLRQ RI 3,' FRQWUROV E\ IX]]\ FRQWURO PHWKRGV )X]]\ 6HWV 6\VW YRO SS

> @ :X =KL 4XDR DQG 0 0L]XPRWR 3,' W\SH IX]]\ FRQWUROOHU DQG SDUDPHWHU DGDSWLYH PHWKRG )X]]\ 6HWV 6\VW YRO SS

> @ 7 7DNDJL DQG 0 6XJHQR )X]]\ LGHQWLILFDWLRQ RI V\VWHPV DQG LWV DSSOLFDWLRQV WR PRGHOLQJ DQG FRQWURO ,((( 7UDQV 6\VW

0DQ &\EHUQ YRO 60& SS

> @ ' 0LVLU + $ 0DONL DQG * &KHQ 'HVLJQ DQG DQDO\VLV RI D IX]]\ SURSRUWLRQDO LQWHJUDO GHULYD WLYH FRQWUROOHU )X]]\ 6HWV 6\VW YRO SS

> @ % $UPVWURQJ )/& GHVLJQ IRU ERXQGHG VHSDUDEOH IXQFWLRQV ZLWK OLQHDU LQSXW RXWSXW UHODWLRQV DV D VSHFLDO FDVH ,((( 7UDQV )X]]\ 6\VW YRO SS

> @ + ; /L DQG + % *DWODQG &RQYHQWLRQDO IX]]\ FRQWURO DQG LWV HQKDQFHPHQW ,((( 7UDQV 6\VW 0DQ &\EHUQ % YRO

SS

> @ : /L 'HVLJQ RI D K\EULG IX]]\ ORJLF SURSRUWLRQDO SOXV FRQYHQWLRQDO LQWHJUDO GHULYDWLYH FRQWUROOHU ,((( 7UDQV )X]]\ 6\VW YRO QR SS

> @ 9 % %DMLF DQG $ 5\EDORY )X]]\ PRGLILHU RI 3,' FRQWURO IRU LPSURYHPHQW RI WUDFNLQJ SURSHUWLHV LQ VHUYR V\VWHPV 3URF ,QW &RQI ,QWHOOLJHQW 7HFK +XPDQ 5HODWHG 6FL /HRQ 6SDLQ -XO\

> @ * . , 0DQQ % * +X DQG 5 * *RVLQH $QDO\VLV RI GLUHFW DFWLRQ IX]]\ 3,' FRQWUROOHU VWUXFWXUHV ,((( 7UDQV 6\VW 0DQ

&\EHUQ YRO QR SS

> @ % * +X * . , 0DQQ DQG 5 * *RVLQH 1HZ PHWKRGRORJ\ IRU DQDO\WLFDO DQG RSWLPDO GHVLJQ RI IX]]\ 3,' FRQWUROOHU ,((( 7UDQV )X]]\ 6\VW YRO QR SS

> @ + <LQJ 7KHRU\ DQG DSSOLFDWLRQ RI D QRYHO IX]]\ 3,' FRQWUROOHU XVLQJ D VLPSOLILHG 7DNDJL 6XJHQR UXOH VFKHPH

,QIRUPDWLRQ 6FLHQFHV YRO SS

> @ - &DUYDMDO * &KHQ DQG + 2JPHQ )X]]\ 3,' FRQWUROOHU 'HVLJQ SHUIRUPDQFH HYDOXDWLRQ DQG VWDELOLW\ DQDO\VLV

,QIRUPDWLRQ 6FLHQFHV YRO SS

> @ &KDQJ +\XQ &KDL 'HVLJQ RI )X]]\ 'LJLWDO 3, ' &RQWUROOHU 8VLQJ 6LPSOLILHG ,QGLUHFW ,QIHUHQFH 0HWKRG -RXUQDO RI &RQWURO $XWRPDWLRQ DQG 6\VWHP (QJLQHHULQJ YRO 1R SS

> @ / ; :DQJ $ &RXUVH LQ )X]]\ 6\VWHP DQG &RQWURO (QJ OHZRRG &OLIIV 1- 3UHQWLFH +DOO

D OLQHDU .W E IX]]\ .W

F OLQHDU .W QRUPDO G IX]]\ .W QRUPDO

H OLQHDU .W I IX]]\ .W

)LJ &RPSDULVRQ EHWZHHQ OLQHDU 3,' FRQWURO DQG IX]]\ 3,' FRQWURO ZLWK WRUTXH FRQVWDQW YDULDWLRQ