Modeling and Optimal Control of a 3-Axis Motion Simulator

8/17/2019 Modeling and Optimal Control of a 3-Axis Motion Simulator

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Mgtorg`tmag`l Daurg`l ah [akatmjs, Xal. 0, Ga. 0 (;>>=) /F.C.Bar`yof, C.[.Come`rm

0=

Faeolmgi `ge Uostmgi ah Ol`stmj Damgts Fakmlo

Fojc`gmj`l F`gmpul`tars

F. C. Bar`yof`*, C. [. Come`rm`

`-[akatmj [oso`rjc L`kar`tary, Jalloio ah Fojc`gmj`l Ogimgoormgi, Mr`g _gmvorsmty ah Zjmogjo `ge Uojcgalaiy, Uocr`g, Mr`g

@ [ U M J L O M G H A @ K Z U [ @ J U @rtmjlo cmstary4

[ojomvoe4 @uiust 3, ;>>=[ojomvoe mg rovmsoe harf4 Ajtakor

0?, ;>>=

@jjoptoe4 Gavofkor ;9, ;>>=

Mg tcms p`por, eosmig `ge f`guh`jturmgi ah ` fakmlo fojc`gmj`l f`gmpul`tar wmtc hloxmklo

damgts `ro prosogtoe. Oriagafmj prmgjmp`ls sujc `s k`l`gjmgi tco cuf`g comict `ge

`gtcrapafotrmj, ogauic sp`jo har favmgi, `jjossmkmlmty ah tco jagtrallors, f`bmgi

ogvmragfogt l`kar-hrmogely è`ptmgi tco f`gmpul`tar wmtc tco laè `ge `gtcrapafotrmj `ro

jagsmeoroe mg areor ta roeujo c`rf `ge h`tmiuo. Hmrst, tco bmgof`tmjs `ge eyg`fmj oqu`tmags

ah tco fojc`gmsf wmtc hloxmklo damgts har tco tcroo f`dar `xms ah tco fakmlo rakat `ro eormvoe

`ge smful`toe. Goxt, ` fotcae har eotorfmg`tmag ah tco eyg`fmj laè j`rrymgi j`p`jmty

(ELJJ) har ` spojmhmj rohorogjo ms oxpl`mgoe sukdojt ta katc `jjur`jy `ge `jtu`tar

jagstr`mgts. Uco f`gmpul`tar ms tostoe har ` imvog tr`dojtary mg areor ta hmge tco

jc`r`jtormstmjs ah tco eosmigoe f`gmpul`tar. Ycmlo tco f`gmpul`tar ms eosmigoe ta j`rry tco

f`xmfuf laè, oge-ohhojtar's spooe, rakat's jafp`tmkmlmty wmtc tco apor`tar's jagemtmag, `ge

`jjur`jy `ro tco fast mfpart`gt `pplmj`klo pamgts ah tco f`gmpul`tar. Ucoroharo, tco

f`gmpul`tar mg emhhorogt tr`dojtarmos wmtc v`rmaus spooes `ge laès `ro tostoe, `ge tcog tco

rosults `ro `g`lyzoe.

Boywares4

Faeolmgi `ge Zmful`tmag

F`gmpul`tar

Oriagafmj prmgjmploHloxmklo damgts

0. MgtraeujtmagUae`y, ago ah tco fast mfpart`gt praklofs mg tco faeorg

mgeustrm`l jafp`gmos ms emhhmjultmos mg tco f`guh`jturmgi har

apor`tars. Mg èemtmag, mg tco ùtaf`tmag, wcmjc gooes

apor`tar's `jjur`jy `ge swmhtgoss, f`gmpul`tmgi fmict jùso

orrars mg fo`surofogt ospojm`lly mg c`re warbmgi smtu`tmags.

Ucms c`re warb smtu`tmag gat agly fmict curt l`kar kut `lsa

jùso ugqu`lmhmoe praeujtmag. Fojc`gmz`tmag ah mgeustrmosc`s koog oforioe `s ` rosult ah rojogt eovolapfogts.

@ltcauic apor`tars jagtrallmgi ralo c`vo eojro`soe, tcoro

`ro safo lmfmt`tmags, wcmjc cmgeor hull ùtaf`tmag. Mg sujc

jagemtmags, wo uso sofm-ùtaf`tmj fojc`gmsfs. Ohhmjmogjy

ms tco f`mg purpaso mg f`gmpul`tars usìo mg mgeustrmos `ge

tcoy `ro trofogeausly usoe mg j`rrymgi pmojos. Uco uso ah

mgeustrm`l fojc`gmsfs ospojm`lly rakatmj f`gmpul`tars mg

praeujtmag mgeustry c`s koog vory mfpart`gt warlewmeo, mg

areor ta roeujo w`stìo, raw f`torm`l `ge mgjro`so

praeujtmvmty. Uco smfplo fojc`gmsf, cmic spooe `ge tco

o`so ah warb `llaw tco apor`tar ta uso tco roqumroe

f`gmpul`tar har ` spojmhmj purpaso. Uco woll-k`l`gjoe

ùtaf`toe rakats `llaw tco apor`tar ta favo pmojos

emrojtmag`lly mg ` ropo`toe prajoss wmtc ` fmgmfuf harjo

roqumroe. Ucms systof (wmtc ar wmtcaut laè) ms jagtralloe ky

pro-eotorfmgoe roiul`tar `ge `mr-d`jb. Ucoro `ro ` gufkor ah

roso`rjc roparts ag ol`stmj damgt f`gmpul`tars `ge rol`toe

smful`tmags. Har mgst`gjo, F. C. Bar`yof ot `l. `pplmoe `

iogor`l jafputor prair`ffo har eormvmgi eyg`fmj

oqu`tmags ah rakat usmgi syfkalmj l`giuìo F`tcof`tmj`

R0V. Ucaf`s ot `l. c`vo usoe tco laè j`p`jmty `s ` jrmtormag

har eotorfmgmgi tco smzo ah tco `jtu`tars `t tco eosmig stìo

har rakatmj f`gmpul`tar R;V. Ztromt `ge Bmf oxpormfogt ag

tco ûf` ??8 rakat damgts rosultoe mg oqu`lmty ah damgt's 0, ;,

* @eeross har jarros ageogjo4 cbar` of must.̀ j.mr


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;>

: stmhhgoss. Ucoroharo, tcoy jaule mgtraeujo ` iogor`l

eyg`fmj faeol har tco ûf` ?88 rakat R:V. Bar`yof `ge

K`su R5V c`vo suiiostoe ` gow harful` wmtc mts guformj`l

salutmag har hmgemgi tco tr`dojtary ah ol`stmj rakat. [ojursmvo

lmgo`r prair`ffmgi w`s `pplmoe mg areor ta hmge tco laè ah

tco ol`stmj rakats wmtc tco jagsmeor`tmag ah tco twa

jagstr`mgts. @ iogor`l prair`ffmgi har fultm-lmgb rakats

c`s koog prosogtoe mg hull eot`ml. [osults hraf tco faeol

f`bmgi har tco favofogt ah twmg-damgtoe rakat ro-ofpc`smzoe tco mfpart`gjo ah tco twa jagstr`mgts. @

syfkalmj prair`f har tco oxp`gsmag ah eyg`fmj oqu`tmag ah

rakats wmtc ol`stmj damgts `ge lmgbs w`s `lsa eovolapoe R?V.

Ucms prair`f ms o`smly `pplmj`klo, euo ta ùtaf`tmj

smfplmhmj`tmags, guformj`l salutmags `ge ir`pcmj harf`ts,

wcmjc j`g ko usoe har fultm-lmgb `rfs. @ j`ljul`tmag

tojcgmquo c`s `lsa koog prosogtoe har akt`mgmgi f`xmfuf

eyg`fmj laè ah `g ol`stmj damgt f`gmpul`tar wmtc spojmhmj

`ttogtmag ta tco twa jagstr`mgts R8V. F`gy mfpart`gt h`jtars

mghluogjo f`xmfuf eyg`fmj laè j`rrymgi j`p`jmty ah

rakats, `fagi tcaso eyg`fmj rakat spojmhmj`tmags, fav`klo

p`rts lmfmt`tmags `ge hloxmkmlmty ah damgts `ro tco agos j`g ko

fogtmagoe. Zcmi`gi ]uo `ge Usa c`vo j`ljul`toe f`xmfufeyg`fmj laè har ` hloxmklo `rf wmtc ` roeuge`gt eoiroo ah

hrooeaf R9V. @ hmgmto olofogt faeol har ` eyg`fmj `rf w`s

usoe. Kartahh ot `l. `pplmoe jafputor faeolmgi `ge eyg`fmj

harfulò ta f`gmpul`tars wmtc ol`stmj damgts R3V. Meor &

Aziarog stuemoe tco mgvorso eyg`fmj jagtral ah `

f`gmpul`tar wmtc ol`stmj damgts R=V. @ jafputor faeolmgi

w`s `pplmoe ta scaw tco `jjur`jy ah tco rosults k`soe ag `

f`gmpul`tar wmtc : eoiroos ah hrooeaf wmtc ol`stmj damgts.

I`frr`èa & ]uc`r` cawovor akt`mgoe mgtorostmgi rosults

ky `pplymgi Gowtag-Oulor fotcae ta jafputor faeolmgi

har `g ol`stmj rakat wmtc twa `rfs `ge rovaluto damgt R0>V.

Fmtsm ot `l. c`vo salvoe tco mgvorso bmgof`tmjs praklof ah `

sp`tm`l roeuge`gt ar gagroeuge`gt f`gmpul`tar t`bmgi mgta`jjaugt `s jrmtorm` tco jallmsmag `vame`gjo `ge tco damgt

hugjtmag`lmty lmfmts R00V. @ smful`tmgi f`gmpul`tar-akst`jlo

faeol wmtc jagvox valufos mg areor ta `vame ` jallmsmag ms

usoe. Uco salutmag ah tco mgvorso bmgof`tmjs c`s koog

jageujtoe ky pog`lty hugjtmag fotcae. Uco eovolapoe

prajoeuro ms eofagstr`toe ky salvmgi ` sp`tm`l f`gmpul`tar

wmtc hmvo rovaluto damgts `ge har tco ahh-lmgo prair`ffmgi ah

tcms f`gmpul`tar, wcmjc usoe mg ` warbst`tmag har v`rmaus

f`guh`jturmgi prajossos. [oigmor ot `l. c`vo salvoe tco

mgvorso bmgof`tmjs ah `ll sorm`l, spojm`l ar iogor`l,

f`gmpul`tar wmtc ` gow guformj`l fotcae R0;V. Ucms

jagjopt w`s usoe wmtc ` gow harful`tmag ah tco praklof

`ssajm`toe ta o`jc laj`l hr`fo. Zzbaegy `pplmoe faeolmgi ah

bmgof`tmjs ah tco M[k-8 f`gmpul`tar `ge akt`mgoe oqu`tmagsah lmgbs `ge `jtu`tars bmgof`tmjs ah tco M[k-8 f`gmpul`tar

mg f`trmx harf R0:V. Mg èemtmag, salutmag ah oqu`tmags ah

lmgb bmgof`tmjs, `s woll `s harful`s damgtmgi lmgb `ge

`jtu`tar g`tur`l jaaremg`to ah tco f`gmpul`tar c`vo koog

prosogtoe. Y`gi `ge [`v`gm c`vo eohmgoe `g `liarmtcf har

tco eotorfmg`tmag ah f`xmfuf laè j`rrymgi j`p`jmty ah

fojc`gmj`l f`gmpul`tars R05V.

Mg tcms p`por, hmrst, wo eormvoe `ge smful`toe tco

f`gmpul`tars bmgof`tmjs oqu`tmags. Ucog, tco Lìr`gio's

fotcae ms usoe har eyg`fmj faeolmgi ah tco ol`stmj damgt

f`gmpul`tar. Uco rosults woro akt`mgoe har emhhorogt damgt

stmhhgoss jaohhmjmogts har ` imvog tr`dojtary. @ fotcae ta

akt`mg eyg`fmj laè j`p`jmty sukdojt ta tco `jjur`jy `ge

`jtu`tar jagstr`mgts ms eosjrmkoe. J`ljul`tmag `lsa w`s

prosogtoe har eyg`fmj laè j`rrymgi j`p`jmty har tco imvog

tr`dojtary. Uco rosults eopmjtoe tco mfpart`gjo ah tco twajagstr`mgts. @jjaremgi ta tco `jjur`jy `ge tr`jbmgi, tcoy

scaw wcmjc ago waule ko tco f`mg. Ky `g`lyzmgi rosults,

faeolmgi `ge smful`tmgi tco rakat f`mg jc`r`jtormstmjs ah

tco rakat c`vo koog `tt`mgoe. Eopogemgi ag tco apor`tmag's

roqumrofogts ar rakat's faeol, f`guh`jturors tost tco p`tc

`ge oge-ohhojtars praportmos. Ucoso tosts eopoge ag tco

apor`tmag's roqumrofogts `ge tco justafor h`varmto. Ycmlo

tco f`gmpul`tar w`s eosmigoe ta j`rry tco ùtafakmlo potral

t`gb, oge-ohhojtar's spooe, rakat's jafp`tmkmlmty wmtc tco

apor`tar's jagemtmag, `jjur`jy `ge tco f`xmfuf eyg`fmj

laè j`rrymgi j`p`jmty woro tco fast mfpart`gt `pplmj`klo

pamgts ah tco f`gmpul`tar. Ucoroharo, ky oxpormfogtmgi mg

v`rmaus tr`dojtarmos wmtc emhhorogt spooe `ge laè, wo c`vo`tt`mgoe f`gmpul`tar's jc`r`jtormstmjs `s `jjur`jy,

ropo`t`kmlmty `ge ELJJ.

;. Mgtraeujmgi tco f`gmpul`tarUcms f`gmpul`tar c`s : rovaluto damgts `ge ` fakmlo k`so.

Ucoso damgts f`bo ` :8> rat`tmag mg tco z-`xms `ge 0?

vortmj`l fatmag. Uco f`gmpul`tar `ge tco jaaremg`tos usoe mg

bmgof`tmjs faeolmgi `ro scawg mg tco Hmi. 0. Euo ta tco

r`ml's carmzagt`l fatmag `ge goilmimklo hloxmkmlmty, wo migaro

hloxmkmlmty ah tco r`ml.

Hmiuro (0)

Zjcof`tmj ah tco f`gmpul`tar


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;0

Hmiuro (;). Uco eosmigoe f`gmpul`tar har j`rrymgi ùtafakmlo potral

t`gb

Uco oge-ohhojtar's pasmtmag mg `ll avor p`tc scaule ko

eotorfmgoe mg areor ta jagtral f`gmpul`tar's hugjtmag `ge

hmge tco `jjur`jy mg tco hmg`l pamgts. _smgi `g ogjaeor mg

roiul`r mgtorv`ls, hmgemgi pasmtmag ah tco rat`tmag`l `xms ms

passmklo. _smgi pasmtmag ah `xms, wo j`g hmge spooe `ge

`jjolor`tmag. @htor ogtormgi mgta tco olojtrmj`l jmrjumt `ge

safo jagvoriogjo @, K `ge T pulsos mgta tco rat`tmag`l

armogt`tmag `ge rat`tmag`l agos mg tco HÎ@ jmrjumt, tco

mgharf`tmag, tcrauic tco ogjaeors, ogtor mgta tco

fmjrajagtrallors. Ucrauic ` fmjrajagtrallor, usmgi tco sorm`l

part `ge tco [Z;:; st`ge`re e`t` waule ko sogt ta `jafputor. Yo j`g jagtral tco ogjaeor's pasmtmag ky `g ag

lmgo jafputor prair`f. Mg o`jc mgtorv`l mg tco oxpormfogt,

wo j`g s`vo e`t` ah ogjaeor's pasmtmag. Ago j`g rovmow tco

r`w e`t`, usmgi F`tl`k sahtw`ro. @pplymgi bmgof`tmjs

oqu`tmags, tco oge-ohhojtar's pasmtmag jaule ko j`ljul`toe.

Cawovor, ta `tt`mg eosmroe ia`l tcoso p`rts `ro gooeoe.

Ucroo ogjaeors2 ta eotorfmgo tco tcroo f`dar damgt's

pasmtmag.

Mgtorfoem`to jmrjumt2 ta jagvort tco pulsos `ge

armogt`tmag.

Jafputor prair`ffmgi2 mg areor ta jagvort `ge

s`vo tco mgharf`tmag `ge e`t`.

Jafputor har rojomvmgi tco mgharf`tmag.Yo wmll mgtraeujo o`jc p`rt4

0. Ogjaeors4

Ogjaeors `s sogsmtmvo sogsars `ro usoe mg rat`tmag`l jc`gimgi

fo`surofogt. Ucoro ms ` jaeo ag o`jc ogjaeor ta eotorfmgo

tco `jjur`jy. Yo c`vo usoe OGK-?>>-:-0 ogjaeor mg tco

damgts ah tco f`gmpul`tar. Gufkor ?>> scaws tco gufkor ah

pulsos mg o`jc rovalutmag. Uco `jjur`jy ah tcms ogjaeor ms

>.9; eoiroo. Uco ogjaeor's valtìo v`rmos hraf ?X ta ;5X.

@jjaremgi ta tco mgtorfoem`to jmrjumt's valtìo, wo usoe ?X.

Hmiuro (:) ms `g ogjaeor mgst`lloe ag tco sojage damgt.

Hmiuro (:) Uco ogjaeor jaggojtmag ag damgts

;.

Mgtorfoem`to jmrjumt4

Mgmtm`lly r`w smig`ls ogtor mgta tco mgtorfoem`to jmrjumt `ge

tcrauic ` HÎ@ jmrjumt, usoe `s ` smig`l jagvortor, `ro

jagvortoe ta prajossar-hrmogely agos. Jafputor `ge tco

c`rew`ro jmrjumt `ro jaggojtoe, usmgi ` JAF0 part `ge

[Z;:; st`ge`re. Zogemgi r`to ms ;5>> kmt por sojage. Uco

eosmigoe mgtorfoem`to jmrjumt `ge tco f`guh`jturoe ago `ro

scawg mg Hmiuros 5 `ge ?.

Hmiuro (5) Uco f`guh`jturoe mgtorfoem`to jmrjumt

Hmiuro (?) Uco sjcof`tmj's mgtorfoem`to jmrjumt

:.

Jafputor prair`ffmgi4Yo c`vo usoe Xmsu`l K`smj prair`f ta rug jafputor

prair`f, wcmjc prajossos tco rojomvoe mgharf`tmag hraf tco

ogjaeors. Mg o`jc tmfo, ugtml `ll tcroo ogjaeor's e`t` `ro

rojomvoe, tco mgharf`tmag waule ko s`voe mg spojm`l `rr`y.

Uco emìr`f waule jc`gio wmtc rogowoe mgharf`tmag.

5.

Jafputor4


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;;

@ll tco mgharf`tmag, tcrauic ` sorm`l part Ga.0, waule ogtor

mgta tco jafputor `ge jafputor prair`f waule er`w

rohroscmgi e`t` emìr`f, wcmjc w`s emspl`yoe mg Hmiuro (8).

Hmiuro (8) Jafputor prair`ffmgi

@ jagtrallmgi pgouf`tmj systof, mgjluemgi pgouf`tmj

jylmgeor `ge ` rol`tmvo roiul`tar ms usoe ta k`l`gjo tco laè

mg `ll tco tmfo. Ucoro `ro safo jafp`jtoe pgouf`tmj

jylmgeors `s kr`bo ta lajb tco fojc`gmsf mg `gy pasmtmag.

:. F`gmpul`tar oriagafmj ̀ g`lyzmgi

F`gmpul`tars `ro eosmigoe ta f`bo systof sofm-ùtaf`toe`ge roeujo apor`tar's tmroegoss. Ucoroharo, wo scaule

jagtofpl`to oriagafmj prmgjmplos sujc `s k`l`gjmgi tco

warb's surh`jo comict `ge `gtcrapafotrmj, ogauic sp`jo har

favmgi, `jjossmkmlmty ah tco jagtrals `ge f`bmgi tco

ogvmragfogt l`kaur-hrmogely `ge è`ptmgi tco f`gmpul`tar

wmtc tco laè, `gtcrapafotrmj `ge tco h`jmlmtmos, hmttmgi bgaks

wmtc cuf`g c`ge2 mg eosmigmgi. Apor`tar's tr`mgmgi ms

mfpart`gt taa.

Mg emhhorogt f`gmpul`tar's p`rts, safo oriagafmj pamgts `ro

jagsmeoroe.

[`ml Zystof4 @lufmguf strujturo, c`gior systof

har suspogsmag, tralloy systof har hrmjtmagloss

favofogt, `ge `jjossarmos lmbo oge staps2 `llaw

ohhartloss favofogts ah laè mg ` smgilo lmgo.

K`l`gjor Zystof4 usmgi v`rmaus jagtral faeulos,

`llaws zora ir`vmty f`gmpul`tmag ah laè `ge tco

c`gelos irmppors ar t`jblos.

Dmk Kaaf Zystofs4 `llaw hlaar ar raah faugtoe

smgilo pamgt suppart har ` j`gtmlovoroe

tr`gspart`tmag ah tco laè.

F`gmpul`tar `rf4 tcoso `rtmjul`toe `rfs `llaw tco

laè ta ko f`gmpul`toe wmtc ` rmime fojc`gmj`l

suppart tc`t `llaws ahhsot ar j`gtmlovoroe apor`tmag

ta apor`to mg jagstr`mgoe sp`jos.

Ermvor Zystof4 mt ms jafpasoe ah ery `ge aml-hroo

jafprossoe, p`rt irmppors `ge v`juuf fojc`gmj`l

taals ta j`rry laès.5. Bmgof`tmjs faeolmgi ah fojc`gmj`l f`gmpul`tarMgmtm`lly, `ksaluto jaaremg`to `ge haur rol`tmvo jaaremg`tos

woro solojtoe. @s scawg mg Hmi. (0), Eog`vmt-C`rtogkori

p`r`fotors j`g ko eohmgoe har tco `kavo fojc`gmsf `s lmstoe

mg U`klo (0).

U`klo 0 -E-C p`r`fotors ah tco imvog f`gmpul`tar

me

m`

m

m Lmgb Gufkor

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0 ;

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L >; :

>; L ;

; 5

5 L : L >5 ?

@ Iogor`l tr`gsharf`tmag f`trmx j`g ko akt`mgoe `s hallaws4

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0>>

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0 5:;0;00 50 5

0 5:;0;00 50 5

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5Z L L L

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U (0)

Ycoro ;00;;00; jas,smg j s . Mt ms akvmaus tc`tmg tco `kavo f`trmx tco gufkor ah ugbgawgs ms iro`tor tc`g

tco gufkor ah oqu`tmags. @s ` rosult, `g oxtr` eoiroo ahhrooeaf j`g ko soog mg tco oqu`tmags. @giul`r volajmty fust

ko j`ljul`toe usmgi psouea mgvorso f`trmx `s kolaw4

X D D D D X U U 0 (;)

?. Zmful`tmag ah tco f`gmpul`tar wmtc F`tl`kMgmtm`lly, tco p`tc tr`vorsoe ky oge-ohhojtar w`s eotorfmgoe

mg :E sp`jo usmgi tco hallawmgi oqu`tmag (Hmi. 9).;

:>0?>3:?5;>;?>??>?3> t t T t ] t S (:)

Hmi.9- :E emìr`f ah tco `ssufoe tr`dojtary

Uco p`tcs tr`vorsoe ky tco oge ohhojtar `tt`mgoe ky

oxpormfogts `ge smful`tmag ky F`tl`k woro jafp`roe. Mg

smful`tmag, tco oqu`tmags akt`mgoe hraf mgvorso bmgof`tmjs

faeolmgi woro salvoe har 5 eoiroo ah hrooeaf.

8. Eyg`fmj faeolmgi ah f`gmpul`tar wmtc ol`stmj

damgtsHar tco jurrogt faeolmgi ah f`gmpul`tar `ge laè eyg`fmjs,

mt ms ossogtm`l ta eotorfmgo “f`xmfuf laè" har ` hloxmklo


5/10


;:

damgt rakat. Uco damgt eohlojtmag ar asjmll`tmag `t cmicor

spooe ms `ssufoe `s fujc `s ;?% ah tco oge-ohhojtar's

eohlojtmag. Uco ol`stmjmty `t tco t cm damgt j`g ko faeoloe `s `

lmgo`r tarsmag sprmgi c`vmgi tco sprmgi jagst`gt mb .

Xojtars ,,;0

L L L

m qqq , `s tco lmgb `gilos `ge

,,;0

D D D

m qqq `s tco ratar `gilos eohmgoe har tco fultm-

lmgb hloxmklo damgt f`gmpul`tar. @ Lìr`gim`g `ppra`jc w`s

usoe mg areor ta akt`mg tco eyg`fmj oqu`tmags ah fatmag har

tco f`gmpul`tar wmtc ol`stmj damgts, `s kolaw4

H qIqqqqJ qq E L L L L L L L

)(),()( (5)

>, D L L L L L L L L qq B qIqqqqJ qq E (?) D L D

r qq B q D (8)

Ycoro Lq E ms tco mgortm` f`trmx har tco `ssajm`toe rmimesystof, L L qqJ , ms tco vojtar ah e`fpmgi, Jarmalms `gejogtrmpot`l harjos, LqI ms tco vojtar ah harjos euo tair`vmty, gb b b emì B ,,, ;0 ms ` emìag`l f`trmx ahrostarmgi harjo jagst`gts faeolmgi tco damgt ol`stmjmty,

rgr r r D D D emì D ,,, ;0

ms emìag`l f`trmx roprosogtmgiratar mgortm`, `ge ms tco iogor`lmzoe harjo eolmvoroe ky tco

`jtu`tar. O`jc lmgb ms favoe ky `g `jtu`tar. Ucms fatmag ms

tr`gsharfoe ta tco goxt lmgb ky omtcor io`rs ar kolts kut mg

o`jc jagemtmag, tco ol`stmjmty ah tcoso damgts ms ro`sag ah

ol`stmj jauplmgi kotwoog `jtu`tar `ge tco lmgb. Ucms ol`stmj

jauplmgi koc`vos lmbo ` sprmgi `ge sujc faeolmgi ms scawg

mg Hmiuro (3).

Hmi.3-[at`tmag`l ol`stmj faeol ah damgts

Mg tcms faeol, Lmq roprosogts tco iogor`l jaaremg`tos ah

t cm lmgb, D

mq roprosogts tco iogor`l ja-aremg`tos ah ol`stmj

t cm damgt,

t mb roprosogts tarsmag`l stmhhgoss jaohhmjmogt ah tco

t cm damgt `ge

mu ms tco `pplmoe tarquo hraf t cm `jtu`tar ta

t cm

lmgb. @jjaremgi ta tcoso, tco eyg`fmj oqu`tmags ah tcof`gmpul`tar wmtc `g `ssufoe ol`stmj damgt woro akt`mgoe har

tco tralloy `ge tcroo f`dar damgts `s scawg kolaw4

H qIqq H qq O

qq EqJ q Kq @ L L L L L

L L L L L

5>55>;;>

;0>:>;>0>

(9)

>000050550

;;0;00:0;000

D L L L L

L L L L L L L

qq B qIqq H

qq O qq EqJ q Kq @

(3)

>;;;;;5;55;

;;;;0;:;;;0;

D L L L L

L L L L L L L

qq B C qIqq H

qq O qq EqJ q Kq @

(=)

>;;::;;:;0:

00:::;:0:

D L L L L L

L L L L L

qq B qq H qq O

qq EqJ q Kq @

(0>)

00000000

D L D

r qq B q D (00)

;;;;;;;;

D L D

r qq B q D (0;)

:::::::: D L D

r qq B q D (0:)

@ssufmgi ` imvog tr`dojtary, v`rm`tmag ah damgts `gilos `ro

eotorfmgoe hraf tco `kavo emhhorogtm`l oqu`tmags. Uco

ir`pcmj roprosogt`tmag ah tco salutmags wmtc emhhorogt

tarsmag`l stmhhgoss jaohhmjmogts `ro eopmjtoe mg Hmiuros (=) ta

(0;) har tralloy `ge damgts 0 ta :, rospojtmvoly. Damgt's tarquos

`ro scawg mg Hmiuro (0:).

> >.? 0 0.? ; ;.? : :.? 5>

0

;

:

5

?

8

9

3

=

U(soj)

S

( f )

[mime

B06?*0>5 ,B;63*0>5 ,B565*0>5

B06?>>> ,B;63>>> ,B565>>>

B06:?>> ,B;6?>>> ,B56:>>>

Hmi.=-Lmgo`r fatmag ah tralloy vorsus tmfo

> >.? 0 0.? ; ;.? : :.? 5-0.5

-0.;

-0

->.3

->.8

->.5

->.;

>

U(soj)

U O U @ 0 ( r ` e )

[mime

B06?*0>5 ,B;63*0>5 ,B565*0>5

B06?>>> ,B;63>>> ,B565>>>

B06:?>> ,B;6?>>> ,B56:>>>

Hmi.0>-@giul`r rospagso ah hmrst damgt vorsus tmfo

> >.? 0 0.? ; ;.? : :.? 5>

>.>;

>.>5

>.>8

>.>3

>.0

>.0;

>.05

>.08

>.03

>.;

U(soj)

U O U

@ ; ( r `

e )

[mime

B06?*0>5 ,B;63*0>5 ,B565*0>5

B06?>>> ,B;63>>> ,B565>>>

B06:?>> ,B;6?>>> ,B56:>>>

Hmi.00-@giul`r rospagso ah sojage damgt vorsus tmfo


6/10


;5

> >.? 0 0.? ; ;.? : :.? 5->.05

->.0;

->.0

->.>3

->.>8

->.>5

->.>;

>

U(soj)

U O U @ 5 ( r ̀ e )

[mime

B06?*0>5 ,B;63*0>5 ,B565*0>5

B06?>>> ,B;63>>> ,B565>>>

B06:?>> ,B;6?>>> ,B56:>>>

Hmi.0;-@giul`r rospagso ah tcmre damgt vorsus tmfo

> >.? 0 0.? ; ;.? : :.? 5-?

>

?

0>

0?

;>

;?

:>

:?

5>

U(soj)

Uarquo(G.f)

H (G)

tarquo0 (G.f)

tarquo; (G.f)

tarquo5 (G.f)

Hmi.0:-X`rm`tmag ah damgt tarquos wmtc tmfo

@s scawg mg tco f`gmpul`tar `gilo emìr`fs (Hmiuros = ta

0;), mt ms soog tc`t mgjro`soe tarsmag`l stmhhgoss jaohhmjmogt

eaos rosult mg damgt stmhhgoss, wcmjc mg turg roeujos vmkr`tmag

mg katc damgt `ge oge-ohhojtar p`tc. Har ` vory cmic

jaohhmjmogt, tco rosult scaws ` salutmag oqumv`logt ta ` purormime systof. Hloxmkmlmty ah damgt's ermvors `ge pawor

tr`gspart systof waule mgjlueo `t lo`st 3>% ah tco tat`l

hloxmkmlmty. Uco f`mg ro`sag ah tco f`gmpul`tar eovm`tmag ms

mts f`dar damgt's hloxmkmlmty. @s scawg mg Hmiuro (=),

goilojtmgi tco r`ml's hloxmkmlmty, tcoro ms ga emhhorogjo mg

emspl`jofogt har emhhorogt stmhhgoss. Cawovor, `jjaremgi ta

tco smful`toe tr`dojtary `ge f`gmpul`tar's strujturo, tco

sojage damgt ms faro sogsmtmvo ta tco stmhhgoss `ge hloxmkmlmty.

9. Uostmgi tco f`gmpul`tarYcmlo tco f`gmpul`tar ms eosmigoe ta j`rry tco ùtafakmlo

potral t`gb, oge-ohhojtar spooe, rakat's jafp`tmkmlmty wmtc

tco apor`tar's jagemtmag, `jjur`jy `ge tco f`xmfufeyg`fmj laè j`rrymgi j`p`jmty `ro tco fast mfpart`gt

`pplmj`klo jc`r`jtormstmjs ah tco f`gmpul`tar. F`xmfuf

orrar ah ` tr`dojtary, `jjur`jy `ge ropo`t`kmlmty `ro akt`mgoe

har tcms f`gmpul`tar.

@g`lyzmgi `ge faeolmgi tcms f`gmpul`tar, wo c`vo tostoe mt

v`rmaus tr`dojtarmos, emhhorogt laès, emhhorogt spooes mg tco

l`kar`tary. X`rmaus fotcaes usoe ta jagtral tco tost `ge

orrar j`ljul`tmag `ge survoymgi emhhorogt v`rm`tmags, scaw

tc`t hloxmkmlmty `ge f`gmpul`tar's mgmtm`l jagemtmag fust ko

jagtralloe. Cawovor, rosults `ro `jjopt`klo.

3. Damgt hloxmkmlmty tostmgi mg ` Jmrjul`r `ge Aklmquo

lmgo fatmagJagstr`mgmgi oge-ohhojtar ta favo ag ` purpasoe tr`dojtary,

wo j`g fo`suro damgt rat`tmag usmgi tco ogjaeors. Uco

rosults har twa-emfogsmag`l Jmrjul`r `ge tcroo-emfogsmag`l

Aklmquo lmgo wmtc mg wcmjc tco oge-ohhojtar prajooe tco

tr`dojtary mg ;? sojage, `ro scawg mg Hmiuros (05) ta (09).

Goxt, wo jafp`roe tco rosults wmtc tco tcoarotmj`l oqu`tmags

agos. Mt scaws tc`t tco rosults woro `jjopt`klo, `ltcauic,

`jjaremgi ta tco hloxmkmlmty, cuf`g's hlujtu`tmag orrar `ge tco

smfplmjmty ah tco jagtrallmgi pgouf`tmj jmrjumt, tcoro w`s

>.0?f orrar. Hmiuros (05), (08) scaw tco damgt `gilos mg

smful`tmag `ge oxpormfogt. Hmiuros (0?), (09) scaw tco

Jmrjul`r `ge Aklmquo lmgo ag wcmjc tco oge-ohhojtar favos.

Uco paso `jjur`jy `ge paso ropo`t`kmlmty `ro ropartoe

MZA=;3: st`ge`re.

> ? 0> 0? ;> ;?-;.?

-;

-0.?

-0

->.?

>

>.?

0

0.?

Umfo(s)

@ g i l o D a m g t s ( r ` e )

Hmi.05-Uco damgt `gilos mg smful`tmag `ge oxpormfogt ag tco Jmrjul`r

p`tc vs. tmfo

->.; ->.0? ->.0 ->.>? > >.>? >.0 >.0? >.; >.;? >.:>.5

>.?

>.8

>.9

>.3

>.=

0

0.0

pasmtmag S (f)

p a s m t m a g ]

( f )

Ucoary

Uost0

Uost;

Uost:

Uost5

Uost?

Uost8

Hmi.0?-;E emìr`f ah tco Jmrjul`r tr`dojtary mg v`rmaus tosts


7/10


;?

> ? 0> 0? ;> ;?-0.?

-0

->.?

>

>.?

0

0.?

Umfo(s)

@gilo

Damgts(rè)

Ucoary0

Uot`0

Ucoary;

Uot`;

Ucoary:

Uot`:

Hmi.08-Uco damgt `gilos mg smful`tmag `ge oxpormfogt ag tco Aklmquo

lmgo p`tc vs. tmfo

>.?>.8

>.9>.3

>.=

->.5->.;

>>.;

>.5>.8

-0.:

-0.;

-0.0

-0

->.=

->.3

pasmtmag S (f)pasmtmag ] (f)

pasmtmagT(f)

Ucoary

Uost

Hmi.09-:E emìr`f ah tco Aklmquo lmgo tr`dojtary mg smful`tmag `ge

oxpormfogt

3-0. âso @jjur`jy ah oge-ohhojtar (pasmtmagmgi

orrar) Uco f`gmpul`tar c`s koog iumeoe hraf ` eotorfmgoe pamgt ta

jaff`ge paso jjj x y z ,, har G tmfos `ge mts `jtu`l paso

d d d x y z ,, ms eotorfmgoe. Uco oqu`tmag (0;) j`ljul`tos tco

paso `jjur`jy ( ^ @̂ ).

)()()( ;;;jjj ^

z z y y x x @̂ (05)

Ycoro4

g

D

d

g

D

g

D

d d z

g z y

g y x

g x

00 0

00,

0 (0?)

x y z ,, ms k`ryjogtro `ge d d d x y z ,, rohor tatc

D `tt`mgoe

paso. Uco paso `jjur`jy ms scawg mg Hmiuro (03).

3-;. ̂ aso [opo`t`kmlmtyâso [opo`t`kmlmty rohor ta tco `jjur`jy ah `tt`mgoe paso `ge

jaff`ge paso, wcmjc c`s koog hauge mg ` eotorfmgoe paso

mg G tmfos. Har ` imvog tr`dojtary, paso ropo`t`kmlmty ( L [̂ )

rohor ta tco rèm`l ah spcoro mg tco jogtor ah jlustor `s kolaw4

g

d

d

L L

Lg

L

Z L [̂

0

0

:

(08)

Ycoro4

0

)(

)()()(

0

;

;;;

g

L L

Z

z z y y x x L

g

d

d

L

d d d d

(09)

âso ropo`t`kmlmty har tcms f`gmpul`tar ms scawg mg Hmiuro

(03).

>

>.>;

>.>5

>.>8

>.>3

>.0

>.0;

>.05

Jagst`gt Xolajmty & _gla è X`rmaus laès X`rmaus Xolajmty

Hmi.03-âso @jjur`jy `ge âso [opo`t`kmlmty ah tco Aklmquo lmgo

tr`dojtary

Hloxmkmlmty `ge mgmtm`l jagemtmags ah `rf `ro twa mfpart`gt

jrmtorm` c`vo koog jagtralloe mg tco oxpormfogts. Uco

`ksaluto orrar mg o`jc pamgt ah tco tr`dojtary jafputoe hraf

tco emhhorogjo kotwoog tco `jtu`l qu`gtmty `ge oxpormfogts.

F`xmfuf `ksaluto orrars f̀ xo har tco Aklmquo lmgo

tr`dojtary `ro scawg mg Hmiuro (0=). X`rm`tmag `ge Zuf

squ`ro orrar ZZO `ro twa jagtrallmgi jrmtorm` tc`t scaw tco

orrar mg o`jc tost, `s eotorfmgoe mg oqu`tmag (03), (0=).

t cb

x x F̀ xo f`x

(03)

b

t cb x xZZO

;

(0=)

;

b g

ZZO X`rm`tmag (;>)

Ycoro b g , b x , tcg rohor tco gufkor ah pamgts, fo`suroe

qu`gtmtmos, `ge tcoarotmj`l qu`gtmtmos. @ltcauic tco

oxpormfogt`l rosults `ro go`r ta tco tcoarotmj`l, `t tco oge ah

tco tr`dojtary, euo ta damgts hloxmkmlmty `ge f`guh`jturmgilaw qu`lmty ah tco f`gmpul`tar, tcoy emvorio. X`rmaus

jagtrallmgi ms scawg mg Hmiuro (;>).

=. Oge-ohhojtar's tr`dojtary mg v`rmaus spooes tostX`rmaus spooes `ge tcomr rol`tmag wmtc tco orrar `ro `g

mfpart`gt f`gmpul`tar's jc`r`jtormstmjs. Yo tostoe smx

emhhorogt spooes mg o`jc tr`dojtary `ge `tt`mgoe tco orrars.


8/10


;8

@jjaremgi ta Hmiuro (0=) orrars eme gat jc`gio mg `g

Aklmquo lmgo.

=-0. Oge-ohhojtar's tr`dojtary mg v`rmaus laès tostF`xmfuf laè j`rrymgi j`p`jmty ms `gatcor mfpart`gt

jc`r`jtormstmj ah ` f`gmpul`tar. Haur emhhorogt laès, 0>, 0;,

05, ;> Bi c`vo koog usoe mg tostmgi `ge hmgemgi tco orrar.

F`xmfuf `jjopt`klo laè eopoges ag tco ermht hraf tco

f`mg tr`dojtary. Mgjro`smgi laè waule mgjro`so tco orrar `gemg ` tr`dojtary tat`l orrar j`ljul`toe mg tco hmg`l pamgt ms

ug`jjopt`klo (Hmi. 0=).

0 ;: 5

? 8

>

>.>;

>.>5

>.>8

>.>3

>.0

>.0;

>.05

>.08

F`xmfuf @ksaluto Orrar

X̀ rmaus la ès Jagst̀ gt Xolajmty & _glaè X̀ rmaus volajmty

Hmi.0=-F`xmfuf @ksaluto Orrar ah tco Aklmquo lmgo tr`dojtary

0 ; : 5 ? 8

>

>.>>0

>.>>;

>.>>:

>.>>5

>.>>?

>.>>8

X r̀m̀ tmag fotcae

X`rmaus laès Jagst`gt Xolajmty & _glaè X̀ rmaus Xolajmty

Hmi.;>-X`rm`tmag @g`lyzmgi ah tco Aklmquo lmgo tr`dojtary

0>. ELJJ harful`tmag har ` imvog tr`dojtary@ hloxmklo f`gmpul`tar j`g ko jagsmeoroe ta j`rry `

f`xmfuf laè wcog tco p`tc `jjur`jy ms f`mgt`mgoe. Ucms

ms cmicly jrmtmj`l wcog eo`lmgi wmtc hloxmklo damgt rakats. Uco

p`tc `jjur`jy fust tcoroharo ko jagsmeoroe mg ELJJ

eotorfmg`tmag ky mfpasmgi tcms jagstr`mgt ta tco oge-

ohhojtar's eohlojtmag `s woll `s ta tco `jtu`tar tarquo, wcmjc

ms ahtog mfpasoe `lago har rmime f`gmpul`tars. H`mlmgi tcms,

`g oxjossmvo eovm`tmag f`yko jùsoe euo ta oge-ohhojtar's

eohlojtmag har ` imvog tr`dojtary, ovog tcauic tco damgt

tarquo jagstr`mgt ms gat vmal`toe.

0>-0. Damgt `jtu`tar tarquo jagstr`mgtK`soe ag tco eohmgmtmag ah typmj`l tarquo-spooe

jc`r`jtormstmjs ah EJ fatars, tco damgt `jtu`tar tarquo

jagst`gt w`s harful`toe `s hallaws4

qjj_ ̀llaw

;0

(;0)

qjj_ ̀llaw

;0

(;;)

Ycoro >;0 /, s s b b , s ms tco st`ll tarquo, > ms

f`xmfuf ga laè spooe ah tco fatar, `ge `

u `ge `

u `ro

tco uppor `ge lawor kauges ah tco `llaw`klo tarquo. Uco loht

c`ge smeo ah katc oqu`tmags ;0 `ge ;; imvos tco uppor `ge

lawor `llaw`klo tarquos ( )()( & ``

_ _ ) ah `gy `jtu`tars. @g

oxpormfogt`l f`ss ( of ), loss tc`g f`xmfuf ostmf`toe laè,

ms tcog usoe mg areor ta j`ljul`too

har `gy t cm pamgt `lagi

tco imvog tr`dojtary. Uco `llaw`klo tarquo lmfmts ( )()( & mm

)

j`g tcog ko j`ljul`toe usmgi tco uppor `ge lawor `llaw`klo

tarquos ah tco `jtu`tars `ge mo )( , `jjaremgi ta hallawmgi

oqu`tmags4

mom`m

_

(;:)

mom`m _

(;5)

Uco f`xmfuf `llaw`klo tarquo ah `gy damgtm`)( j`g tcog

ko j`ljul`toe `s hallaws4

mmm`

,f̀ x (;?)

Mg areor ta eotorfmgo tco f`xmfuf `llaw`klo laè, ky

jagsmeormgi tco `jtu`tar jagstr`mgt, mt ms ossogtm`l ta eohmgo `

laè jaohhmjmogt d`

j )( har `gy pamgt `lagi tco imvog

tr`dojtary `s hallaws

gmj

go

m`

d` ,,;,0,f`xf`x

fmg

(;8)

Ycorog

roprosogt tco ga-laè tarquo.

0>-;. @jjur`jy jagstr`mgt harful`tmag har tco oge-

ohhojtarUco eovm`tmag ah tco oge-ohhojtar j`g ko rol`toe ta emhhorogt

eyg`fmj `ge/ar st`tmj h`jtars. @s ` rosult, tco eyg`fmj laè

j`p`jmty ms tcoroharo emhhorogt har `gy pamgt `lagi ` suppasoe

tr`dojtary. Jagsoquogtly, har eotorfmgmgi ah f`xmfuf

`llaw`klo ELJJ, ky jagsmeormgi tco `jjur`jy jagstr`mgt,

tco p`tc ms emsjrmtmzoe mgta f sop`r`to pamgts. Uco eovm`tmag

ah oge-ohhojtar hraf ` eosmroe tr`dojtary ms tcog j`ljul`toe

har o`jc pamgt, wcoro dg)( roprosogts ga-laè eohlojtmag

`ge do)( roprosogts eohlojtmag ugeor oxpormfogt`l laè.

Uco qu`gtmty `ge emrojtmag ah eovm`tmag euo ta tco

oxpormfogt`l f`ss )(o

f har ` solojtoe pamgt d `lagi tco

imvog tr`dojtary j`g ko soog mg Hmi. (;0). @ jukmj`l kauge`ry

ah rèmus p

[ `s tco oge-ohhojtar's eohlojtmag jagstr`mgt j`g

ko usoe wmtc tco jogtor ah tco juko pasmtmagoe ag tco

solojtoe pamgt ag tco imvog tr`dojtary. do)( ms ` p`rt ah

p [


9/10


;9

tc`t scaws caw fujc laè j`g ko j`rrmoe wmtcaut migarmgi

tco `jjur`jy jagstr`mgt `t pamgt d. Uco emhhorogjo kotwoog

`llaw`klo eovm`tmag ( p

[ ) `ge tco `faugt ah eovm`tmag euo ta

oxpormfogt`l f`ss do)( j`g ko jagsmeoroe `s tco

rof`mgmgi `llaw`klo eovm`tmag hraf tco imvog tr`dojtary tc`t

j`g ko talor`toe. @s oxpl`mgoe provmausly, tcoro ms `

gojossmty ta eohmgo ` gow laè jaohhmjmogt d p

j )( har o`jc

pamgt `lagi tco imvog tr`dojtary `s hallaws4

f d

[j

go

do p

d p ,,;,0,f`xf`x

fmg

(;9)

Ycorog

roprosogts ga-laè eovm`tmag ah tco oge-ohhojtar

hraf tco imvog tr`dojtary.

Hmi.;0-Uco jukmj`l kauge`ry ag oge-ohhojtar's eohlojtmag

00. Eotorfmgmgi tco f`xmfuf eyg`fmj laè

j`rrymgi j`p`jmtyMg areor ta ogsuro tc`t katc tco `jjur`jy `ge tco `jtu`tar

tarquo lmfmts jagstr`mgts `ro s`tmshmoe har `ll emsjrotmzoe pamgt

`lagi tco imvog tr`dojtary, ` iogor`l laè jaohhmjmogt j j`g ko eohmgoe `s hallaws4

f djjj d` d p

,,;,0},)(,)fmg{( (;3)

@s ` rosult, tco f`xmfuf `llaw`klo f`ssla`

f j`g ko

j`ljul`toe `s hallaws4

olaè jff (;=)

Ycoroof ms oxpormfogt`l f`ss `ge fafogt ah mgortm`. Uco

`jtu`tar j`g hallaw tco tr`dojtary wmtcmg tco `llaw`klo oge-

ohhojtar's eohlojtmag, ugloss tco `jtu`l f`ss `ge tco fafogt

ah mgortm` ah tco laè `ro faro tc`g f`xmfuf j`ljul`toe

laè. @pplymgi 5-`tfaspcoro prossuro ag tcms pgouf`tmj

systof ah tco f`gmpul`tar, wcmlo tco `jjur`jy mg tco oge-ohhojtar c`s koog `ssufoe >.0? f, `llaw`klo eyg`fmj laè

waule ko 0> Bi. @jjaremgi ta tco fmgmf`l smzo ah tcms

f`gmpul`tar, tcms laè ms jagsmeor`klo.

0;. EmsjussmagUa eosmig ` rakat, ago scaule jagsmeor bmgof`tmjs `ge

eyg`fmj smtu`tmags. Mt gooes ta salvo jafplmj`toe lagi

l`stmgi oqu`tmags. Govortcoloss, ga oxpormfogt jaule ko

`pplmoe ugtml ` pratatypo c`s koog jagstrujtoe ovog tco

iogumgo ogimgoors uso tco smful`tmag sahtw`ro `ge tco

pratatypo. Mg tcms stuey, wo c`vo eosmigoe ` f`gmpul`tar har

j`rrymgi ùtafakmlo potral t`gb. _smgi smful`tmag `ge

jaemgi mg jafforjm`l sahtw`ro, wo c`vo hauge tco

f`gmpul`tar jc`r`jtormstmj `htor bmgof`tmjs `ge eyg`fmj

stueymgi. Har ox`fplo, wo c`vo stuemoe f`gmpul`tar

warbsp`jo, `jjur`jy mg emhhorogt tr`dojtarmos. L`kar`tarytosts mg emhhorogt tr`dojtarmos woro `jjafplmscoe `ge tco

rosults woro jafp`roe wmtc tco tcoary `ge smful`tmag. @s

scawg mg Hmiuros (=) ta (0;) damgts hloxmkmlmty `ge qu`lmty

f`guh`jturmgi c`vo sukst`gtm`l ohhojts mg tco rosults.

@jjaremgi ta Aklmquo lmgo tost, jagtrallmgi v`rm`tmag waule

colp ta roeujo orrars `ge jagtrallmgi orrars saurjos. Mg

èemtmag, cuf`g's hlujtu`tmag orrar `ge damgts hloxmkmlmty `ro

ohhojtmvo h`jtars ag f`gmpul`tar `jjur`jy. F`xmfuf

eyg`fmj laè j`rrymgi j`p`jmty waule ko `tt`mgoe mg

oxpormogjo mg emhhorogt tr`dojtarmos wmtc emhhorogt laès `ge

^ [ qu`gtmty. Ycmlo mg coro ^ [ 6>.0? f, tco f`xmfuf

laè ms 0? Bi mg jafp`rmsag wmtc 0> Bi har smful`tmagf`xmfuf laè wmtc tco s`fo ^ [ . @jjaremgi ta [E's potral

t`gb womict, 0> Bi, tco rosult ms `jjopt`klo. Mfpravmgi safo

eot`mls `ge jagsmeormgi justafor's prmarmtmos tco f`gmpul`tar

waule ko roèy har mgeustrm`l usìo.

0:. JagjlusmagUco f`gmpul`tar ms eosmigoe, smful`toe `ge tostoe mg

emhhorogt tr`dojtarmos `ge paso. Ycmlo tco f`gmpul`tar ms

eosmigoe ta j`rry tco ùtafakmlo potral t`gb, apor`tar's

h`jmlmty, oge-ohhojtar spooe, `jjur`jy `ge ELJJ `ro

jagsmeoroe tco f`mg jrmtorm`. Uco f`mg orrar saurjos `ro

cuf`g's hlujtu`tmag, gamso, fo`surofogt taals otj. `ltcauic

tco oxpormfogt`l rosults `ro go`r tco tcoarotmj`l agos, `t tcooge ah tr`dojtary, `jjaremgi ta damgt hloxmkmlmty `ge gag-

`jjur`to f`guh`jturmgi tcoy emvorio, `ge tco orrar mgtorv`l

ms `kaut ?-0> porjogt. Pu`lmty f`guh`jturmgi, f`gmpul`tar

jagemtmags, è`pt`klo warbmgi sp`jo `ge aptmfmzmgi tco

pgouf`tmj systof eosmig `ro f`mg jrmtorm` mg f`gmpul`tar

f`guh`jturmgi. @jjaremgi ta f`gmpul`tar usìo, f`xmfuf

orrar mg o`jc tr`dojtary, paso `jjur`jy `ge paso ropo`t`kmlmty

`ro mts mfpart`gt jc`r`jtormstmjs. [oi`remgi orrar saurjos, `s

cuf`g's hlujtu`tmag mg ùtafakmlo potral t`gb j`rrymgi,

eovm`tmag hraf eosmroe p`tc p`rtmjul`rly mg emrojt @giul`rrat`tmag ah tco damgts, ms `jjopt`klo.

[ohorogjosR0V F. C. Bar`yof, `ge I`rmklu, “@g`lysms ah Ycooloe

Fakmlo Hloxmklo F`gmpul`tar Eyg`fmj Fatmags Ymtc

F`xmfuf Laè J`rrymgi J`p`jmtmos‖, [akatmjs `ge

@utagafaus Zystofs, Xal. 53, Ga. ;-:, pp. 8:-98, ;>>5.

R;V F. Ucaf`s, C. J. ]u`g-Jcau `ge E. Uos`r, "Aptmf`l

`jtu`tar smzmgi har rakatmj f`gmpul`tars k`soe ag laj`l

eyg`fmj jrmtorm`", @ZFO Daurg`l ah Fojc`gmsfs,


10/10


;3

Ur`gs`jtmags `ge @utaf`tmag Eosmig, 0>9 (0=3?), p08:-

08=.

R:V C. ]. Bmf, E. @. Ztromt, "Jaghmiur`tmag eopogeogt

stmhhgoss ah tco puf` ?8> f`gmpul`tar4 @g`lytmj`l `ge

oxpormfogt`l rosults", Fojc. F`jc tcoary :>-3 (0==?),

p0;8=-0;99.

R5V F. C. Bar`yof, @. K`su, "Zyfkalmj eormv`tmag ah

eyg`fmj oqu`tmags ah fatmag har ol`stmj f`gmpul`tar",

Daurg`l ah jafput`tmag`l Uojc. `ge `pplmj`tmags, JU@(0==?), p?8-8=.

R?V F. C. Bar`yof, @. K`su, "Harful`tmag `ge guformj`l

salutmag ah ol`stmj rakat eyg`fmj fatmag wmtc f`xmfuf

laè j`rrymgi j`p`jmtmos", [akatmj`, 0; (0==5), p;?:-;80.

R8V F. C. Bar`yof, C. I`rmklu `ge, @. K`su “Eyg`fmj

Laè J`rrymgi J`p`jmty ah Fakmlo K`so Hloxmklo Damgt

F`gmpul`tars,“ Mgtorg`tmag`l Daurg`l ah @FU, Xal. ;?, Ga.

0-;, pp. 8;-9>, ;>>?.

R9V Zc. ]uo, Z. B. Usa, "F`xmfuf eyg`fmj p`ylaè

tr`dojtary har hloxmklo rakat f`gmpul`tars wmtc bmgof`tmj

roeuge`gjy", Fojc`gmsf `ge F`jcmgo Ucoary, :8 (;>>0),

p93?- 3>>.

R3V Z. @. Kartahh, D. ]. Cugi, `ge F. Y. Zpagi, "@emsjroto-tmfo aksorvor har hloxmklo damgt f`gmpul`tars", ^raj.

MOOO Mgt. Jagh [akatmjs `ge @utaf`tmag, 0=3=, p ;>93-

;>3;.

R=V Z. Bof`l Meor, F. Bof`l Aziarog, “Ur`dojtary tr`jbmgi

jagtral ah hloxmklo damgt rakats, Jafputors `ge strujturos‖,

98 (;>>>), p9?9-98:.

R0>V X. A. I`f`rr`èa, O. @. A. ]uc`r`, “Eyg`fmjs

faeolmgi `ge smful`tmag ah hloxmklo rakatmj f`gmpul`tar‖,

[akatmj`, (0===), Xal. 09, p.?;:-?;3.

R00V Z. Fmtsm, B. E. Kauz`bms, I. F`gsaur, "Aptmfmz`tmag ah

rakat lmgbs fatmag mg mgvorso bmgof`tmjs salutmag

jagsmeormgi jallmsmag `vame`gjo `ge damgt lmfmts", Fo`jc.

F`jc. Ucoary :> (?) (0==?), p8?:-88:.R0;V Z. [oigmor, H. K. Auoteau, ^. Kmeùe, "Emstrmkutoe

fotcae har mgvorso bmgof`tmjs ah `ll sorm`l f`gmpul`tars",

Fojc. F`jc. Ucoary :; (9) (0==9), p3??- 389.

R0:V U. Zzbaegy, "Faeollmgi ah bmgof`tmjs ah tco M[k-8

f`gmpul`tar", Jafputors f`tc. @ppl4 j ;= (=) (0==?), p99-

=5.

R05V L. U. Y`gi `ge K. [`v`gm, "Eyg`fmj laè j`rrymgi

j`p`jmty ah fojc`gmj`l f`gmpul`tars ‚ ̂ `rt M4 ^raklof

harful`tmag", Ur`gs`jtmags ah @ZFO, Daurg`l ah Eyg`fmj

Zystof, Fo`surofogt `ge Jagtral, 00>(0=33), p58-?;.

R0?V Lo`g Ol`dp`c, "Zmful`tmag ah g-[ pl`gor f`gmpul`tars

smful`tmag", ^r`jtmjo `ge Ucoary 8 (0==3), p:>?-:;0.

Modeling and Optimal Control of a 3-Axis Motion Simulator

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