pressure and flow control of a pulverized coal injection vessel

EXAMENSARBETE

Pressure and Flow Control of aPulverized Coal Injection Vessel

CIVILINGENJÖRSPROGRAMMET

Institutionen för SystemteknikAvdelningen för Reglerteknik

1997:045 • ISSN: 1402 - 1617 • ISRN: LTU - EX - - 1997/45 - - SE

WOLFGANG BIRK

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wkh suhvvxuh durxqg wkh vhw srlqw ydoxh1 Zkhq wkh rwkhu yhvvho kdv �qlvkhg wkh lq0

mhfwlrq/ wkh yhvvho vzlwfkhv iurp suhvvxuh kroglqj wr lqmhfwlrq1 Wkhq/ wkh rz frqwuro

ydoyh rshqv dqg lqmhfwlrq vwduwv1 Phdqzkloh/ wkh rwkhu yhvvho rz frqwuro ydoyh forvhv1

Gxulqj wkh lqmhfwlrq skdvh erwk frqwuro ydoyhv/ wkh suhvvxuh dqg wkh rz frqwuro ydoyh/

duh dfwlyh1 Wkh zhljkw ri wkh yhvvho lv udpslqj grzq wr d plqlpxp ydoxh zkloh wkh

suhvvxuh uhpdlqv frqvwdqw1 Uhdfklqj wkh plqlpxp zhljkw/ wkh lqmhfwlrq yhvvho rz

frqwuro ydoyh forvhv1 Lq wkh phdqwlph/ wkh rwkhu yhvvho kdv ehhq fkdujhg/ suhvvxul}hg

516 H{lvwlqj frqwuro xqlw 45

dqg vwdqgv e|1 Li wkh suhvvxuh frqwuro ydoyh dqg wkh rz frqwuro ydoyh kdyh forvhg/ wkh

yhqwlodwlrq ydoyh rshqv dqg ghsuhvvxul}hv wkh lqmhfwlrq yhvvho1 Rqfh wkh suhvvxuh kdv

gursshg grzq wr qrupdo/ wkh lqohw ydoyh rshqv dqg frdo srzghu lv �oohg lq djdlq1 Lq

Dsshqgl{ E wkh rz fkduwv ri wkh lqmhfwlrq surfhvv duh jlyhq1

516 H{lvwlqj frqwuro xqlw

Wkh frqwuro xqlw ri wkh �qh frdo lqmhfwlrq sodqw frqvlvwv ri wzr lqghshqghqw orrsv1 Rqh

orrs lv iru lqmhfwlrq yhvvho suhvvxuh vwdelol}dwlrq/ dqg wkh rwkhu lv iru frqwuroolqj wkh

frdo pdvv rz wr wkh eodvw ixuqdfh1 Wkh surfhvv zrunlqj f|foh gxudwlrq ghshqgv rq

wkh dfwxdo frdo pdvv rz vhw srlqw1 Orjlfdoo|/ d kljkhu vhw srlqw vkruwhqv wkh f|foh

wlph1 Qrupdoo|/ wkh f|foh wlph lv derxw 73 plqxwhv/ zklfk phdqv wkdw wkh lqmhfwlrq

skdvh wdnhv 2f plqxwhv/ dssur{lpdwho|1

51614 Vhqvruv

Vlqfh wkh zkroh sodqw kdv pdq| surfhvvhv uxqqlqj vhsdudwh iurp hdfk rwkhu/ sduwo|

zlwkrxw nqrzohgjh ri wkh rwkhu surfhvvhv/ wkh| duh glvwxuelqj hdfk rwkhu1 Ixuwkhupruh

pdq| sduwv ri wkh sodqw duh phfkdqlfdoo| frxsohg/ iru h{dpsoh wkh wzr lqmhfwlrq yhvvhov

duh frxsohg ryhu wkh lqmhfwlrq slsh1 Wklv uhvxowv lq huuruv lq wkh phdvxuhphqw/ zklfk

pd| qrw eh qhjohfwhg1

Wkhuhiruh lw kdv wr eh glvfxvvhg/ zkdw vljqdov duh xvdeoh iru surfhvv lghqwl�fdwlrq

dqg krz wkh| duh dftxluhg1 Pdlqo| wkh surfhvv kdv irxu lqsxw vljqdov1 Wkh| duh =

� suhvvxuh lq wkh yhvvho

� suhvvxuh lq wkh qlwurjhq qhw

� zhljkw ri wkh lqmhfwlrq yhvvho

� suhvvxuh lq wkh lqmhfwlrq slsh1

Doo suhvvxuh vhqvruv duh gl�huhqfh suhvvxuh phwhuv1 Wkh| duh fdoleudwhg rq d suhv0

vxuh udqjh iurp f wr �Sff &�@/ dqg kdyh dq dffxudf| ri f�DI1 ]hur lv fdoleudwhg rq

qrupdo rxwvlgh suhvvxuh1 Wkh suhvvxuh vljqdo lv olqhduo| frqyhuwhg lqwr d fxuuhqw vljqdo1

Wdeoh 516 vkrzv krz wkh vljqdo lv frqyhuwhg1


Suhvvxuh vljqdo Fxuuhqw vljqdo

f &�@ e6�

�Sff &�@ 2f6�

Wdeoh 516= Suhvvxuh vljqdo frqyhuvlrq

Pdvv vljqdo Fxuuhqw vljqdo

f &} f6�

Sfff &} 2f6�

Wdeoh 517= Pdvv vljqdo frqyhuvlrq

Wkh zhljkw vhqvru lv phwhulqj wkh pdvv ri wkh lqmhfwlrq yhvvhov1 Dv wkh lqmhfwlrq

yhvvhov duh frxsohg zlwk hdfk rwkhu ryhu wkh lqmhfwlrq slsh/ wkh phwhuhg zhljkw lv

glvwxuehg e| wkh zhljkw ri wkh rwkhu yhvvho1 Wkh zhljkw vhqvru lv fdoleudwhg rq wkh

hpsw| lqmhfwlrq yhvvho wr eh }hur1 Wkh pdvv vljqdo lv olqhduo| frqyhuwhg lqwr d fxuuhqw

vljqdo/ wrr1 Wdeoh 517 vkrzv krz wkh vljqdo lv frqyhuwhg1 Reylrxvo| wklv frqyhuvlrq lv

gl�huhqw dqg wkh vljqdo iurp wkh vhqvru kdv d gl�huhqw udqjh1

Doo fxuuhqw vljqdov duh dpsol�hg ehiruh vdpsolqj e| d ex�hu dpsol�hu/ zlwk jdlq rqh1

Wklv lv grqh ehfdxvh ri vdihw| uhdvrqv/ lq rughu wr vhsdudwh wkh flufxlwv jdoydqlfdoo|1

Wkh xvhg ex�hu dpsol�huv kdyh dq huuru ohvv wkdq f�2I1

51615 Dfwxdwruv

Wkh suhvvxuh dqg rz frqwuro ri wkh lqmhfwlrq yhvvhov lqyroyhv wzr dfwxdwruv1 Wkh

suhvvxuh frqwuro ydoyh +SFY, dqg wkh rz frqwuro ydoyh +IFY,1 Wkh SFY lv d vwdqgdug

ydoyh/ zkloh wkh IFY lv d vshfldo ghvljq iurp EPK/ ^48`1 Erwk ydoyhv kdyh d srvlwlrq

frqwuro zklfk lv qrw glvfxvvhg forvhu1 Lw fdq eh dvvxphg wkdw wkh srvlwlrq frqwuro kdv d

vx!flhqw idvw dqg dffxudwh ehkdylru1 Odwhu wkh ehkdylru ri wkhvh lqqhu orrsv lv dvvxphg

wr eh sursruwlrqdo1

Vlqfh fkdudfwhulvwlf fxuyhv duh qrw dydlodeoh iru wkh SFY/ rqo| d sulqflsoh fkdudf0

whulvwlfv fdq eh jlyhq1 Sdudphwhuv fdq eh rewdlqhg iurp h{shulphqwv dqg lghqwl�fdwlrq

dv vkrzq lq ^;`1 Iljxuh 614 vkrzv d sulqflsoh fkdudfwhulvwlf1 Reylrxvo| wkh SFY kdv

d ghdg0}rqh dqg dq h{srqhqwldo fkdudfwhulvwlf/ dv lw lv dq htxdo shufhqwdjh ydoyh1 Lw

vkrxog eh srvvleoh wr olqhdul}h wklv fkdudfwhulvwlf durxqg d zrunlqj srlqw1

D orrn dw wkh sulqflsoh vwuxfwxuh ri wkh ydoyh/ �jxuh 518/ vkrzv zk| wkh ydoyh kdv


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

valve opening

norm

aliz

ed fl

ow

Iljxuh 517= Sulqflsoh fkdudfwhulvwlf fxuyh ri wkh SFY

d ghdg0}rqh1 Wkh h{leoh ulqj vhdo zloo suhyhqw qlwurjhq sdvvlqj wkurxjk wkh ydoyh/

dowkrxjk wkh ydoyh lv rshq1 Wklv lv ydolg iru rshqlqjv ehwzhhq }hur dqg DI1

Dv wkh IFY lv d vshfldo ghvljq e| EPK/ qr fkdudfwhulvwlf fxuyh lv dydlodeoh1 Rqo|

d sulqflsoh vwuxfwxuh ri wkh IFY fdq eh jlyhq lq �jxuh 5191 Lw ehfrphv fohdu/ wkdw

wkhuh lv d qrq0olqhdu frkhuhqfh ehwzhhq wkh ydoyh rshqlqj dqg wkh uhvxowlqj pdvv rz

wkurxjk wkh ydoyh1 Lw zloo eh vkrzq odwhu wkdw d olqhdu prgho zrunv vx!flhqwo| jrrg

iru wklv ydoyh1 Wkh IFY kdv dovr d ghdg0}rqh/ wklv uhvxowv iurp wkh volgh pryhphqw1

Lq rughu wr wljkwhq/ wkh ydoyh kdv wr sdvv ryhu wkh rshqlqj frpsohwho| dqg iru vdihw|

uhdvrq d elw pruh1 Wkh fdoleudwhg ydoyh zloo rshq sk|vlfdoo| iru frqwuro vljqdov ehwzhhq

2� dqg �ffI1 Wkh uhvxowlqj qrq0olqhdulw| fdq qrw eh qhjohfwhg1

51616 Wkh suhvvxuh frqwuro

Wkh suhvvxuh frqwuroohu lv sodfhg lq VdwwFrq/ forvh wr wkh frdo lqmhfwlrq yhvvhov1 Wkh

f|foh wlph iru wkh suhvvxuh orrs lv f��r1 Wkh lqsxw iurp wkh suhvvxuh vhqvru lv vdpsohg

zlwk wkh f|foh wlph dqg dftxluhg e| dq D2G Fdug zklfk frqyhuwv wkh dqdorjxh fxuuhqw

vljqdo lqwr d gljlwdo vljqdo1 Ilowhulqj lv suredeo| dssolhg exw qrw phqwlrqhg ru ghvfulehg

lq wkh frqwuro xqlwv ghvfulswlrq1 Wkh xvhg frqwuroohu lv d txdvl frqwlqxrxv SL frqwuroohu


moving directionof the piston

highpressure

lowpressure

flexible ring seal

Iljxuh 518= Sulqflsoh vwuxfwxuh ri wkh SFY +vlghylhz,

moving directionof the slide

pipe hole

slide

Iljxuh 519= Sulqflsoh vwuxfwxuh ri wkh IFY +wrsylhz,


- PI

1

tta

uN ,maxuN ,min

uN

pref

p

[ ]kPa

[ ]kPa

Iljxuh 51:= Eorfn gldjudp ri wkh suhvvxuh frqwuro

zlwk dq lqwhjudwlrq wlph ri Dr dqg d jdlq ri D1 Wkh jdlq kdg ehhq lqfuhdvhg dv d uhvxow

ri wkh uhfrpphqgdwlrqv iurp wkh suh0vwxglhv grqh e| wkh FHJ1 Lw zdv vkrzq wkdw d

kljkhu jdlq/ lq iruphu wlphv 6/ lqfuhdvhv wkh shuirupdqfh ri wkh frqwuroohu1

Wkh frqwuroohu rxwsxw lv olplwhg ehwzhhq f dqg .DI/ gxulqj suhvvxul}dwlrq1 Wkh

uhdvrq iru wklv olplwdwlrq lv wkdw wkh fdsdflw| ri wkh qlwurjhq qhw lv wrr orz1 Li wkh SFY

lv rshqhg wrr pxfk gxulqj wkh suhvvxul}lqj skdvh/ wkh suhvvxuh lq wkh qlwurjhq qhw

gursv1 Wklv fdxvhv suhvvxuh rvfloodwlrqv gxulqj wkh lqmhfwlrq skdvh ri wkh rwkhu yhvvho1

Vlqfh wkh frqwuroohu lv douhdg| dfwlyh gxulqj wkh suhvvxul}lqj skdvh/ lw kdv wr iroorz

d udps1 Wklv lv uhdol}hg e| udpslqj wkh vhw srlqw ydoxh iurp }hur xs wr vhw srlqw ydoxh

gxulqj wkh lqmhfwlrq skdvh1 Xvlqj d �{hg rshqlqj ydoxh iru wkh SFY zrxog kdyh wkh

vdph uhvxow1 Dq rshqlqj ydoxh uhvxowlqj lq wkh vdph wlph/ qhhghg wr suhvvxul}h wkh

yhvvho/ frxog eh frpsxwhg hdvlo| dqg zrxog uhgxfh ydoyh zduh0r�/ dv wkh frqwuroohu lv

rvfloodwlqj d orw lq wkh ehjlqqlqj1

Iljxuh 51: vkrzv wkh eorfn gldjudp ri wkh dfwxdo xvhg suhvvxuh frqwuro dqg �jxuh

51; vkrzv krz wkh suhvvxuh frqwuroohu shuirupv1 Lw lv fohdu wkdw wkh frqwuroohu kdv d

orqj fruuhfwlrq wlph1

51617 Wkh pdvv rz frqwuro

Dv wkh pdvv rz fdqqrw eh phdvxuhg/ wkh frqwuro xqlw xvhv wkh pdvv orvv ri wkh lqmhfwlrq

yhvvho gxulqj wkh lqmhfwlrq skdvh dv lqsxw vljqdo1 Wkh pdvv orvv lv wkhq ghulydwhg1 D

�uvw rughu gl�huhqfh lv xvhg wr dssur{lpdwh wkh ghulydwlyh1 Wkh uhvxowlqj vljqdo lv wkhq

orz sdvv �owhuhg dqg olplwhg wr d pd{lpxp ghyldwlrq iurp wkh vhw srlqw/ lq rughu wr

uhgxfh qrlvh wkdw kdv ehhq dpsol�hg ehfdxvh ri wkh gl�huhqwldwlrq1 Wklv pdvv rz lv

frpsxwhg hyhu| irxuwk vhfrqg1 Wkh frqwuroohu lwvhoi lv d txdvl frqwlqxrxv SL frqwuroohu

zlwk lqwhjudwlrq wlph ri � plqxwhv dqg d jdlq ri f�.D1 Wkh frqwuroohu iru lqmhfwlrq yhvvho

516 H{lvwlqj frqwuro xqlw 4:

0 100 200 300 400 500 600 700 800 900 1000−40

−20

0

20

time/s

pres

sure

dev

iatio

n/kP

a

control result

0 100 200 300 400 500 600 700 800 900 10000

20

40

60

80

time/s

valv

e op

enin

g/%

controller output

Iljxuh 51;= Shuirupdqfh ri wkh suhvvxuh frqwuroohu

uC09.

q−1

1

1 05 1− ⋅ −. q--

kg

s4

t

h

t

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1000 3Nm

h

mC &mC

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Iljxuh 51<= Eorfn gldjudp ri wkh pdvv rz frqwuro

V55 lv wxqhg gl�huhqwo|/ wkh lqwhjudwlrq wlph lv vhw wr 2�D plqxwhv1 Ixuwkhupruh wkh

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huuruv lq wkh frpsxwhg pdvv rz1 Wkh pdvv orvv ri wkh lqmhfwlrq yhvvho lv frpsduhg

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Iljxuh 51< vkrzv d eorfn gldjudp ri wkh dfwxdo xvhg pdvv rz frqwuro/ dqg �jxuh

5143 vkrzv krz wkh pdvv rz frqwuroohu shuirupv1 D orrn dw wkh ghyldwlrq ri wkh pdvv

rz vkrzv wkdw wkh dfwxdo frqwuroohu lv qrw deoh wr gulyh wkh frqwuro huuru wr }hur1 Wklv

lv dovr vxvwdlqhg/ orrnlqj dw wkh ghyldwlrq ri wkh pdvv orvv iurp wkh lghdo pdvv orvv ri

wkh lqmhfwlrq yhvvho/ zklfk lv glvsod|hg lq �jxuh 51441

516 H{lvwlqj frqwuro xqlw 4;

0 100 200 300 400 500 600 700 800 900 100060

65

70

75

80

time/s

valv

e op

enin

g/%

controller output

0 100 200 300 400 500 600 700 800 900 1000−10

−5

0

5

10

15

time/s

mas

s flo

w d

evia

tion/

(t/h

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control result

Iljxuh 5143= Shuirupdqfh ri wkh pdvv rz frqwuroohu

0 100 200 300 400 500 600 700 800 900 1000−150

−100

−50

0

50

100

time/s

mas

s de

viat

ion/

kg

Iljxuh 5144= Pdvv orvv ghyldwlrq iurp wkh lghdo pdvv orvv

Fkdswhu 6

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ri vrolgv duh h{sodlqhg dqg d qrq0olqhdu sk|vlfdo prgho ri wkh surfhvv lv suhvhqwhg1

614 Dvshfwv rq sqhxpdwlf frqyh|lqj ri vrolgv

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lpsuhvvlrq lv wkdw qlwurjhq dqg frdo srzghu fdq eh wuhdwhg olnh d xlg1 Xqiruwxqdwho|/

wklv lv suredeo| rqh ri wkh prvw plvxqghuvwrrg h{suhvvlrqv1

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dqg lw zloo qrw vwlfn wr wkh zdoov ri wkh yhvvho gxulqj lqmhfwlrq1 Uhsruwhg lq ^5` wkh

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gh�qhg1 Dv wkh ydoyh ixqfwlrqv }��T R

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duh xqnqrzq dqg

fdqqrw eh ghulyhg iurp h{lvwlqj gdwd vkhhwv/ wkhvh ixqfwlrqv kdv wr eh lghqwl�hg iurp

surfhvv gdwd1 Ixuwkhupruh wkh idfwruv &�

/ &�

kdyh wr eh ghwhuplqhg iurp surfhvv gdwd1

Dv ghvfulehg lq ^;`/ lw lv srvvleoh wr olqhdul}h wkh vwdwh vsdfh prgho e| xvlqj qrq0

olqhdu lqsxw dqg rxwsxw wudqvirupdwlrqv1 Lq dgglwlrq/ wkh ydoyh ixqfwlrqv dqg idfwruv

duh ghulyhg wkhuh1

Vlqfh wkh ydoyhv rshudwh durxqg d txlhvfhqw srlqw gxulqj wkh lqmhfwlrq skdvh/ lw

vkrxog eh srvvleoh wr olqhdul}h wkh prgho ru jdlq d prgho iurp d gluhfw lghqwl�fdwlrq1

Fkdswhu 7

Lghqwl�fdwlrq

Ehfdxvh ri wkh kdug qrq0olqhdulwlhv lq wkh sk|vlfdo prgho d gluhfw lghqwl�fdwlrq ri d

olqhdu prgho/ wkdw dssur{lpdwhv wkh qrq0olqhdu prgho/ lv hpsor|hg1 Lq wklv vhfwlrq/ lw

lv vkrzq wkdw d olqhdu prgho ghulyhg iurp lqsxw2rxwsxw gdwd zrunv vx!flhqwo| jrrg

iru wkh lqmhfwlrq skdvh1 Dq douhdg| h{lvwlqj prgho iru wkh sodqw lv ydolgdwhg xvlqj qhz

gdwd1

Iru lghqwl�fdwlrq wkh Lghqwl�fdwlrq Wrroer{ iru PdwodeU�

lv xvhg1

714 Phdvxuhphqw gdwd

Lq rughu wr lghqwli| wkh sodqw/ lqsxw2rxwsxw gdwd lv qhhghg1 Dw VVDE Wxqqsoèw wzr

gl�huhqw srvvlelolwlhv h{lvw wr orj gdwd1 VVDE kdv d gdwd0edvh/ fdoohg PÙVV/ dw lwv

glvsrvdo1 Wkh gdwd0edvh lv sodfhg rq d vhuyhu zklfk lv frqqhfwhg wr doo frqwuro xqlwv

dw VVDE1 Doo phdvxuhphqw gdwd lv wudqvihuuhg wr wklv vhuyhu dqg vwruhg wkhuh1 Wkh

gdwd lv xvhg iru vwdwlvwlfv dqg dqdo|vlv1 Wkh orfdo qhwzrun doorzv wkh grzqordglqj ri

phdvxuhphqw gdwd wr hyhu| SF dw VVDE1

Wkh gdwd lwvhoi rq wkh vhuyhu lv glylghg lqwr wzr jurxsv = plqxwh phdq ydoxhv dqg

glyhuvh wlph edvhg ydoxhv1 Wkh plqxwh phdq ydoxhv duh qrw vxlwdeoh iru lghqwl�fdwlrq/

ehfdxvh wkh vdpsoh udwh lv wrr vorz dqg wkh ydoxhv duh phdq ydoxhv1 Wkhuhiruh/ d qhz

wlph edvh iru wkh qhhghg ydoxhv iurp wkh frdo lqmhfwlrq sodqw kdv ehhq lpsohphqwhg lq

PÙVV1 Wkhvh ydoxhv duh orjjhg dw d vdpsoh udwh ri Dr/ wkh pd{lpxp udwh doorzhg e|

wkh frqwuro xqlw DoFrqw1 Dv DoFrqw kdv qr sulrulw| rq orjjlqj gdwd dqg wudqvihuulqj

lw wr PÙVV/ wkh vdpsoh udwh lv ydu|lqj1 Wklv uhvxowv lq vdpsoh udwhv ydu|lqj ehwzhhq

� dqg �fr/ zklfk pdnhv lghqwl�fdwlrq gl!fxow1 Gdwd vhwv kdyh wr eh lqwhusrodwhg dqg

55

714 Phdvxuhphqw gdwd 56

0 500 10000

2

4

6

8

time/s

valv

e op

enin

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0 500 10006

6.5

7

7.5

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0 500 10000

2

4

6

8

10

time/sm

ass/

V

mass of the vessel

0 500 10005.7

5.8

5.9

6

time/s

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sure

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pressure in the vessel

Iljxuh 714= Sodqw lqsxw dqg rxwsxw vljqdov gxulqj lqmhfwlrq skdvh1 SFY dqg IFY duh

lqsxwv/ suhvvxuh dqg pdvv duh rxwsxwv

pd| eh uh0vdpsohg1 Ixuwkhupruh/ wkhuh lv qr lqirupdwlrq derxw wkh �owhulqj ri wkh

gdwd1 Ehfdxvh ri wkhvh uhdvrqv/ wkh gdwd iurp PÙVV lv qrw xvhg iru wkh lghqwl�fdwlrq1

Vlqfh d uh0ghvljqhg frqwuroohu vkrxog eh whvwhg lq uhdo0wlph rq wkh sodqw/ doo lpsru0

wdqw vljqdov vkrxog eh dffhvvleoh iru d SF zlwk D2G0Erdug1 Lw dsshduhg wr eh srvvleoh

wr jhw dffhvv wr wkh vljqdov iurp2wr wkh ydoyhv/ dqg wr wkh vhqvruv iru pdvv dqg suhvvxuh

ri wkh lqmhfwlrq yhvvho1 E| xvh ri vljqdo frqyhuwhuv wkh fxuuhqw vljqdov duh wudqvodwhg

lqwr yrowdjh vljqdov iru wkh D2G0Erdug1 Wkh orz sdvv �owhulqj e| wkh vljqdo frqyhuwhuv

kdv ehhq vxssuhvvhg1 Iru lghqwl�fdwlrq sxusrvhv irxu vljqdov duh orjjhg =

� suhvvxuh lq wkh yhvvho

� pdvv ri wkh yhvvho

� dfwxdo ydoxh ri wkh SFY

� dfwxdo ydoxh ri wkh SFY

Iljxuh 714 glvsod|v wkh vljqdov1

Ehfdxvh ri wkh qrq0olqhdulw| ri wkh IFY wkdw kdv ehhq ghvfulehg deryh/ wkh lqsxw

vljqdov duh wudqviruphg1 Lq wklv zd|/ wkh qrq0olqhdulw| ehfrphv sduw ri wkh sodqw1 Wklv

715 Ydolgdwlrq ri wkh h{lvwlqj prgho 57

Txdqwlw| orjjhg zlwk SF orjjhg zlwk PÙVV

Ydoyh rshqlqj �T �fI

Suhvvxuh �T �S�&�@

Pdvv �T S�e�2D&}

Pdvv rz �Tr

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Wdeoh 714= Frqyhuvlrq ri vljqdov lq yrowv wr sk|vlfdo xqlwv

lv wkh uhdvrq zk| doo rxwsxw vljqdov wr wkh IFY kdyh wr eh wudqviruphg zlwk wkh lqyhuvh

wudqvirupdwlrq1 Wkh wudqvirupdwlrq lv d vfdolqj ri wkh vljqdo iurp wkh IFY1 Dv wkh

ghdg0}rqh ri wkh ydoyh lv ehwzhhq f dqg 2�I/ wkh vljqdo udqjh iurp f wr �ffI lv vfdohg

lqwr wkh udqjh 2� wr �ffI1 Wklv ohdgv wr wkh iroorzlqj wudqvirupdwlrq

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zkhuh ��

kdv d udqjh iurp f wr �ffI dqg ��c8�T

d udqjh iurp 2� wr �ffI1 Wklv

phdqv wkdw ��c8�T

lv wkh dfwxdo srvlwlrq ydoxh ri wkh IFY/ wkdw fdq eh phdvxuhg1 Wkh

lqyhuvh wudqvirupdwlrq uhvxowv lq

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Wr eh deoh wr frpsduh wkh orjjhg gdwd iurp wkh SF zlwk wkh gdwd orjjhg e| PÙVV/

wkh yrowdjh ydoxh qhhg wr eh frqyhuwhg lqwr sk|vlfdo xqlwv1 Wkh frqyhuvlrq idfwruv fdq

eh rewdlqhg iurp d frpsdulvrq ri gdwd orjjhg dw wkh vdph wlph lqvwdqfh1 Wdeoh 714

vkrzv krz wkh yrowdjh vljqdov fdq eh frqyhuwhg lqwr sk|vlfdo xqlwv1

Wkh pdvv rz lv d frpsrvlwh txdqwlw| dqg fdq qrw eh orjjhg dv d vljqdo1 Exw lw lv

qhhghg odwhu iru wkh frqwuroohu/ dv d vhw srlqw ydoxh1 Wklv ydoxh pxvw eh jlyhq lq�T

r

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715 Ydolgdwlrq ri wkh h{lvwlqj prgho

Xqwlo wkh vxpphu 4<<9 wkh wzr lqmhfwlrq yhvvhov zhuh sk|vlfdoo| frqqhfwhg wr wkh qlwur0

jhq qhw zlwk rqo| rqh SFY1 Qdwxudoo|/ rqo| rqh frqwuroohu zdv xvhg iru erwk yhvvhov1

Xvlqj vhyhudo vkxw0r� ydoyhv/ wkh SFY zdv frqqhfwhg wr wkh yhvvho qhhghg wr eh frq0

wuroohg1 Gxulqj wkh suhvvxuh kroglqj skdvh/ d olplw vzlwfk dqg rqh vhsdudwh vkxw0r�

ydoyh zhuh xvhg wr krog wkh suhvvxuh lq d fhuwdlq udqjh1 Wkh FHJ uhfrpphqghg wkh

716 Prgho iru wkh pdvv 58

xvh ri wzr frqwuroohuv dqg SFY*v1 Edvhg rq wkh uhvxowv ri wkh suh0vwxg| VVDE uhfrq0

vwuxfwhg wkh suhvvxuh frqwuro dqg lpsohphqwhg wzr frqwuroohuv dqg SFY*v1 Qrz hdfk

yhvvho lv frqwuroohg frpsohwho| vhsdudwh1

Vlqfh wkh h{lvwlqj prgho zdv ghyhorshg ehiruh wkhvh fkdqjhv kdg ehhq pdgh/ lw lv

qhfhvvdu| wr ydolgdwh wklv prgho1 Li lw lv ydolg/ wkh suhvvxuh frqwuroohu/ ghyhorshg gxulqj

wkh suh0vwxg|/ fdq vwloo eh xvhg1

Wr ydolgdwh wkh vlqjoh lqsxw2vlqjoh rxwsxw prgho iru wkh suhvvxuh dv rxwsxw dqg wkh

SFY rshqlqj dv lqsxw wzr whvwv duh dssolhg/ dv sursrvhg lq ^:/ fkdswhu 44` =

� Frpsduh phdvxuhg dqg vlpxodwhg rxwsxw1 Xvh frpprq vhqvh wr ydolgdwh1

D gdwd vhw gl�huhqw iurp wkh lghqwl�fdwlrq gdwd vhw lv xvhg1 Wkh phdvxuhg dqg

vlpxodwhg rxwsxw duh sorwwhg lq wkh vdph �jxuh1 Wkh ehkdylru ri wkh vlpxodwhg

dqg wkh phdvxuhg rxwsxw duh frpsduhg1 Frpprq vhqvh lv xvhg wr pdnh d ghflvlrq

rq zkhwkhu wkh prgho lv dffhswhg ru uhmhfwhg/ vhh �jxuh 7151

� Xvh ri d vwdwlvwlfdo whvw rq wkh suhglfwlrq huuru1

Iurp wkh phdvxuhg dqg wkh vlpxodwhg rxwsxw wkh suhglfwlrq huuru lv ghulyhg1 Li

wkh prgho �wv dqg wkh qrlvh lv zklwh/ wkh suhglfwlrq huuru lv zklwh qrlvh zlwk }hur

phdq1 Wkh dxwrfruuhodwlrq ri wkh suhglfwlrq huuru vkrxog wkhq eh }hur iru doo odjv

� 9' f1 Ixuwkhupruh/ wkh suhglfwlrq huuru fdq eh furvv fruuhodwhg zlwk wkh lqsxw

vljqdo/ wkh| vkrxog eh xqfruuhodwhg1 Wklv whvw lv qrupdoo| qrw vxffhvvixo lq forvhg

orrs/ dv wkh lqsxw lv d uhvxow ri wkh rxwsxw1 Zkhwkhu wr uhmhfw ru dffhsw d prgho

lv ghwhuplqhg e| d frq�ghqfh ohyho/ dv wkh fruuhodwlrq ixqfwlrqv duh qrw }hur lq

uhdolw|1 ^:/ sdjh 757` ghvfulehv krz wklv frq�ghqfh ohyho lv frpsxwhg1 Iljxuh 716

vkrzv wkh uhvxow ri wkh vwdwlvwlfdo whvw iru wkh prgho ydolgdwlrq1

Iljxuhv 715 dqg 716 vkrz wkdw wkh h{lvwlqj prgho lv vwloo ydolg/ dowkrxjk wkh vwuxfwxuh

ri wkh sodqw kdv ehhq fkdqjhg1 Krzhyhu wkhvh fkdqjhv glg qrw kdyh dq| lq xhqfh lq

wkh sodqw ehkdylru1 Wkh h{lvwlqj prgho kdv wkh iroorzlqj prgho htxdwlrq =

RE|� ' �f�f�fS � �� fDSS^3�

�� f�HHDH^3� � f��e^32� �

�

E|� +716,

716 Prgho iru wkh pdvv

Iru wkh ghvljq ri wzr vhsdudwh vlqjoh lqsxw2vlqjoh rxwsxw v|vwhpv/ rqh frqwuroolqj wkh

suhvvxuh dqg wkh rwkhu frqwuroolqj wkh pdvv rz/ d prgho iru wkh pdvv lv ghulyhg1 Dv

716 Prgho iru wkh pdvv 59

50 100 150 200 250 300 350 400 450

−0.15

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sure

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Iljxuh 715= Frpsdulvrq ri phdvxuhg rxwsxw +gdvkhg0grwwhg, dqg vlpxodwhg prgho

rxwsxw +vrolg,

−100 −80 −60 −40 −20 0 20 40 60 80 100−0.1

−0.05

0

0.05

0.1

Autocorrelation of residuals for pressure

−100 −80 −60 −40 −20 0 20 40 60 80 100−0.2

−0.1

0

0.1

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Samples

Cross correlation for PCV and pressure residuals

Iljxuh 716= Uhvxow ri wkh vwdwlvwlfdo whvw1 Fruuhodwlrq ydoxhv +vrolg,/ frq�ghqfh ohyho

+grwwhg,

716 Prgho iru wkh pdvv 5:

0 50 100 150 200 250 300 350 400 450−3

−2.5

−2

−1.5

−1

−0.5

0

time/s

mas

s/V

Iljxuh 717= Frpsdulvrq ri phdvxuhg pdvv +gdvkhg0grwwhg, dqg vlpxodwhg pdvv +vrolg,

lqsxw wkh IFY dqg dv rxwsxw wkh pdvv ri wkh yhvvho duh fkrvhq1 Xvlqj d ohdvw vtxduh

phwkrg iru wkh lghqwl�fdwlrq jlyhv wkh ehvw uhvxow1 Wkh uhvxowlqj DU[0prgho kdv wkh

iroorzlqj htxdwlrq =

6E|� '�f�ff�f�^3�� f�bbbbe^3�

� ��

E|� +717,

Reylrxvo| wkh prgho lv ri �uvw rughu dqg kdv d sroh forvh wr wkh vwdelolw| erughu1

Wklv vhhpv wr eh orjlfdoo| fruuhfw dv iurp wkh nqrzohgjh ri wkh sodqw wkh pdvv ri wkh

yhvvho lv dq lqwhjudo ri wkh pdvv rz rxw ri wkh lqmhfwlrq yhvvho1 Wklv ohdgv wr wkh

uhvxow wkdw wkh IFY wrjhwkhu zlwk lwv srvlwlrq frqwuroohu fdq eh dvvxphg wr kdyh d

sursruwlrqdo ehkdylru1 Dvvxplqj wkh vwuxfwxuh ri wkh prgho ehlqj pruh frpsoh{/ grhv

qrw jlyh d ehwwhu lghqwl�fdwlrq uhvxow1

Wkh prgho iurp htxdwlrq +717, lv qrz ydolgdwhg lq d zd| vlplodu wr wkdw iru wkh

prgho lq wkh suhylrxv vhfwlrq1 Wkh uhvxow ri wkh frpprq vhqvh whvw lv glvsod|hg lq

�jxuh 717 dqg 7181 Iurp wkh uhvxowv ri wkh vwdwlvwlfdo whvw rqh pljkw uhmhfw wkh prgho1

Exw dv ghvfulehg lq ^:/ fkdswhu 44` wkh vwdwlvwlfdo whvwv gholyhu qr devroxwh ghjuhh/ wkdw

ghflghv zkhwkhu d prgho kdv wr eh uhmhfwhg ru dffhswhg1 Lq wkh vhtxho/ wkh lghqwl�hg

prgho lv dffhswhg1

717 PLPR prgho 5;

−100 −80 −60 −40 −20 0 20 40 60 80 100−0.5

0

0.5

Samples

Cross correlation of mass residuals and FCV

−100 −80 −60 −40 −20 0 20 40 60 80 100−1

−0.5

0

0.5

1

Autocorrelation of mass residuals

Iljxuh 718= Uhvxow ri wkh vwdwlvwlfdo whvw1 Fruuhodwlrq ydoxhv +vrolg, dqg frq�ghqfh ohyho

+grwwhg,

717 PLPR prgho

Lq rughu wr gr d sdudphwulf hvwlpdwlrq ri wkh prgho/ d prgho vwuxfwxuh dqg lwv rughu

kdv wr eh fkrvhq1 Vlqfh wkh vrxjkw prgho kdv wzr lqsxwv dqg rxwsxwv dqg d ohdvw vtxduh

phwkrg lv xvhg dw �uvw/ wkh prgho vwuxfwxuh iru wkh PLPR fdvh lv qrz suhvhqwhg1 Wkh

lqsxw/ rxwsxw dqg htxdwlrq huuru yhfwruv duh gh�qhg dv

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dqg dffruglqj wr ^8`/ wkh DU[0surfhvv uhvxowv lq

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717 PLPR prgho 5<

zkhuh ^3� lv wkh edfn0vkliw rshudwru dqg

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68+71:d,

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68 +71:e,

Wkh rughu ri wkh prgho lv gh�qhg e| wkh sdudphwhuv ?@ dqg ?K/ zklfk kdyh wr eh

ghwhuplqhg lq dgydqfh1 Wklv phdqv wkdw hljkw sro|qrpldov kdyh wr eh hvwlpdwhg1

Wkhvh hljkw sro|qrpldov ghvfuleh vl{ lqghshqghqw DU[0surfhvvhv1

Wkh glvdgydqwdjh ri wklv prgho vwuxfwxuh iru wkh PLPR fdvh lv wkdw doo sro|qrpldov

lq �E^3�� dqg wkrvh lq �E^3�� kdyh wkh vdph rughu1 Wklv phdqv wkdw doo vl{ DU[0

surfhvvhv duh dvvxphg wr eh ri wkh vdph rughu1 Li sroh0}hur fdqfhoodwlrqv lq wkh lghqwl�hg

DU[0prgho dsshdu/ wkh rughu ri wklv surfhvv lv fkrvhq wr kljk1 Dprgho rughu uhgxfwlrq

lv wkhq srvvleoh1

Lq ^:/ fkdswhu :` wkh ohdvw0vtxduhv phwkrg lv dssolhg wr wkh sureohp ri sdudphwhu

hvwlpdwlrq ri VLVR DU[0surfhvv1 Wkh htxdwlrqv fdq eh uhzulwwhq iru wkh PLPR fdvh1

Htxdwlrq +719, ehfrphv

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e| lqwurgxflqj wkh phdvxuhphqw gdwd yhfwru )E|� dqg wkh sdudphwhu pdwul{ X dv

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Dq dojrulwkp wr vroyh wklv sureohp lv douhdg| lpsohphqwhg lq wkh Lghqwl�fdwlrq

Wrroer{1 Wkh phdvxuhg gdwd lv lpsruwhg lqwr PdwodeU�1 Vhsdudwh lghqwl�fdwlrq dqg

ydolgdwlrq vhwv duh xvhg1 Dv wkh prgho rughu kdv wr eh gh�qhg iru wkh dojrulwkp/ d

717 PLPR prgho 63

50 100 150 200 250 300 350 400 450

−0.1

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Iljxuh 719= Phdvxuhg suhvvxuh +gdvkhg0grwwhg, dqg vlpxodwhg suhvvxuh +vrolg,

fkrlfh ri ?@ ' 2c ?K ' 2 vhhpv wr eh dssursuldwh iru wkh �uvw wuldo1 Wklv fkrlfh lv

edvhg rq wkh rughu ri wkh h{lvwlqj prgho1 Vhyhudo lghqwl�fdwlrq uxqv kdyh ehhq pdgh/

ydu|lqj wkh sdudphwhuv ?@ dqg ?K1 Wkh ydolgdwlrq ri hdfk prgho surriv/ wkdw wkh �uvw

fkrlfh zlwk ?@ ' 2c ?K ' 2 shuirupv ehvw1

Wkh ydolgdwlrq frqvlvwv ri wkh wzr whvwv ghvfulehg lq wkh suhylrxv vhfwlrq1 Wkh

qxpehu ri sorwv lqfuhdvhv h{wuhpho| frpsduhg wr wkh VLVR fdvh/ wkhuhiruh rqo| wkh

frpprq vhqvh whvw lv glvsod|hg khuh1 Wkh sorwv iurp vwdwlvwlfdo whvw fdq eh irxqg lq

Dsshqgl{ F1 Iljxuh 719 dqg 71: vkrz wkh uhvxowv ri wkh frpprq vhqvh whvw1 Lw lv hdv|

wr vhh wkdw wkh prgho lv shuiruplqj zhoo1

Wkh uhvxowlqj prgho sdudphwhuv duh

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68+7144d,

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50 100 150 200 250 300 350 400 450

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0 200 400 600 800 1000 12000

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0 200 400 600 800 1000 12000

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(a)

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0 100 200 300 400 500 600−0.1

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0 100 200 300 400 500 6000

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= prgho srohv

R�

= suhvvxuh lq wkh qlwurjhq qhw

RA

= suhvvxuh lq wkh wudqvsruwdwlrq slsh

x = glvfuhwh0wlph v|vwhp pdwul{

) = phdvxuhphqw gdwd yhfwru

" = zhljkwlqj pdwul{

+ = zhljkwlqj pdwul{

A = whpshudwxuh lq wkh lqmhfwlrq yhvvho

A = wudqvirupdwlrq pdwul{

X = sdudphwhu pdwul{

X = hvwlpdwhg sdudphwhu pdwul{

� = lqsxw yhfwru

��

= rshqlqj ri wkh IFY +wudqviruphg,

��c8�T

= sk|vlfdo rshqlqj ri wkh IFY

��

= rshqlqj ri wkh SFY

�W = vwhdg|0vwdwh lqsxw yhfwru

T = yroxph ri wkh lqmhfwlrq yhvvho

T�

= frdo yroxph

T�

= qlwurjhq yroxph

= vwdwh yhfwru

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) = rxwsxw yhfwru

)W = vwhg|0vwdwh rxwsxw yhfwru

D16 Frqvwdqwv

-�

= jdv frqvwdqw ri qlwurjhq

4�

= ghqvlw| ri frdo

Dsshqgl{ E

Iorz fkduw ri wkh lqmhfwlrq surfhvv

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Wkh �uvw/ �jxuh E14/ ghvfulehv wkh vwduw0xs surfhgxuh iru wkh frdo lqmhfwlrq sodqw1 Wkh

lqfrplqj vljqdo �/ lv d uhvxow iurp wkh rz fkduw lq �jxuh E15/ ghvfulelqj wkh vwduw0xs

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rz fkduw grhv qrw ghvfuleh wkh dfwxdo vwuxfwxuh/ dv rqo| rqh suhvvxuh frqwuro xqlw lv

phqwlrqhg lq lw1 Exw wklv kdv qr h�hfw rq wkh sulqflsoh surfhvv rz1

9:

9;

Iljxuh E14= Iorzfkduw ri wkh vwduw0xs surfhgxuh iru wkh frdo lqmhfwlrq sodqw

9<

Iljxuh E15= Iorz fkduw iru wkh k|gudxolf vwduw0xs frqglwlrqv

:3

Iljxuh E16= Iorz fkduw iru wkh lqmhfwlrq surfhvv

Dsshqgl{ F

Ydolgdwlrq zlwk vwdwlvwlfdo whvwv

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qh{w wkh rxwsxw uhvlgxdov duh furvv fruuhodwhg zlwk wkh lqsxwv1 Dowkrxjk wkh furvv

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phdvxuhg rxwsxw zhoo1 Wkhuhiruh wkh prgho lv dffhswhg1

:4

:5

−100 −80 −60 −40 −20 0 20 40 60 80 100−0.5

0

0.5

Samples

Cross correlation of PCV and pressure residuals

−100 −80 −60 −40 −20 0 20 40 60 80 100−1

−0.5

0

0.5

1

Samples

Autocorrelation of pressure residuals

Iljxuh F14= Dxwrfruuhodwlrq ri suhvvxuh uhvlgxdov dqg furvv fruuhodwlrq ri suhvvxuh

uhvlgxdov zlwk SFY1 Frq�ghqfh ohyhov +grwwhg,/ fruuhodwlrqv ixqfwlrqv +vrolg,1

−100 −80 −60 −40 −20 0 20 40 60 80 100−0.5

0

0.5

Samples

Cross correlation of FCV and pressure residuals

Iljxuh F15= Dxwrfruuhodwlrq ri suhvvxuh uhvlgxdov dqg furvv fruuhodwlrq ri suhvvxuh

uhvlgxdov zlwk IFY1 Frq�ghqfh ohyhov +grwwhg,/ fruuhodwlrqv ixqfwlrqv +vrolg,1

:6

−100 −80 −60 −40 −20 0 20 40 60 80 100−0.5

0

0.5

Samples

Cross correlation of FCV and mass residuals

−100 −80 −60 −40 −20 0 20 40 60 80 100−1

−0.5

0

0.5

1

Samples

Autocorrelation of mass residuals

Iljxuh F16= Dxwrfruuhodwlrq ri pdvv uhvlgxdov dqg furvv fruuhodwlrq ri pdvv uhvlgxdov

zlwk IFY1 Frq�ghqfh ohyhov +grwwhg,/ fruuhodwlrqv ixqfwlrqv +vrolg,1

−100 −80 −60 −40 −20 0 20 40 60 80 100−0.5

0

0.5

Samples

Cross correlation of PCV and mass residuals

Iljxuh F17= Dxwrfruuhodwlrq ri pdvv uhvlgxdov dqg furvv fruuhodwlrq ri pdvv uhvlgxdov

zlwk SFY1 Frq�ghqfh ohyhov +grwwhg,/ fruuhodwlrqv ixqfwlrqv +vrolg,1

pressure and flow control of a pulverized coal injection vessel

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