Otomatik Kontrol Sistemleri - Sakarya Üniversitesi 2012 Vize Soruları

892019 Otomatik Kontrol Sistemleri - Sakarya Uumlniversitesi 2012 Vize Soruları

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Qgt)

Q2)

Q1)

o R

o I

o m

o k (t)

nm 6sbt

G

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Z y

]ucnrľjn nine cdetrdiiugrave JA-fncmek snyľsni mŔikfam `ugraveagrave cuvvktikejmrmam C vk hľz yumliagravekr Cv vkrmifkctkjmrnyrľc-znfne snyľsni hľz cdetrdiugrave `kragravekcikŔtmrmifkc mstkefkctkjmr (_mscdz sugravertugraveefk B 6 lt)

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983138) 983121983149983153983162983147983142983147 983150983149983162 983162983078983146983140983142983147983141983149 983146983147983141983139983145983147983142983145983147983154983149 983165983150983159ľ983141ľ983159 983112983147983154 983138983149983154 983138983145983140983139 983162983154983150983141983153983151983147983154 983151983140983141983139983153983149983165983140983141983145983150983154ľ983141ľ 983147983145983146983147 983147983146983147983154983147983139 983139983150983164983150983145ľ 983264983147983167983154983149983142

983139983140983141983162983154983140983145 983138983145983140983139 983146983149983165983150983136983154983150983142ľ983141ľ 983264983149983159983149983141983149983159

Q)

gtgt

gtgt

gt( ) ( ) ( )

( gt) m

fef c

mf z zm

j x cZ z z X z z

f jz

minus

minus

minus 66

6 minus minus

infin gt

gtgt

gt( ) ( ) ( )

( gt)m

fef

mf sZ m s s

j z X z s s X s

f js z k

minus

minus

6 6

6 minus

minus minus infin

ynejn vkrmike smstkf magraveme

n)

Z6ltgts

b) ( ) ( )t t r u6 vk Cj 6gt magraveme3 m) a(c) 6 a(cZ) 6 4

mm) ( ) ( )imfc

c a ararr∕

∕ 6 vkgt

( ) ( )( gt)imf z

z za A rarr

∕ 6 minus monjkikrmem hksnpinyľeľz

a) a(∕) 6 lt8 dinbmifksm magraveme Cj 6 4

Qugraverk gtltltjc983106983150Ŕ983150983154ľ983145983150983154991279

983114983140983264983114983154983118983165983144983150983141 983263983127983114983115983110ļ983122 983078 983133983154983146983114983140983264983114983154ļ983154983151983150983141 983133983118983127983117983105983117

ynejn vkrmike smstkf magraveme

m) jmenfmc jkecikfikrm ynzľeľz

mm)

]nejn vkrmike cdetrdi smstkfmejk983150) 983106983140983159983163983137983163 983136983149983154983149Ŕ983149 983114(983153) 983149983264983149983141 983264ľ983139ľŔ 983137983147983167983150983138ľ983141ľ 983147983145983146983147

983147983146983149983141983149983159

983138) ( ) gtgt

ss

6

+ ( ) gt H s 6 983167983147 ( ) gt J s

s6 983140983145983146983163Ĕ983163983141983150

983136983295983154983147 983138983140983159983163983137983163 983136983149983154983149Ŕ 983114(983153) 983149983264983149983141 983137983147983167983150983138ľ983141 983153ľ983151ľ983154

983140983145983150983138983149983145983142983147983153983149 983149983264983149983141 983107991261983165ľ 983144983147983153983150983164983145983150983165ľ983141ľ983159 983130983094lt2



2

Agt

n)

gtltgtltgt gt

( )lt

gt

lt ltgt lt

gt lt=ltsZ Z s

z W s

z z zs

s z k z k zminus6 6minus

6 6

+

+ 6 6

+ minus minus minus

b) ( ) ( )lt

lt lt=ltj

j

z zC

A RC

z

z z6

+ minus ( ) ( ) ( )

gtt t zr u R

z

zrArr6 6

minus magraveme

2

( )lt

( gt)(gt lt=lt) zA

z

z z6

minus minus

22

gt gt

ltlt1

gt

( )

ltlt111gt( gt) ( ltlt1)

lt=lt ( gt)( ltlt1)( gt)( )gt

c c

z

z

c a

z z

z z z z z z

z z

minus minus

6

6

6 minus + minusminus minus

minus minus

( )lt111 lt111ltlt1

ltlt1 lt81= ltlt ltlt1lt1=0 (ltlt1 gt)

c c c a 6 + 6 minus

minus

mm)2 2

gt gt( ) ( )

lt ltgtimf( gt) imf( gt) lt8

( gt)(gt lt=lt) (gtgt lt=lt) z z

za z

z A z

z zrarr rarr

∕ 6 minus 6 minus 6 6minus minus minus

( ) ( )imf imf(lt81= ltltltlt1 ) lt81=c

c c c a a

rarr∕ rarr∕

∕ 6 6 minus 6

a) ( )lt

lt lt=lt gtj

j

zC

A C

z z

z z z6

+ minus minus

2

gt( ) ( )

ltimf( gt)

lt lt=ltj

zj

zC

aC

z z A

z zrarr

∕ 6 minus 6+ minus

ltlt8

gt lt lt=ltj

j

C

C 6 rArr

+ minus lt0 lt ltj j

C C + 6 rArr 0j C 6

A2) m- _krmike smstkfjkCgt vk Bgt kikfneinrľ ckejm nrninrľejn skrm bnĔiľjľr nyeľ ykr jkĔmŔtmrfk x(t)rdquoyk snhmptmrikr

Nyeľ Ŕkcmijk C2 B2 vk F kikfneinrľ jn ckejm nrninrľejn skrm bnĔiľjľr nyeľ ykr jkĔmŔtmrfk xgt(t)rdquoyksnhmptmrikr

Qkrm bnĔiľ fkcnemc kikfneinrn ktcm kjke cuvvkt kikfneinrľe cuvvktikrm tdpinfnjľr

mm- Cgt Bgt kikfneinrľ C2 B2 F fkcnemc kikfneinrľ mik pnrniki bnĔiľjľr nrniki bnĔiľ fkcnemckikfneinrn nyeľ cuvvkt ktcm kjkr

m-) vk mm-) jk vkrmike bmi`mikr ľŔľĔľ nitľejn nŔnĔľjncm monjkikr ynzľiľr

Cgt vk Bgt kikfneinrľen ktcm kjke cuvvkt7 gt gt

( )c Bt O O O 6 +

jmr

( )( )

( ) ( )gt

ltltlt=lt

lt lt lt=ltgtlt=lt

j j j

j j j

z z

z z

C C C A

R C C C

z

z z z z z

z

6 6

+

minus6

+ minus+

minus



1

C2 B2 vk F kikfneinrľen ktcm kjke cuvvkt7 2 2( )

f c Bt O O O O 6 + +

jmr

( ) ( )gt

gt gt gt

( ) ( )( ) ( ) ( )

t t t t t

j x xO c x x B

jt

minus

minus6 + ( ) ( )gt gt gt gt( ) ( ) ( ) ( ) ( )s s s s sO c X X sB X X minus minusrArr 6 +

2 gt gt2 2 gt2

( ) ( )( ) ( )

t t t t

j x jxO f B c xjt jt

6 + +2

gt 2 gt 2 gt( ) ( ) ( ) ( )s s s sO s fX sB X c X rArr 6 + + gt 22 2

( ) ( )( ) 6

( )

s ss

O O X s f sB c N s

rArr 6+ +

gt gt gt gt gt gt( ) ( ) ( ) ( ) ( )s s s s sO c X c X sB X sB X minus minus 66 + gt gt gt gt

( ) ( )( ) ( )

( ) ( )

s ss s

O O c X c sB X sB

N s N sminus minus+

gt gtgt gt( ) ( ) ( )gt

( ) ( )s s s

c sBO c X sB X

N s N srArr

+ + 6 +

gt gt

gt gt

( )

( )

gt( ) ( )s

s

c sB

N s N s X

O sB c

+ +

6 6

+ ( )gt gt

gt gt

( )

( )

N s sB c

N s sB c

+ +

+

( )

( )( )

22 gt 2 gt

22 2 gt gt

( )

( )

s

s

s f s B B c c X

O s f sB c sB c

+ + + +6

+ + +

A1 n) Nyrľc-znfne snyľsni cdetrdi ynpľinanĔľejne sugraverkcim znfne mŔnrktikr Nenid` Jmgmtni JyumleugraveŔ tugraverugraveaugrave (NJA) mik Z yumlrekcikfk znfne nrniľcinrľ mik yumlrekcikemr vk snyľsnin jyumleugraveŔtugraverugraveiugraver Cdetrdi curniľ snyľsnimŔikfam mik mŔikemr vk snyľsni cdetrdi mŔnrktm ugraverktmimr Bu snyľsni cdetrdi mŔnrktm nyeľ yumlrekcikfk znfnenrniľĔľejn Jm`mtni Nenid` JyumleugraveŔugravetrugraveaugrave (JNA) mik tkcrnr sugraverkcim znfne mŔnrktk jyumleugraveŔtugraverugraveikrkccuvvktikejmrmam ugravezkrmejke smstkf `mrmŔmek uy`uineľr Nyrľc-znfne snyľsni prkesmp cdetrdi jkvrksm nŔnĔľjn

vkrmifmŔtmr

b) szligeak Nine Cdetrdiiugrave JA-fncmekyk nmt jkecikfikr ynzľiľr

gt-)( )

( ) ( ) o

o o o o

jm t k t R m t I

jt 6 +

2-) ( ) ( )k m o Z t C m t 6 kikctrmcm fdfket

1-)( )

( )f y

jw t Z t G Z

jt 6 + fkcnemc fdfket

-) ( ) ( )k f

Z t Z t 6 (sugraverkcim rkgmfjk) edt7 rdtdrue snbmt ncľf cnyen Ĕ ľ mik bksikejm Ĕ m cnbui

kjmijm Ĕ mejke zľt kfc syumlz cdeusu difnz



t- jdfkemejk kijk kjmike gt- jkecikfikrmeme Inpinak jyumleugrave Ŕugravefikrm n Ŕn Ĕ ľjn vkrmifm Ŕtmr

gt-)( )

( ) ( ) ( ) ( ) o

o o o o o o

o o

K s K s R M s sI M s M s

sI R6 + rArr 6

+

2-) ( ) ( )k m o Z s C M s6

1-)( ) ( )

( ) ( ) ( ) ( ) f y

f y

Z s Z sZ s sG s Z s s

sG

minus6 ℯ + rArr ℯ 6

-) ( ) ( )k f

Z s Z s6 (sugraverkcim rkgmfjk)

n) _krmike cdetrdi bidc jmyn`rnfľ R(s)6lt magraveme nŔnĔľjn vkrmijmĔm `mbm ykemjke jugravezkeikemr

b) ]ucnrľjn kijk kjmike cdetrdi bidc jmyn`rnf ynrjľfľ mik J(s) `mrmŔ magraveme A(z) kijk kjmimr

gt ( ) ( ) ( ) X s J s ] s6 minus

( )2 ( ) ( ) ( ) ( ) ( ) () )( A s J s s ] sA s X s s m k r s s jm6 minus6

1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) W s A s H s msk W s J s s H s ] s s H s jmr 6 6 minus

vk ( ) ( ) ( ) ( ) W s JH s ] r s H s jm6 minus

( ) ( ) ( ) ( ) ( ) ( ) ] s CJ] s CW s H s C] s H ms msk j r 66 minus

Kijk kjmike monjk( )] s magraveme jugravezkeikemr

( )( )

gt ( )

CJH s] s

CH s6

+ vk 2 ediu jkecikfjk ykrmek cdyuiur

( )( ) ( ) ( ) ( )

gt ( )

CJH sA s J s s s

CH s

6 minus+

yľijľzineľr msk

( )( ) ( ) ( )

gt ( )

CJH sA s J s s

CH s6 minus

+ vk

( )( ) ( ) ( )

gt ( )

CJH zA z J z z

CH z6 minus

+ dinrnc ynzľiľr



983138983085 983130983094lt2 983153983141 983167983147 983144983147983154 983138983149983154 983138983149983145983147Ŕ983147983141 983149983264983149983141 983159983078983146983295983141983289Ŕ983289983142983145983147983154983149 983144983147983153983150983164983145983150983141ľ983154

2

gt lt222gt

( gt) gt00= lt00( ) ( )

8)

8( J z W J

z W

s s z s

zs

6 6

+ minus + 6

2

lt( ) ( ) ( )

222gt

( gt) gt00= lt00 8(

8)

C z W C

sCJH z W CJ s s H

zs

s z

6 6

+ minus + 6

( gt) lt( ) ( 00 8) ) 8( C z W C sCH z W C s H s z

6 6 minus

6 +

gt

( gt) lt0088( ) ( )

s W W

z z s

z

6 6

minus 6

+

2

2

lt222gtlt222gt gt00= lt0088

gt00= lt0088 lt0088gtlt00

( )( ) ( ) ( )

gt ( )88

CJH zA z

zC

z z z z z z z z

C

J z zC

z

H z

minus +minus

minus + minus+

+

minus

6 minus 6

2

2

2

lt222gt

lt222gt gt00= lt0088gt00= lt0088 lt( ) 0088A z

zC

z z z z z z Cz

minus +minusminus + minus +

6

983105(983159) 983149983151983150983146983147983153983149 983142983147983167983137983163983162 983162983140983164983140983145983140983143983149 983149983145983147 983106983140983159983163983137983163 983136983149983154983149Ŕ983149 983107 983139983150983159983150983141983137ľ 983149983145983147 983264ľ983139ľŔ983162983150 983153ľ983151ľ983154983145983150983141983150983142983150983159 C 6 ∕ 983140983145983153983150 983146983150983144983149 ( ) ltA ∕ 6

983140983145983142983150983159



2

Agt

n)

gtltgtltgt gt

( )lt

gt

lt ltgt lt

gt lt=ltsZ Z s

z W s

z z zs

s z k z k zminus6 6minus

6 6

+

+ 6 6

+ minus minus minus

b) ( ) ( )lt

lt lt=ltj

j

z zC

A RC

z

z z6

+ minus ( ) ( ) ( )

gtt t zr u R

z

zrArr6 6

minus magraveme

2

( )lt

( gt)(gt lt=lt) zA

z

z z6

minus minus

22

gt gt

ltlt1

gt

( )

ltlt111gt( gt) ( ltlt1)

lt=lt ( gt)( ltlt1)( gt)( )gt

c c

z

z

c a

z z

z z z z z z

z z

minus minus

6

6

6 minus + minusminus minus

minus minus

( )lt111 lt111ltlt1

ltlt1 lt81= ltlt ltlt1lt1=0 (ltlt1 gt)

c c c a 6 + 6 minus

minus

mm)2 2

gt gt( ) ( )

lt ltgtimf( gt) imf( gt) lt8

( gt)(gt lt=lt) (gtgt lt=lt) z z

za z

z A z

z zrarr rarr

∕ 6 minus 6 minus 6 6minus minus minus

( ) ( )imf imf(lt81= ltltltlt1 ) lt81=c

c c c a a

rarr∕ rarr∕

∕ 6 6 minus 6

a) ( )lt

lt lt=lt gtj

j

zC

A C

z z

z z z6

+ minus minus

2

gt( ) ( )

ltimf( gt)

lt lt=ltj

zj

zC

aC

z z A

z zrarr

∕ 6 minus 6+ minus

ltlt8

gt lt lt=ltj

j

C

C 6 rArr

+ minus lt0 lt ltj j

C C + 6 rArr 0j C 6

A2) m- _krmike smstkfjkCgt vk Bgt kikfneinrľ ckejm nrninrľejn skrm bnĔiľjľr nyeľ ykr jkĔmŔtmrfk x(t)rdquoyk snhmptmrikr

Nyeľ Ŕkcmijk C2 B2 vk F kikfneinrľ jn ckejm nrninrľejn skrm bnĔiľjľr nyeľ ykr jkĔmŔtmrfk xgt(t)rdquoyksnhmptmrikr

Qkrm bnĔiľ fkcnemc kikfneinrn ktcm kjke cuvvkt kikfneinrľe cuvvktikrm tdpinfnjľr

mm- Cgt Bgt kikfneinrľ C2 B2 F fkcnemc kikfneinrľ mik pnrniki bnĔiľjľr nrniki bnĔiľ fkcnemckikfneinrn nyeľ cuvvkt ktcm kjkr

m-) vk mm-) jk vkrmike bmi`mikr ľŔľĔľ nitľejn nŔnĔľjncm monjkikr ynzľiľr

Cgt vk Bgt kikfneinrľen ktcm kjke cuvvkt7 gt gt

( )c Bt O O O 6 +

jmr

( )( )

( ) ( )gt

ltltlt=lt

lt lt lt=ltgtlt=lt

j j j

j j j

z z

z z

C C C A

R C C C

z

z z z z z

z

6 6

+

minus6

+ minus+

minus



1



jmr

( ) ( )gt

gt gt gt

( ) ( )( ) ( ) ( )

t t t t t

j x xO c x x B

jt

minus


2 gt gt2 2 gt2

( ) ( )( ) ( )

t t t t


6 + +2


( ) ( )( ) 6

( )

s ss

O O X s f sB c N s

rArr 6+ +


( ) ( )( ) ( )

( ) ( )

s ss s

O O c X c sB X sB

N s N sminus minus+


( ) ( )s s s

c sBO c X sB X

N s N srArr

+ + 6 +

gt gt

gt gt

( )

( )

gt( ) ( )s

s

c sB

N s N s X

O sB c

+ +

6 6

+ ( )gt gt

gt gt

( )

( )

N s sB c

N s sB c

+ +

+

( )

( )( )

22 gt 2 gt

22 2 gt gt

( )

( )

s

s

s f s B B c c X

O s f sB c sB c

+ + + +6

+ + +


vkrmifmŔtmr


gt-)( )

( ) ( ) o

o o o o

jm t k t R m t I

jt 6 +


1-)( )

( )f y

jw t Z t G Z


-) ( ) ( )k f






gt-)( )

( ) ( ) ( ) ( ) o

o o o o o o

o o


sI R6 + rArr 6

+

2-) ( ) ( )k m o Z s C M s6

1-)( ) ( )

( ) ( ) ( ) ( ) f y

f y


sG


-) ( ) ( )k f




gt ( ) ( ) ( ) X s J s ] s6 minus






( )( )

gt ( )

CJH s] s

CH s6


( )( ) ( ) ( ) ( )

gt ( )

CJH sA s J s s s

CH s

6 minus+

yľijľzineľr msk

( )( ) ( ) ( )

gt ( )

CJH sA s J s s

CH s6 minus

+ vk

( )( ) ( ) ( )

gt ( )

CJH zA z J z z

CH z6 minus

+ dinrnc ynzľiľr



983138983085 983130983094lt2 983153983141 983167983147 983144983147983154 983138983149983154 983138983149983145983147Ŕ983147983141 983149983264983149983141 983159983078983146983295983141983289Ŕ983289983142983145983147983154983149 983144983147983153983150983164983145983150983141ľ983154

2

gt lt222gt

( gt) gt00= lt00( ) ( )

8)

8( J z W J

z W

s s z s

zs

6 6

+ minus + 6

2

lt( ) ( ) ( )

222gt

( gt) gt00= lt00 8(

8)

C z W C

sCJH z W CJ s s H

zs

s z

6 6

+ minus + 6


6 6 minus

6 +

gt

( gt) lt0088( ) ( )

s W W

z z s

z

6 6

minus 6

+

2

2



( )( ) ( ) ( )

gt ( )88

CJH zA z

zC

z z z z z z z z

C

J z zC

z

H z

minus +minus

minus + minus+

+

minus

6 minus 6

2

2

2

lt222gt


zC

z z z z z z Cz


6

983105(983159) 983149983151983150983146983147983153983149 983142983147983167983137983163983162 983162983140983164983140983145983140983143983149 983149983145983147 983106983140983159983163983137983163 983136983149983154983149Ŕ983149 983107 983139983150983159983150983141983137ľ 983149983145983147 983264ľ983139ľŔ983162983150 983153ľ983151ľ983154983145983150983141983150983142983150983159 C 6 ∕ 983140983145983153983150 983146983150983144983149 ( ) ltA ∕ 6

983140983145983142983150983159



1



jmr

( ) ( )gt

gt gt gt

( ) ( )( ) ( ) ( )

t t t t t

j x xO c x x B

jt

minus


2 gt gt2 2 gt2

( ) ( )( ) ( )

t t t t


6 + +2


( ) ( )( ) 6

( )

s ss

O O X s f sB c N s

rArr 6+ +


( ) ( )( ) ( )

( ) ( )

s ss s

O O c X c sB X sB

N s N sminus minus+


( ) ( )s s s

c sBO c X sB X

N s N srArr

+ + 6 +

gt gt

gt gt

( )

( )

gt( ) ( )s

s

c sB

N s N s X

O sB c

+ +

6 6

+ ( )gt gt

gt gt

( )

( )

N s sB c

N s sB c

+ +

+

( )

( )( )

22 gt 2 gt

22 2 gt gt

( )

( )

s

s

s f s B B c c X

O s f sB c sB c

+ + + +6

+ + +


vkrmifmŔtmr


gt-)( )

( ) ( ) o

o o o o

jm t k t R m t I

jt 6 +


1-)( )

( )f y

jw t Z t G Z


-) ( ) ( )k f






gt-)( )

( ) ( ) ( ) ( ) o

o o o o o o

o o


sI R6 + rArr 6

+

2-) ( ) ( )k m o Z s C M s6

1-)( ) ( )

( ) ( ) ( ) ( ) f y

f y


sG


-) ( ) ( )k f




gt ( ) ( ) ( ) X s J s ] s6 minus






( )( )

gt ( )

CJH s] s

CH s6


( )( ) ( ) ( ) ( )

gt ( )

CJH sA s J s s s

CH s

6 minus+

yľijľzineľr msk

( )( ) ( ) ( )

gt ( )

CJH sA s J s s

CH s6 minus

+ vk

( )( ) ( ) ( )

gt ( )

CJH zA z J z z

CH z6 minus

+ dinrnc ynzľiľr



983138983085 983130983094lt2 983153983141 983167983147 983144983147983154 983138983149983154 983138983149983145983147Ŕ983147983141 983149983264983149983141 983159983078983146983295983141983289Ŕ983289983142983145983147983154983149 983144983147983153983150983164983145983150983141ľ983154

2

gt lt222gt

( gt) gt00= lt00( ) ( )

8)

8( J z W J

z W

s s z s

zs

6 6

+ minus + 6

2

lt( ) ( ) ( )

222gt

( gt) gt00= lt00 8(

8)

C z W C

sCJH z W CJ s s H

zs

s z

6 6

+ minus + 6


6 6 minus

6 +

gt

( gt) lt0088( ) ( )

s W W

z z s

z

6 6

minus 6

+

2

2



( )( ) ( ) ( )

gt ( )88

CJH zA z

zC

z z z z z z z z

C

J z zC

z

H z

minus +minus

minus + minus+

+

minus

6 minus 6

2

2

2

lt222gt


zC

z z z z z z Cz


6

983105(983159) 983149983151983150983146983147983153983149 983142983147983167983137983163983162 983162983140983164983140983145983140983143983149 983149983145983147 983106983140983159983163983137983163 983136983149983154983149Ŕ983149 983107 983139983150983159983150983141983137ľ 983149983145983147 983264ľ983139ľŔ983162983150 983153ľ983151ľ983154983145983150983141983150983142983150983159 C 6 ∕ 983140983145983153983150 983146983150983144983149 ( ) ltA ∕ 6

983140983145983142983150983159




gt-)( )

( ) ( ) ( ) ( ) o

o o o o o o

o o


sI R6 + rArr 6

+

2-) ( ) ( )k m o Z s C M s6

1-)( ) ( )

( ) ( ) ( ) ( ) f y

f y


sG


-) ( ) ( )k f




gt ( ) ( ) ( ) X s J s ] s6 minus






( )( )

gt ( )

CJH s] s

CH s6


( )( ) ( ) ( ) ( )

gt ( )

CJH sA s J s s s

CH s

6 minus+

yľijľzineľr msk

( )( ) ( ) ( )

gt ( )

CJH sA s J s s

CH s6 minus

+ vk

( )( ) ( ) ( )

gt ( )

CJH zA z J z z

CH z6 minus

+ dinrnc ynzľiľr



983138983085 983130983094lt2 983153983141 983167983147 983144983147983154 983138983149983154 983138983149983145983147Ŕ983147983141 983149983264983149983141 983159983078983146983295983141983289Ŕ983289983142983145983147983154983149 983144983147983153983150983164983145983150983141ľ983154

2

gt lt222gt

( gt) gt00= lt00( ) ( )

8)

8( J z W J

z W

s s z s

zs

6 6

+ minus + 6

2

lt( ) ( ) ( )

222gt

( gt) gt00= lt00 8(

8)

C z W C

sCJH z W CJ s s H

zs

s z

6 6

+ minus + 6


6 6 minus

6 +

gt

( gt) lt0088( ) ( )

s W W

z z s

z

6 6

minus 6

+

2

2



( )( ) ( ) ( )

gt ( )88

CJH zA z

zC

z z z z z z z z

C

J z zC

z

H z

minus +minus

minus + minus+

+

minus

6 minus 6

2

2

2

lt222gt


zC

z z z z z z Cz


6

983105(983159) 983149983151983150983146983147983153983149 983142983147983167983137983163983162 983162983140983164983140983145983140983143983149 983149983145983147 983106983140983159983163983137983163 983136983149983154983149Ŕ983149 983107 983139983150983159983150983141983137ľ 983149983145983147 983264ľ983139ľŔ983162983150 983153ľ983151ľ983154983145983150983141983150983142983150983159 C 6 ∕ 983140983145983153983150 983146983150983144983149 ( ) ltA ∕ 6

983140983145983142983150983159



983138983085 983130983094lt2 983153983141 983167983147 983144983147983154 983138983149983154 983138983149983145983147Ŕ983147983141 983149983264983149983141 983159983078983146983295983141983289Ŕ983289983142983145983147983154983149 983144983147983153983150983164983145983150983141ľ983154

2

gt lt222gt

( gt) gt00= lt00( ) ( )

8)

8( J z W J

z W

s s z s

zs

6 6

+ minus + 6

2

lt( ) ( ) ( )

222gt

( gt) gt00= lt00 8(

8)

C z W C

sCJH z W CJ s s H

zs

s z

6 6

+ minus + 6


6 6 minus

6 +

gt

( gt) lt0088( ) ( )

s W W

z z s

z

6 6

minus 6

+

2

2



( )( ) ( ) ( )

gt ( )88

CJH zA z

zC

z z z z z z z z

C

J z zC

z

H z

minus +minus

minus + minus+

+

minus

6 minus 6

2

2

2

lt222gt


zC

z z z z z z Cz


6

983105(983159) 983149983151983150983146983147983153983149 983142983147983167983137983163983162 983162983140983164983140983145983140983143983149 983149983145983147 983106983140983159983163983137983163 983136983149983154983149Ŕ983149 983107 983139983150983159983150983141983137ľ 983149983145983147 983264ľ983139ľŔ983162983150 983153ľ983151ľ983154983145983150983141983150983142983150983159 C 6 ∕ 983140983145983153983150 983146983150983144983149 ( ) ltA ∕ 6

983140983145983142983150983159

Documents

Otomatik Kontrol Sistemleri - Sakarya Üniversitesi 2012 Vize Soruları