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NRNMFRļH HNERTNJ SCJļIumlļ WCEFYC lt0lt24ltlt3

W-6)

W-4)

W-7)

T J

+Y

yHs

DHM

HB

F

G

WfyĶsfjļŞjamgc

F

B

G

+Y

Hs

yr

a(t)+

-

c(t) u

FBGx(t)

B(z)m

xrai

(t)Ajahtrn-

mĶheftĶs

czjaycgc `abai

ŕahcjba `abai bchay bnĞrujtubf fyfrjfefdcjmahtabcr ļzjaycgc csa ajahtrnmĶheftĶs yfrbĶmĶ cja `abaic tfhcpatmahtabcr Prai (t) va x(t) hneumjfrĶ H s hftsfyĶjĶ ugravezbaŞ pntfescynmatrajar cja ugravejiumluacutejmahtabcr AjahtrnmĶheftĶs

huvvatc sbquoI(t)= lt6trdquo njfrfh varcjmahtabcr (mahfech scstam baeoaba)

f) Yarcjae hnetrnj scstamcea fct fyrĶh -hfpfjĶ iumlavrcm hnetrnj djnh bcyforfmĶeĶ iumlczcecz WfyĶsfj cŞjamgcB(z) fjĶefgfh njup bcĞar djnhjfrf fct trfesiar inehscynejfr Ķ pfrfmatrch njfrfh ajba abcjagahtcr

d)

m(hR)= 7a(hR)-4aX(h-6)R]+6ltmX(h-6)R]+mX(h-2)R] njfrfh varcjbcĞcea ougravera prnorfmjfmf

bcyforfmĶeĶ iumlczcecz (a(hR) `ftf8 m(hR) B(z) sfyĶsfj cŞjamgc iumlĶhĶŞĶ)

6lt0

1lt19

4lt 7lt t(se)

G(t)

O(s)T(s)=6lts G(s)

r(t)

( )6

H O s

s

njbuĞuef va

dfsfmfh gavfdĶ varcjbcĞcea ougravera

f)

H va eabcrgt

d) 6lt( ) T s

s

ciumlce G(t)ndashyc ajba

abcecz

g) ciumlce G(z)=gt Ya G(hR)=gt asfpjfyĶeĶz ( 4lt lt060

R

a

fjĶefgfhtĶr) 6lt( ) T s

s

Yarcjae scstamba dcrcm dfsfmfh ocrcŞc ciumlce

G(t) yfebf Şahcjba varcjbcĞc ocdcbcr

f) HndashyĶ `asfpjfyĶeĶz HfpfjĶ-iumlavrcm

hutupjfrĶeĶe s-hnmpjahs buacutezjamcebaougravestarcecz

d) Wcstam gavfdĶeĶe hrctch sugraveeuacutemjuacute

njfdcjmasc ciumlce H=gt `asfpjfyĶeĶz

T(s)

4

6ltlt

6262 s s

H

6lt7

6

6lt4

lt30

4dfet

ltlt77ltlt11

(se)t

G(t)

G(s)

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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NRNMFRļH HNERTNJ SCJļIumlļ WCEFYC GAYFJFT lt0lt24ltlt3

G-6) f)

B(z) H

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RHs +

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sR a

s

u A 6

T sJlt6

C I

4

( ) I s

Ms Ds H

S(s)yr (t) 6

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4

4

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M

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s

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cc x t H y t

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A s H u s

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T sJ

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Ms Ds H

HfpfjĶ-iumlavrcm hnetrnj djnh bcyforfmĶ

R

+

-a(hR)4

7

R+ +

R R

6lt

m(h)

m(h)

m(h-6) m(h-4)

Rm(h-7) m(h-2)a(h-6)

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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G-4)

6lt

0

1lt19

4lt 7lt t(se)

G(t)

O(s)T(s)=6lts G(s)

[fmfe sfdctc lt974 ( )G ya vfrĶegfyf

hfbfr oaiumlae suacuterabcr lt974 ( )G =lt9740=1lt19 bĶr ŕahcjbae 1lt19 yf hfrŞĶjĶh suacutera 4lt se

bcr

d)

g) 4lt lt060

R

a

njmfh uacutezara

ŕahcjbae O(s) yfzĶjĶr csa

6 lt lt2( )

6( )

4lt

sR a

O s

s s

ajba abcjcr [- bugraveeuacuteŞuacutemuacute ciumlce

6 lt lt2( )

6( )

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yfzĶjĶr

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H O s

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6

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t

G sO s G s O s T s

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s s

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s

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6( ) lt lt2

66( )

4lt

z O z [

z s s

va frf cŞjamjara bavfm abcjcr csa

( ) lt lt26

z O z s

z

6

s

lt

6( )

6 4lt( )

4lt

sR

s

z s

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6

6( )

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z G z z z

( ) ( 6)G hR z 621

( 6)

z

z

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( lt060)

h z

z

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( lt060)

z

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z

z z

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6 21 6 21( ) 6 lt060

lt6067 lt6067

h h G hR

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Wnru 7-

kw

k0292

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4

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( lt 02 92)( lt 02 92)

s s H s s

s k s k

4

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H

s s H

d)

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Baehjamcece hugravehjarc hftjĶ va raaj njmfjĶbĶr

4

4

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626 2 2 6 6ltlt lt 2330

d f g

H H

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj SĶj ļiumlc WĶefvĶ 62Ecsfe4lt66

W^6

FŞfĞĶbf varcjae Hnetrnj djnh bcyforfmĶebf6

6O (s)

s 6

4O (s) 6lt 7

sO (s)

s 1

njmfh uacutezara

varcjmahtabcr

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

G6-f

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

4

6

O

O (s)6

T(s) G(s)A(s)

4

6

O

4

4 7

HO

6 HO O

46

4 7

46

4 7 4

HOO

6 HO O

HO 66 O

6 HO O O

T(s) G(s)

HfpfjĶ-iumlavrcm trfesiar

inehscyneu ajba abcecz

G(s)gt

T(s)

d) r(t ) u(t ) ciumlce g( ) 6

njmfsĶ ciumlce H gt `asfp abcecz

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4

4

6

4 7

6

HOO

G s 6 HO O

T s H O6 O

4

4 7

6

6 HO O O

4

6

4 7 6 4

4 7 6 4 7 6

4 74

HO 6O H6lt

6 HO O O HO s 6

6 HO O O H s 66 HO O O H 6 H 6lt H

s 1 s 66 HO O

6 6H 6lt H 6lt

G s H 6lt s 1s 6 s 6

s 6 s 1 s 6 H 6lt s s 6 s 1 H T s s 1 s 6 H 6lt s s 6 s 1 H6 H 6lt H

s 1 s 6 s 1 s 6

G s 6ltH s 1R s

T s s 1 s 6 6ltHs s 6 s 1 H

4 4

G s 6ltH s 1R sT s s s 1s 1 6ltHs 6ltHs Hs 1H

4

G s 6ltH s 1R s

T s 6ltH 6 s 66H 9 s 1 1H

G6-d

Wr (t ) u (t ) 6T(s)s

dujueur

W

t s lt s ltg( ) jcm g(t) g( ) jcm sG(s) jcm sR(s)T s

bcr

ļstaeae

s ltjcmsR(sg( )) 6T s

s lt 4

6ltH s 1 6

6ltH 6 s 66H

g( ) jcm s

s 1H

6

9 1 s

s ltjcm s

4

lt

lt

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6ltH 6 66H 9 1 1 slt H

6

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1 1H

6

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7

W^4

G4-f

Wb6 a t Tc t J c t A s TC s JsC s

bt

6

C s A sJs T

W

m m4 i t h c t I s h C s

mI s h C s

4

W 4

4

b b7 i t hx t D x t M x t I s hP s DsP s Ms P s

bt bt

4

6P s I s

Ms Ds h

djnh bcyforfm

A(s) 6

Js T

C(s)hm

I(s) P(s)4

6

Ms Ds h

A(s)

m

4

h

Js T Ms Ds h

P(s)

m

4

P s h

A s Js T Ms Ds h

Sfebf varcjae huacutetja yfy va ajahtrnmĶheftĶs scstamceba ajahtrn

mĶheftĶs huvvatc mI(t) h c(t) njfrfh varcjmahtabcr

f- Wcstama fct bcefmch baehjamjarc yfzĶeĶz Hnetrnj djnh

bcyforfmĶeĶ ajba abcecz ( xy x(t) ugravejiumluacutejae hneum)

d-

r y raiarfes hneum ocrcŞc njmfh uacutezara fyrĶh-zfmfe sfyĶsfj

hfpfjĶ iumlavrcm hnetrnj djnh bcyforfmĶeĶ iumlczcecz

Ent Huacutetja yfy baeoaba

T J c(t)

a(t)Ajahtrn

mĶheftĶs

M

D h+ Y

x

yx

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2

G4-d

A(s) P(s)sR6 a

s

[NBFG

B(z)P(z)

FBG

R

R

m

4

h

Js T Ms Ds h

W^7

FyrĶh zfmfe fiumlĶh-iumlavrcm trfesiar inehscyneu O(z) ajba abcecz ([Nndash ju)

g) Dcrcm dfsfmfh ocrcŞ ciumlce g(h) ndash yĶ ajba abcecz va h=1 ciumlce g(h) yĶ `asfpjfyĶeĶz

G7-f

6

H

s 6 Baragabae mnbajce pfrfmatrajarc baeaysaj ynj cja ajba abcjagahtcr

FiumlĶh iumlavrcm hfzfeiuml H csa

lt01

lt016

iumlĶhĶŞ

ocrc Ş

v H

v

ajba abcjcr

FiumlĶh iumlavrcm zfmfe sfdctc csa lt974 lt174iumlĶhĶŞv ndashya baeh oajae zfmfe baĞarc njup dcrcm

dfsmfh gavfp aĞrcscebae 6lt se njfrfh nhueur

6 Baragabae trfesiar inehscyneuebf pfrfmatrajar yarjarcea hneursf

lt01

6lt 6O s

s

dujueur

Sfebf C Baragabae scstama fct fiumlĶh -iumlavrcm dcrcm dfsfmfh gavfdĶ varcjmcŞtcr

f) O(s) trfesiar inehscyneueu dujueuz

d) ugravereahjama zfmfeĶ R1

njmfh uacutezara

zfmfe sfdctc

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1

G7-d

sR z a

6lt4

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6

66

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c

me

m

cm sR

c s s

b z P z s s P sm bs z a

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a [ R s O s RO z [ z [

s s s s

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z

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s

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s lt

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s

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z z z z z z RO z

z z a z a z z z

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6(z

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z

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T z

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9

66

66

6( ) ( ) ( )

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me

m h

cm z z

c

b x h z z P z z

m bz

lt6126z

z lt060 z 6g h [ G z [

g h z lt060

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z lt060 h 6

z lt060

z z 6z 6

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h 6

z 6

z

h h

h lt6126 lt6lt060 6lt060

lt060 6

126g h lt01 6

6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

W^2 R= lt6 se ciumlce r(t) u(t) ciumlce G(z) ndashc ajba abcecz G( ) baĞarcec `asfp abcecz

T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

zn` s zn` s zn` sG s T s G s O s O s T s O s O s G s O s O s

zn` s zn` sG s T s O O s G s O O s

zn` s zn` sG s G s O O s T s O O s

6

zn` s

zn` s

G s O O s

T s O O s

6

zn` s

zn` s

G z O O z

T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

6-)( )

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i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

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( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

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+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

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+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

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983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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NRNMFRļH HNERTNJ SCJļIumlļ WCEFYC GAYFJFT lt0lt24ltlt3

G-6) f)

B(z) H

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RHs +

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s

u A 6

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4

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s

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HfpfjĶ-iumlavrcm hnetrnj djnh bcyforfmĶ

R

+

-a(hR)4

7

R+ +

R R

6lt

m(h)

m(h)

m(h-6) m(h-4)

Rm(h-7) m(h-2)a(h-6)

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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G-4)

6lt

0

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4lt 7lt t(se)

G(t)

O(s)T(s)=6lts G(s)

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bcr

d)

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R

a

njmfh uacutezara

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6 lt lt2( )

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sR a

O s

s s

ajba abcjcr [- bugraveeuacuteŞuacutemuacute ciumlce

6 lt lt2( )

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yfzĶjĶr

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6

4lt

t

G sO s G s O s T s

T s s s s s

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s s

G s G t a s

s

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6( ) lt lt2

66( )

4lt

z O z [

z s s

va frf cŞjamjara bavfm abcjcr csa

( ) lt lt26

z O z s

z

6

s

lt

6( )

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4lt

sR

s

z s

z a s

6

6( )

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s

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z

z

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lt621( )

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z

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z z

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z G z z z

( ) ( 6)G hR z 621

( 6)

z

z

6

( lt060)

h z

z

6

( lt060)

z

z

621

( 6) ( lt060)

z

z z

6h z

lt060 z

6 21 6 21( ) 6 lt060

lt6067 lt6067

h h G hR

( ) 0(6 lt060 )h G hR

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Wnru 7-

kw

k0292

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f) 4

4

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( ) 6262

6ltlt( )6

6262

H

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( lt 02 92)( lt 02 92)

s s H s s

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4

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Baehjamcece hugravehjarc hftjĶ va raaj njmfjĶbĶr

4

4

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d f g

H H

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj SĶj ļiumlc WĶefvĶ 62Ecsfe4lt66

W^6

FŞfĞĶbf varcjae Hnetrnj djnh bcyforfmĶebf6

6O (s)

s 6

4O (s) 6lt 7

sO (s)

s 1

njmfh uacutezara

varcjmahtabcr

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

G6-f

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

4

6

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O (s)6

T(s) G(s)A(s)

4

6

O

4

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46

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6 HO O O

T(s) G(s)

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inehscyneu ajba abcecz

G(s)gt

T(s)

d) r(t ) u(t ) ciumlce g( ) 6

njmfsĶ ciumlce H gt `asfp abcecz

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

4

6

4 7

6

HOO

G s 6 HO O

T s H O6 O

4

4 7

6

6 HO O O

4

6

4 7 6 4

4 7 6 4 7 6

4 74

HO 6O H6lt

6 HO O O HO s 6

6 HO O O H s 66 HO O O H 6 H 6lt H

s 1 s 66 HO O

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G s H 6lt s 1s 6 s 6

s 6 s 1 s 6 H 6lt s s 6 s 1 H T s s 1 s 6 H 6lt s s 6 s 1 H6 H 6lt H

s 1 s 6 s 1 s 6

G s 6ltH s 1R s

T s s 1 s 6 6ltHs s 6 s 1 H

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G s 6ltH s 1R sT s s s 1s 1 6ltHs 6ltHs Hs 1H

4

G s 6ltH s 1R s

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G6-d

Wr (t ) u (t ) 6T(s)s

dujueur

W

t s lt s ltg( ) jcm g(t) g( ) jcm sG(s) jcm sR(s)T s

bcr

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s ltjcmsR(sg( )) 6T s

s lt 4

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g( ) jcm s

s 1H

6

9 1 s

s ltjcm s

4

lt

lt

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6

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1 1H

6

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7

W^4

G4-f

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bt

6

C s A sJs T

W

m m4 i t h c t I s h C s

mI s h C s

4

W 4

4

b b7 i t hx t D x t M x t I s hP s DsP s Ms P s

bt bt

4

6P s I s

Ms Ds h

djnh bcyforfm

A(s) 6

Js T

C(s)hm

I(s) P(s)4

6

Ms Ds h

A(s)

m

4

h

Js T Ms Ds h

P(s)

m

4

P s h

A s Js T Ms Ds h

Sfebf varcjae huacutetja yfy va ajahtrnmĶheftĶs scstamceba ajahtrn

mĶheftĶs huvvatc mI(t) h c(t) njfrfh varcjmahtabcr

f- Wcstama fct bcefmch baehjamjarc yfzĶeĶz Hnetrnj djnh

bcyforfmĶeĶ ajba abcecz ( xy x(t) ugravejiumluacutejae hneum)

d-

r y raiarfes hneum ocrcŞc njmfh uacutezara fyrĶh-zfmfe sfyĶsfj

hfpfjĶ iumlavrcm hnetrnj djnh bcyforfmĶeĶ iumlczcecz

Ent Huacutetja yfy baeoaba

T J c(t)

a(t)Ajahtrn

mĶheftĶs

M

D h+ Y

x

yx

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

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s

[NBFG

B(z)P(z)

FBG

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h

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s 6 Baragabae mnbajce pfrfmatrajarc baeaysaj ynj cja ajba abcjagahtcr

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ocrc Ş

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v

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f) O(s) trfesiar inehscyneueu dujueuz

d) ugravereahjama zfmfeĶ R1

njmfh uacutezara

zfmfe sfdctc

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

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6lt4

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66

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c

me

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cm sR

c s s

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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9

66

66

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me

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cm z z

c

b x h z z P z z

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g h z lt060

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z 6

z

h h

h lt6126 lt6lt060 6lt060

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6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

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T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

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zn` s

zn` s

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6

zn` s

zn` s

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T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

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fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

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983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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G-4)

6lt

0

1lt19

4lt 7lt t(se)

G(t)

O(s)T(s)=6lts G(s)

[fmfe sfdctc lt974 ( )G ya vfrĶegfyf

hfbfr oaiumlae suacuterabcr lt974 ( )G =lt9740=1lt19 bĶr ŕahcjbae 1lt19 yf hfrŞĶjĶh suacutera 4lt se

bcr

d)

g) 4lt lt060

R

a

njmfh uacutezara

ŕahcjbae O(s) yfzĶjĶr csa

6 lt lt2( )

6( )

4lt

sR a

O s

s s

ajba abcjcr [- bugraveeuacuteŞuacutemuacute ciumlce

6 lt lt2( )

6( )

4lt

sR a

O z [

s s

yfzĶjĶr

( )6

0lt0 lt0

( )6lt

4lt 64lt

H O s

s

H O s

s se

4lt

lt0

( ) 6lt lt 24lt( ) ( ) ( ) ( )6 6( )

( )4lt 4lt

08 06

4lt

0 0( ) ( ) 0(6 )

6

4lt

t

G sO s G s O s T s

T s s s s s

F D F D

s s

G s G t a s

s

f)

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6( ) lt lt2

66( )

4lt

z O z [

z s s

va frf cŞjamjara bavfm abcjcr csa

( ) lt lt26

z O z s

z

6

s

lt

6( )

6 4lt( )

4lt

sR

s

z s

z a s

6

6( )

4lt s s

6

4lt

sR

s

z

z a

6ltlt2

z

z

4lt

z 4lt

6

z

z

4lt 4lt

6lt0 6

R R

z

z a z a

lt621( )

lt060O z

z

6lt lt621( ) ( ) ( )

6 lt060

z G z T z O z

z z

621( )( 6) ( lt060)

z G z z z

( ) ( 6)G hR z 621

( 6)

z

z

6

( lt060)

h z

z

6

( lt060)

z

z

621

( 6) ( lt060)

z

z z

6h z

lt060 z

6 21 6 21( ) 6 lt060

lt6067 lt6067

h h G hR

( ) 0(6 lt060 )h G hR

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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Wnru 7-

kw

k0292

-lt

-k0292

f) 4

4

6ltlt

( ) 6262

6ltlt( )6

6262

H

G s s s

H T s

s s

4 4626 2 6ltlt 626 2 6ltlt 646 96

( lt 02 92)( lt 02 92)

s s H s s

s k s k

4

6ltlt

6262 6ltlt

H

s s H

d)

4

6262 6ltlt lt s s H

Baehjamcece hugravehjarc hftjĶ va raaj njmfjĶbĶr

4

4

lt 2

626 2 2 6 6ltlt lt 2330

d f g

H H

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj SĶj ļiumlc WĶefvĶ 62Ecsfe4lt66

W^6

FŞfĞĶbf varcjae Hnetrnj djnh bcyforfmĶebf6

6O (s)

s 6

4O (s) 6lt 7

sO (s)

s 1

njmfh uacutezara

varcjmahtabcr

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

G6-f

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

4

6

O

O (s)6

T(s) G(s)A(s)

4

6

O

4

4 7

HO

6 HO O

46

4 7

46

4 7 4

HOO

6 HO O

HO 66 O

6 HO O O

T(s) G(s)

HfpfjĶ-iumlavrcm trfesiar

inehscyneu ajba abcecz

G(s)gt

T(s)

d) r(t ) u(t ) ciumlce g( ) 6

njmfsĶ ciumlce H gt `asfp abcecz

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4

4

6

4 7

6

HOO

G s 6 HO O

T s H O6 O

4

4 7

6

6 HO O O

4

6

4 7 6 4

4 7 6 4 7 6

4 74

HO 6O H6lt

6 HO O O HO s 6

6 HO O O H s 66 HO O O H 6 H 6lt H

s 1 s 66 HO O

6 6H 6lt H 6lt

G s H 6lt s 1s 6 s 6

s 6 s 1 s 6 H 6lt s s 6 s 1 H T s s 1 s 6 H 6lt s s 6 s 1 H6 H 6lt H

s 1 s 6 s 1 s 6

G s 6ltH s 1R s

T s s 1 s 6 6ltHs s 6 s 1 H

4 4

G s 6ltH s 1R sT s s s 1s 1 6ltHs 6ltHs Hs 1H

4

G s 6ltH s 1R s

T s 6ltH 6 s 66H 9 s 1 1H

G6-d

Wr (t ) u (t ) 6T(s)s

dujueur

W

t s lt s ltg( ) jcm g(t) g( ) jcm sG(s) jcm sR(s)T s

bcr

ļstaeae

s ltjcmsR(sg( )) 6T s

s lt 4

6ltH s 1 6

6ltH 6 s 66H

g( ) jcm s

s 1H

6

9 1 s

s ltjcm s

4

lt

lt

6ltH 1 6

6ltH 6 66H 9 1 1 slt H

6

H1lt6

1 1H

6

H 3

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7

W^4

G4-f

Wb6 a t Tc t J c t A s TC s JsC s

bt

6

C s A sJs T

W

m m4 i t h c t I s h C s

mI s h C s

4

W 4

4

b b7 i t hx t D x t M x t I s hP s DsP s Ms P s

bt bt

4

6P s I s

Ms Ds h

djnh bcyforfm

A(s) 6

Js T

C(s)hm

I(s) P(s)4

6

Ms Ds h

A(s)

m

4

h

Js T Ms Ds h

P(s)

m

4

P s h

A s Js T Ms Ds h

Sfebf varcjae huacutetja yfy va ajahtrnmĶheftĶs scstamceba ajahtrn

mĶheftĶs huvvatc mI(t) h c(t) njfrfh varcjmahtabcr

f- Wcstama fct bcefmch baehjamjarc yfzĶeĶz Hnetrnj djnh

bcyforfmĶeĶ ajba abcecz ( xy x(t) ugravejiumluacutejae hneum)

d-

r y raiarfes hneum ocrcŞc njmfh uacutezara fyrĶh-zfmfe sfyĶsfj

hfpfjĶ iumlavrcm hnetrnj djnh bcyforfmĶeĶ iumlczcecz

Ent Huacutetja yfy baeoaba

T J c(t)

a(t)Ajahtrn

mĶheftĶs

M

D h+ Y

x

yx

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2

G4-d

A(s) P(s)sR6 a

s

[NBFG

B(z)P(z)

FBG

R

R

m

4

h

Js T Ms Ds h

W^7

FyrĶh zfmfe fiumlĶh-iumlavrcm trfesiar inehscyneu O(z) ajba abcecz ([Nndash ju)

g) Dcrcm dfsfmfh ocrcŞ ciumlce g(h) ndash yĶ ajba abcecz va h=1 ciumlce g(h) yĶ `asfpjfyĶeĶz

G7-f

6

H

s 6 Baragabae mnbajce pfrfmatrajarc baeaysaj ynj cja ajba abcjagahtcr

FiumlĶh iumlavrcm hfzfeiuml H csa

lt01

lt016

iumlĶhĶŞ

ocrc Ş

v H

v

ajba abcjcr

FiumlĶh iumlavrcm zfmfe sfdctc csa lt974 lt174iumlĶhĶŞv ndashya baeh oajae zfmfe baĞarc njup dcrcm

dfsmfh gavfp aĞrcscebae 6lt se njfrfh nhueur

6 Baragabae trfesiar inehscyneuebf pfrfmatrajar yarjarcea hneursf

lt01

6lt 6O s

s

dujueur

Sfebf C Baragabae scstama fct fiumlĶh -iumlavrcm dcrcm dfsfmfh gavfdĶ varcjmcŞtcr

f) O(s) trfesiar inehscyneueu dujueuz

d) ugravereahjama zfmfeĶ R1

njmfh uacutezara

zfmfe sfdctc

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1

G7-d

sR z a

6lt4

1 1R se

6

66

6( ) ( ) ( )( 6)

c

me

m

cm sR

c s s

b z P z s s P sm bs z a

6lt01 6 lt01 66

6lt 6 6lt lt6

Rs

[N [N

a [ R s O s RO z [ z [

s s s s

6

ltlt01 lt6 [N

z RO z s

z

6

lt6 s s

lt6

lt sR

s

z s

z a

6

s lt

lt6 sR

s

z

z a s

lt64 lt4

lt6 lt

6 6 6 6ltlt01 ltlt01 6lt 6lt

lt6 lt060 6 [N

z z z z z z RO z

z z a z a z z z

6

lt01 [N

z RO z

z

z

lt060

z

z

6 lt060 6lt01 6 lt01

6 lt060 lt060

z z z

z z z

lt6126

lt060 [N RO z

z

G7-g

OcrcŞ cŞfratc W z6r(t) u(t) T(s) T )

6(z

s

z

z

dujueur

[N

G zRO z

T z

[NG z RO z T z

[N

lt6126

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z

z 6

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9

66

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( 6) c

me

m h

cm z z

c

b x h z z P z z

m bz

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g h z lt060

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z lt060 h 6

z lt060

z z 6z 6

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h 6

z 6

z

h h

h lt6126 lt6lt060 6lt060

lt060 6

126g h lt01 6

6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

W^2 R= lt6 se ciumlce r(t) u(t) ciumlce G(z) ndashc ajba abcecz G( ) baĞarcec `asfp abcecz

T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

zn` s zn` s zn` sG s T s G s O s O s T s O s O s G s O s O s

zn` s zn` sG s T s O O s G s O O s

zn` s zn` sG s G s O O s T s O O s

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zn` s

zn` s

G s O O s

T s O O s

6

zn` s

zn` s

G z O O z

T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

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fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

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W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

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1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

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+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

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983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6( ) lt lt2

66( )

4lt

z O z [

z s s

va frf cŞjamjara bavfm abcjcr csa

( ) lt lt26

z O z s

z

6

s

lt

6( )

6 4lt( )

4lt

sR

s

z s

z a s

6

6( )

4lt s s

6

4lt

sR

s

z

z a

6ltlt2

z

z

4lt

z 4lt

6

z

z

4lt 4lt

6lt0 6

R R

z

z a z a

lt621( )

lt060O z

z

6lt lt621( ) ( ) ( )

6 lt060

z G z T z O z

z z

621( )( 6) ( lt060)

z G z z z

( ) ( 6)G hR z 621

( 6)

z

z

6

( lt060)

h z

z

6

( lt060)

z

z

621

( 6) ( lt060)

z

z z

6h z

lt060 z

6 21 6 21( ) 6 lt060

lt6067 lt6067

h h G hR

( ) 0(6 lt060 )h G hR

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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Wnru 7-

kw

k0292

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f) 4

4

6ltlt

( ) 6262

6ltlt( )6

6262

H

G s s s

H T s

s s

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( lt 02 92)( lt 02 92)

s s H s s

s k s k

4

6ltlt

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H

s s H

d)

4

6262 6ltlt lt s s H

Baehjamcece hugravehjarc hftjĶ va raaj njmfjĶbĶr

4

4

lt 2

626 2 2 6 6ltlt lt 2330

d f g

H H

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj SĶj ļiumlc WĶefvĶ 62Ecsfe4lt66

W^6

FŞfĞĶbf varcjae Hnetrnj djnh bcyforfmĶebf6

6O (s)

s 6

4O (s) 6lt 7

sO (s)

s 1

njmfh uacutezara

varcjmahtabcr

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

G6-f

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

4

6

O

O (s)6

T(s) G(s)A(s)

4

6

O

4

4 7

HO

6 HO O

46

4 7

46

4 7 4

HOO

6 HO O

HO 66 O

6 HO O O

T(s) G(s)

HfpfjĶ-iumlavrcm trfesiar

inehscyneu ajba abcecz

G(s)gt

T(s)

d) r(t ) u(t ) ciumlce g( ) 6

njmfsĶ ciumlce H gt `asfp abcecz

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

4

6

4 7

6

HOO

G s 6 HO O

T s H O6 O

4

4 7

6

6 HO O O

4

6

4 7 6 4

4 7 6 4 7 6

4 74

HO 6O H6lt

6 HO O O HO s 6

6 HO O O H s 66 HO O O H 6 H 6lt H

s 1 s 66 HO O

6 6H 6lt H 6lt

G s H 6lt s 1s 6 s 6

s 6 s 1 s 6 H 6lt s s 6 s 1 H T s s 1 s 6 H 6lt s s 6 s 1 H6 H 6lt H

s 1 s 6 s 1 s 6

G s 6ltH s 1R s

T s s 1 s 6 6ltHs s 6 s 1 H

4 4

G s 6ltH s 1R sT s s s 1s 1 6ltHs 6ltHs Hs 1H

4

G s 6ltH s 1R s

T s 6ltH 6 s 66H 9 s 1 1H

G6-d

Wr (t ) u (t ) 6T(s)s

dujueur

W

t s lt s ltg( ) jcm g(t) g( ) jcm sG(s) jcm sR(s)T s

bcr

ļstaeae

s ltjcmsR(sg( )) 6T s

s lt 4

6ltH s 1 6

6ltH 6 s 66H

g( ) jcm s

s 1H

6

9 1 s

s ltjcm s

4

lt

lt

6ltH 1 6

6ltH 6 66H 9 1 1 slt H

6

H1lt6

1 1H

6

H 3

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7

W^4

G4-f

Wb6 a t Tc t J c t A s TC s JsC s

bt

6

C s A sJs T

W

m m4 i t h c t I s h C s

mI s h C s

4

W 4

4

b b7 i t hx t D x t M x t I s hP s DsP s Ms P s

bt bt

4

6P s I s

Ms Ds h

djnh bcyforfm

A(s) 6

Js T

C(s)hm

I(s) P(s)4

6

Ms Ds h

A(s)

m

4

h

Js T Ms Ds h

P(s)

m

4

P s h

A s Js T Ms Ds h

Sfebf varcjae huacutetja yfy va ajahtrnmĶheftĶs scstamceba ajahtrn

mĶheftĶs huvvatc mI(t) h c(t) njfrfh varcjmahtabcr

f- Wcstama fct bcefmch baehjamjarc yfzĶeĶz Hnetrnj djnh

bcyforfmĶeĶ ajba abcecz ( xy x(t) ugravejiumluacutejae hneum)

d-

r y raiarfes hneum ocrcŞc njmfh uacutezara fyrĶh-zfmfe sfyĶsfj

hfpfjĶ iumlavrcm hnetrnj djnh bcyforfmĶeĶ iumlczcecz

Ent Huacutetja yfy baeoaba

T J c(t)

a(t)Ajahtrn

mĶheftĶs

M

D h+ Y

x

yx

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

G4-d

A(s) P(s)sR6 a

s

[NBFG

B(z)P(z)

FBG

R

R

m

4

h

Js T Ms Ds h

W^7

FyrĶh zfmfe fiumlĶh-iumlavrcm trfesiar inehscyneu O(z) ajba abcecz ([Nndash ju)

g) Dcrcm dfsfmfh ocrcŞ ciumlce g(h) ndash yĶ ajba abcecz va h=1 ciumlce g(h) yĶ `asfpjfyĶeĶz

G7-f

6

H

s 6 Baragabae mnbajce pfrfmatrajarc baeaysaj ynj cja ajba abcjagahtcr

FiumlĶh iumlavrcm hfzfeiuml H csa

lt01

lt016

iumlĶhĶŞ

ocrc Ş

v H

v

ajba abcjcr

FiumlĶh iumlavrcm zfmfe sfdctc csa lt974 lt174iumlĶhĶŞv ndashya baeh oajae zfmfe baĞarc njup dcrcm

dfsmfh gavfp aĞrcscebae 6lt se njfrfh nhueur

6 Baragabae trfesiar inehscyneuebf pfrfmatrajar yarjarcea hneursf

lt01

6lt 6O s

s

dujueur

Sfebf C Baragabae scstama fct fiumlĶh -iumlavrcm dcrcm dfsfmfh gavfdĶ varcjmcŞtcr

f) O(s) trfesiar inehscyneueu dujueuz

d) ugravereahjama zfmfeĶ R1

njmfh uacutezara

zfmfe sfdctc

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1

G7-d

sR z a

6lt4

1 1R se

6

66

6( ) ( ) ( )( 6)

c

me

m

cm sR

c s s

b z P z s s P sm bs z a

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Rs

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a [ R s O s RO z [ z [

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s lt

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s

z

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6 6 6 6ltlt01 ltlt01 6lt 6lt

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z z z z z z RO z

z z a z a z z z

6

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z

z

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T z

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z ltG z RO z T z

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z

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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9

66

66

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( 6) c

me

m h

cm z z

c

b x h z z P z z

m bz

lt6126z

z lt060 z 6g h [ G z [

g h z lt060

lt6126z

z lt060 h 6

z lt060

z z 6z 6

lt6126z

z lt060 z 6

h 6

z 6

z

h h

h lt6126 lt6lt060 6lt060

lt060 6

126g h lt01 6

6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

W^2 R= lt6 se ciumlce r(t) u(t) ciumlce G(z) ndashc ajba abcecz G( ) baĞarcec `asfp abcecz

T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

zn` s zn` s zn` sG s T s G s O s O s T s O s O s G s O s O s

zn` s zn` sG s T s O O s G s O O s

zn` s zn` sG s G s O O s T s O O s

6

zn` s

zn` s

G s O O s

T s O O s

6

zn` s

zn` s

G z O O z

T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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Wnru 7-

kw

k0292

-lt

-k0292

f) 4

4

6ltlt

( ) 6262

6ltlt( )6

6262

H

G s s s

H T s

s s

4 4626 2 6ltlt 626 2 6ltlt 646 96

( lt 02 92)( lt 02 92)

s s H s s

s k s k

4

6ltlt

6262 6ltlt

H

s s H

d)

4

6262 6ltlt lt s s H

Baehjamcece hugravehjarc hftjĶ va raaj njmfjĶbĶr

4

4

lt 2

626 2 2 6 6ltlt lt 2330

d f g

H H

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj SĶj ļiumlc WĶefvĶ 62Ecsfe4lt66

W^6

FŞfĞĶbf varcjae Hnetrnj djnh bcyforfmĶebf6

6O (s)

s 6

4O (s) 6lt 7

sO (s)

s 1

njmfh uacutezara

varcjmahtabcr

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

G6-f

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

4

6

O

O (s)6

T(s) G(s)A(s)

4

6

O

4

4 7

HO

6 HO O

46

4 7

46

4 7 4

HOO

6 HO O

HO 66 O

6 HO O O

T(s) G(s)

HfpfjĶ-iumlavrcm trfesiar

inehscyneu ajba abcecz

G(s)gt

T(s)

d) r(t ) u(t ) ciumlce g( ) 6

njmfsĶ ciumlce H gt `asfp abcecz

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4

4

6

4 7

6

HOO

G s 6 HO O

T s H O6 O

4

4 7

6

6 HO O O

4

6

4 7 6 4

4 7 6 4 7 6

4 74

HO 6O H6lt

6 HO O O HO s 6

6 HO O O H s 66 HO O O H 6 H 6lt H

s 1 s 66 HO O

6 6H 6lt H 6lt

G s H 6lt s 1s 6 s 6

s 6 s 1 s 6 H 6lt s s 6 s 1 H T s s 1 s 6 H 6lt s s 6 s 1 H6 H 6lt H

s 1 s 6 s 1 s 6

G s 6ltH s 1R s

T s s 1 s 6 6ltHs s 6 s 1 H

4 4

G s 6ltH s 1R sT s s s 1s 1 6ltHs 6ltHs Hs 1H

4

G s 6ltH s 1R s

T s 6ltH 6 s 66H 9 s 1 1H

G6-d

Wr (t ) u (t ) 6T(s)s

dujueur

W

t s lt s ltg( ) jcm g(t) g( ) jcm sG(s) jcm sR(s)T s

bcr

ļstaeae

s ltjcmsR(sg( )) 6T s

s lt 4

6ltH s 1 6

6ltH 6 s 66H

g( ) jcm s

s 1H

6

9 1 s

s ltjcm s

4

lt

lt

6ltH 1 6

6ltH 6 66H 9 1 1 slt H

6

H1lt6

1 1H

6

H 3

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7

W^4

G4-f

Wb6 a t Tc t J c t A s TC s JsC s

bt

6

C s A sJs T

W

m m4 i t h c t I s h C s

mI s h C s

4

W 4

4

b b7 i t hx t D x t M x t I s hP s DsP s Ms P s

bt bt

4

6P s I s

Ms Ds h

djnh bcyforfm

A(s) 6

Js T

C(s)hm

I(s) P(s)4

6

Ms Ds h

A(s)

m

4

h

Js T Ms Ds h

P(s)

m

4

P s h

A s Js T Ms Ds h

Sfebf varcjae huacutetja yfy va ajahtrnmĶheftĶs scstamceba ajahtrn

mĶheftĶs huvvatc mI(t) h c(t) njfrfh varcjmahtabcr

f- Wcstama fct bcefmch baehjamjarc yfzĶeĶz Hnetrnj djnh

bcyforfmĶeĶ ajba abcecz ( xy x(t) ugravejiumluacutejae hneum)

d-

r y raiarfes hneum ocrcŞc njmfh uacutezara fyrĶh-zfmfe sfyĶsfj

hfpfjĶ iumlavrcm hnetrnj djnh bcyforfmĶeĶ iumlczcecz

Ent Huacutetja yfy baeoaba

T J c(t)

a(t)Ajahtrn

mĶheftĶs

M

D h+ Y

x

yx

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2

G4-d

A(s) P(s)sR6 a

s

[NBFG

B(z)P(z)

FBG

R

R

m

4

h

Js T Ms Ds h

W^7

FyrĶh zfmfe fiumlĶh-iumlavrcm trfesiar inehscyneu O(z) ajba abcecz ([Nndash ju)

g) Dcrcm dfsfmfh ocrcŞ ciumlce g(h) ndash yĶ ajba abcecz va h=1 ciumlce g(h) yĶ `asfpjfyĶeĶz

G7-f

6

H

s 6 Baragabae mnbajce pfrfmatrajarc baeaysaj ynj cja ajba abcjagahtcr

FiumlĶh iumlavrcm hfzfeiuml H csa

lt01

lt016

iumlĶhĶŞ

ocrc Ş

v H

v

ajba abcjcr

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dfsmfh gavfp aĞrcscebae 6lt se njfrfh nhueur

6 Baragabae trfesiar inehscyneuebf pfrfmatrajar yarjarcea hneursf

lt01

6lt 6O s

s

dujueur

Sfebf C Baragabae scstama fct fiumlĶh -iumlavrcm dcrcm dfsfmfh gavfdĶ varcjmcŞtcr

f) O(s) trfesiar inehscyneueu dujueuz

d) ugravereahjama zfmfeĶ R1

njmfh uacutezara

zfmfe sfdctc

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1

G7-d

sR z a

6lt4

1 1R se

6

66

6( ) ( ) ( )( 6)

c

me

m

cm sR

c s s

b z P z s s P sm bs z a

6lt01 6 lt01 66

6lt 6 6lt lt6

Rs

[N [N

a [ R s O s RO z [ z [

s s s s

6

ltlt01 lt6 [N

z RO z s

z

6

lt6 s s

lt6

lt sR

s

z s

z a

6

s lt

lt6 sR

s

z

z a s

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lt6 lt

6 6 6 6ltlt01 ltlt01 6lt 6lt

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z z z z z z RO z

z z a z a z z z

6

lt01 [N

z RO z

z

z

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z

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z

G7-g

OcrcŞ cŞfratc W z6r(t) u(t) T(s) T )

6(z

s

z

z

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G zRO z

T z

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z ltG z RO z T z

060

z

z 6

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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9

66

66

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( 6) c

me

m h

cm z z

c

b x h z z P z z

m bz

lt6126z

z lt060 z 6g h [ G z [

g h z lt060

lt6126z

z lt060 h 6

z lt060

z z 6z 6

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z lt060 z 6

h 6

z 6

z

h h

h lt6126 lt6lt060 6lt060

lt060 6

126g h lt01 6

6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

W^2 R= lt6 se ciumlce r(t) u(t) ciumlce G(z) ndashc ajba abcecz G( ) baĞarcec `asfp abcecz

T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

zn` s zn` s zn` sG s T s G s O s O s T s O s O s G s O s O s

zn` s zn` sG s T s O O s G s O O s

zn` s zn` sG s G s O O s T s O O s

6

zn` s

zn` s

G s O O s

T s O O s

6

zn` s

zn` s

G z O O z

T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj SĶj ļiumlc WĶefvĶ 62Ecsfe4lt66

W^6

FŞfĞĶbf varcjae Hnetrnj djnh bcyforfmĶebf6

6O (s)

s 6

4O (s) 6lt 7

sO (s)

s 1

njmfh uacutezara

varcjmahtabcr

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

G6-f

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

4

6

O

O (s)6

T(s) G(s)A(s)

4

6

O

4

4 7

HO

6 HO O

46

4 7

46

4 7 4

HOO

6 HO O

HO 66 O

6 HO O O

T(s) G(s)

HfpfjĶ-iumlavrcm trfesiar

inehscyneu ajba abcecz

G(s)gt

T(s)

d) r(t ) u(t ) ciumlce g( ) 6

njmfsĶ ciumlce H gt `asfp abcecz

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

4

6

4 7

6

HOO

G s 6 HO O

T s H O6 O

4

4 7

6

6 HO O O

4

6

4 7 6 4

4 7 6 4 7 6

4 74

HO 6O H6lt

6 HO O O HO s 6

6 HO O O H s 66 HO O O H 6 H 6lt H

s 1 s 66 HO O

6 6H 6lt H 6lt

G s H 6lt s 1s 6 s 6

s 6 s 1 s 6 H 6lt s s 6 s 1 H T s s 1 s 6 H 6lt s s 6 s 1 H6 H 6lt H

s 1 s 6 s 1 s 6

G s 6ltH s 1R s

T s s 1 s 6 6ltHs s 6 s 1 H

4 4

G s 6ltH s 1R sT s s s 1s 1 6ltHs 6ltHs Hs 1H

4

G s 6ltH s 1R s

T s 6ltH 6 s 66H 9 s 1 1H

G6-d

Wr (t ) u (t ) 6T(s)s

dujueur

W

t s lt s ltg( ) jcm g(t) g( ) jcm sG(s) jcm sR(s)T s

bcr

ļstaeae

s ltjcmsR(sg( )) 6T s

s lt 4

6ltH s 1 6

6ltH 6 s 66H

g( ) jcm s

s 1H

6

9 1 s

s ltjcm s

4

lt

lt

6ltH 1 6

6ltH 6 66H 9 1 1 slt H

6

H1lt6

1 1H

6

H 3

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7

W^4

G4-f

Wb6 a t Tc t J c t A s TC s JsC s

bt

6

C s A sJs T

W

m m4 i t h c t I s h C s

mI s h C s

4

W 4

4

b b7 i t hx t D x t M x t I s hP s DsP s Ms P s

bt bt

4

6P s I s

Ms Ds h

djnh bcyforfm

A(s) 6

Js T

C(s)hm

I(s) P(s)4

6

Ms Ds h

A(s)

m

4

h

Js T Ms Ds h

P(s)

m

4

P s h

A s Js T Ms Ds h

Sfebf varcjae huacutetja yfy va ajahtrnmĶheftĶs scstamceba ajahtrn

mĶheftĶs huvvatc mI(t) h c(t) njfrfh varcjmahtabcr

f- Wcstama fct bcefmch baehjamjarc yfzĶeĶz Hnetrnj djnh

bcyforfmĶeĶ ajba abcecz ( xy x(t) ugravejiumluacutejae hneum)

d-

r y raiarfes hneum ocrcŞc njmfh uacutezara fyrĶh-zfmfe sfyĶsfj

hfpfjĶ iumlavrcm hnetrnj djnh bcyforfmĶeĶ iumlczcecz

Ent Huacutetja yfy baeoaba

T J c(t)

a(t)Ajahtrn

mĶheftĶs

M

D h+ Y

x

yx

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

G4-d

A(s) P(s)sR6 a

s

[NBFG

B(z)P(z)

FBG

R

R

m

4

h

Js T Ms Ds h

W^7

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g) Dcrcm dfsfmfh ocrcŞ ciumlce g(h) ndash yĶ ajba abcecz va h=1 ciumlce g(h) yĶ `asfpjfyĶeĶz

G7-f

6

H

s 6 Baragabae mnbajce pfrfmatrajarc baeaysaj ynj cja ajba abcjagahtcr

FiumlĶh iumlavrcm hfzfeiuml H csa

lt01

lt016

iumlĶhĶŞ

ocrc Ş

v H

v

ajba abcjcr

FiumlĶh iumlavrcm zfmfe sfdctc csa lt974 lt174iumlĶhĶŞv ndashya baeh oajae zfmfe baĞarc njup dcrcm

dfsmfh gavfp aĞrcscebae 6lt se njfrfh nhueur

6 Baragabae trfesiar inehscyneuebf pfrfmatrajar yarjarcea hneursf

lt01

6lt 6O s

s

dujueur

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f) O(s) trfesiar inehscyneueu dujueuz

d) ugravereahjama zfmfeĶ R1

njmfh uacutezara

zfmfe sfdctc

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1

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6lt4

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66

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c

me

m

cm sR

c s s

b z P z s s P sm bs z a

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Rs

[N [N

a [ R s O s RO z [ z [

s s s s

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z

6

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lt6

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s

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6

s lt

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s

z

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6 6 6 6ltlt01 ltlt01 6lt 6lt

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z z z z z z RO z

z z a z a z z z

6

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z

z

lt060

z

z

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z

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6(z

s

z

z

dujueur

[N

G zRO z

T z

[NG z RO z T z

[N

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z ltG z RO z T z

060

z

z 6

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9

66

66

6( ) ( ) ( )

( 6) c

me

m h

cm z z

c

b x h z z P z z

m bz

lt6126z

z lt060 z 6g h [ G z [

g h z lt060

lt6126z

z lt060 h 6

z lt060

z z 6z 6

lt6126z

z lt060 z 6

h 6

z 6

z

h h

h lt6126 lt6lt060 6lt060

lt060 6

126g h lt01 6

6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

W^2 R= lt6 se ciumlce r(t) u(t) ciumlce G(z) ndashc ajba abcecz G( ) baĞarcec `asfp abcecz

T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

zn` s zn` s zn` sG s T s G s O s O s T s O s O s G s O s O s

zn` s zn` sG s T s O O s G s O O s

zn` s zn` sG s G s O O s T s O O s

6

zn` s

zn` s

G s O O s

T s O O s

6

zn` s

zn` s

G z O O z

T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj SĶj ļiumlc WĶefvĶ 62Ecsfe4lt66

W^6

FŞfĞĶbf varcjae Hnetrnj djnh bcyforfmĶebf6

6O (s)

s 6

4O (s) 6lt 7

sO (s)

s 1

njmfh uacutezara

varcjmahtabcr

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

G6-f

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

4

6

O

O (s)6

T(s) G(s)A(s)

4

6

O

4

4 7

HO

6 HO O

46

4 7

46

4 7 4

HOO

6 HO O

HO 66 O

6 HO O O

T(s) G(s)

HfpfjĶ-iumlavrcm trfesiar

inehscyneu ajba abcecz

G(s)gt

T(s)

d) r(t ) u(t ) ciumlce g( ) 6

njmfsĶ ciumlce H gt `asfp abcecz

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4

4

6

4 7

6

HOO

G s 6 HO O

T s H O6 O

4

4 7

6

6 HO O O

4

6

4 7 6 4

4 7 6 4 7 6

4 74

HO 6O H6lt

6 HO O O HO s 6

6 HO O O H s 66 HO O O H 6 H 6lt H

s 1 s 66 HO O

6 6H 6lt H 6lt

G s H 6lt s 1s 6 s 6

s 6 s 1 s 6 H 6lt s s 6 s 1 H T s s 1 s 6 H 6lt s s 6 s 1 H6 H 6lt H

s 1 s 6 s 1 s 6

G s 6ltH s 1R s

T s s 1 s 6 6ltHs s 6 s 1 H

4 4

G s 6ltH s 1R sT s s s 1s 1 6ltHs 6ltHs Hs 1H

4

G s 6ltH s 1R s

T s 6ltH 6 s 66H 9 s 1 1H

G6-d

Wr (t ) u (t ) 6T(s)s

dujueur

W

t s lt s ltg( ) jcm g(t) g( ) jcm sG(s) jcm sR(s)T s

bcr

ļstaeae

s ltjcmsR(sg( )) 6T s

s lt 4

6ltH s 1 6

6ltH 6 s 66H

g( ) jcm s

s 1H

6

9 1 s

s ltjcm s

4

lt

lt

6ltH 1 6

6ltH 6 66H 9 1 1 slt H

6

H1lt6

1 1H

6

H 3

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7

W^4

G4-f

Wb6 a t Tc t J c t A s TC s JsC s

bt

6

C s A sJs T

W

m m4 i t h c t I s h C s

mI s h C s

4

W 4

4

b b7 i t hx t D x t M x t I s hP s DsP s Ms P s

bt bt

4

6P s I s

Ms Ds h

djnh bcyforfm

A(s) 6

Js T

C(s)hm

I(s) P(s)4

6

Ms Ds h

A(s)

m

4

h

Js T Ms Ds h

P(s)

m

4

P s h

A s Js T Ms Ds h

Sfebf varcjae huacutetja yfy va ajahtrnmĶheftĶs scstamceba ajahtrn

mĶheftĶs huvvatc mI(t) h c(t) njfrfh varcjmahtabcr

f- Wcstama fct bcefmch baehjamjarc yfzĶeĶz Hnetrnj djnh

bcyforfmĶeĶ ajba abcecz ( xy x(t) ugravejiumluacutejae hneum)

d-

r y raiarfes hneum ocrcŞc njmfh uacutezara fyrĶh-zfmfe sfyĶsfj

hfpfjĶ iumlavrcm hnetrnj djnh bcyforfmĶeĶ iumlczcecz

Ent Huacutetja yfy baeoaba

T J c(t)

a(t)Ajahtrn

mĶheftĶs

M

D h+ Y

x

yx

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

G4-d

A(s) P(s)sR6 a

s

[NBFG

B(z)P(z)

FBG

R

R

m

4

h

Js T Ms Ds h

W^7

FyrĶh zfmfe fiumlĶh-iumlavrcm trfesiar inehscyneu O(z) ajba abcecz ([Nndash ju)

g) Dcrcm dfsfmfh ocrcŞ ciumlce g(h) ndash yĶ ajba abcecz va h=1 ciumlce g(h) yĶ `asfpjfyĶeĶz

G7-f

6

H

s 6 Baragabae mnbajce pfrfmatrajarc baeaysaj ynj cja ajba abcjagahtcr

FiumlĶh iumlavrcm hfzfeiuml H csa

lt01

lt016

iumlĶhĶŞ

ocrc Ş

v H

v

ajba abcjcr

FiumlĶh iumlavrcm zfmfe sfdctc csa lt974 lt174iumlĶhĶŞv ndashya baeh oajae zfmfe baĞarc njup dcrcm

dfsmfh gavfp aĞrcscebae 6lt se njfrfh nhueur

6 Baragabae trfesiar inehscyneuebf pfrfmatrajar yarjarcea hneursf

lt01

6lt 6O s

s

dujueur

Sfebf C Baragabae scstama fct fiumlĶh -iumlavrcm dcrcm dfsfmfh gavfdĶ varcjmcŞtcr

f) O(s) trfesiar inehscyneueu dujueuz

d) ugravereahjama zfmfeĶ R1

njmfh uacutezara

zfmfe sfdctc

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

G7-d

sR z a

6lt4

1 1R se

6

66

6( ) ( ) ( )( 6)

c

me

m

cm sR

c s s

b z P z s s P sm bs z a

6lt01 6 lt01 66

6lt 6 6lt lt6

Rs

[N [N

a [ R s O s RO z [ z [

s s s s

6

ltlt01 lt6 [N

z RO z s

z

6

lt6 s s

lt6

lt sR

s

z s

z a

6

s lt

lt6 sR

s

z

z a s

lt64 lt4

lt6 lt

6 6 6 6ltlt01 ltlt01 6lt 6lt

lt6 lt060 6 [N

z z z z z z RO z

z z a z a z z z

6

lt01 [N

z RO z

z

z

lt060

z

z

6 lt060 6lt01 6 lt01

6 lt060 lt060

z z z

z z z

lt6126

lt060 [N RO z

z

G7-g

OcrcŞ cŞfratc W z6r(t) u(t) T(s) T )

6(z

s

z

z

dujueur

[N

G zRO z

T z

[NG z RO z T z

[N

lt6126

z ltG z RO z T z

060

z

z 6

lt6126zG z

z lt060 z 6

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9

66

66

6( ) ( ) ( )

( 6) c

me

m h

cm z z

c

b x h z z P z z

m bz

lt6126z

z lt060 z 6g h [ G z [

g h z lt060

lt6126z

z lt060 h 6

z lt060

z z 6z 6

lt6126z

z lt060 z 6

h 6

z 6

z

h h

h lt6126 lt6lt060 6lt060

lt060 6

126g h lt01 6

6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

W^2 R= lt6 se ciumlce r(t) u(t) ciumlce G(z) ndashc ajba abcecz G( ) baĞarcec `asfp abcecz

T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

zn` s zn` s zn` sG s T s G s O s O s T s O s O s G s O s O s

zn` s zn` sG s T s O O s G s O O s

zn` s zn` sG s G s O O s T s O O s

6

zn` s

zn` s

G s O O s

T s O O s

6

zn` s

zn` s

G z O O z

T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj SĶj ļiumlc WĶefvĶ 62Ecsfe4lt66

W^6

FŞfĞĶbf varcjae Hnetrnj djnh bcyforfmĶebf6

6O (s)

s 6

4O (s) 6lt 7

sO (s)

s 1

njmfh uacutezara

varcjmahtabcr

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

G6-f

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

4

6

O

O (s)6

T(s) G(s)A(s)

4

6

O

4

4 7

HO

6 HO O

46

4 7

46

4 7 4

HOO

6 HO O

HO 66 O

6 HO O O

T(s) G(s)

HfpfjĶ-iumlavrcm trfesiar

inehscyneu ajba abcecz

G(s)gt

T(s)

d) r(t ) u(t ) ciumlce g( ) 6

njmfsĶ ciumlce H gt `asfp abcecz

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4

4

6

4 7

6

HOO

G s 6 HO O

T s H O6 O

4

4 7

6

6 HO O O

4

6

4 7 6 4

4 7 6 4 7 6

4 74

HO 6O H6lt

6 HO O O HO s 6

6 HO O O H s 66 HO O O H 6 H 6lt H

s 1 s 66 HO O

6 6H 6lt H 6lt

G s H 6lt s 1s 6 s 6

s 6 s 1 s 6 H 6lt s s 6 s 1 H T s s 1 s 6 H 6lt s s 6 s 1 H6 H 6lt H

s 1 s 6 s 1 s 6

G s 6ltH s 1R s

T s s 1 s 6 6ltHs s 6 s 1 H

4 4

G s 6ltH s 1R sT s s s 1s 1 6ltHs 6ltHs Hs 1H

4

G s 6ltH s 1R s

T s 6ltH 6 s 66H 9 s 1 1H

G6-d

Wr (t ) u (t ) 6T(s)s

dujueur

W

t s lt s ltg( ) jcm g(t) g( ) jcm sG(s) jcm sR(s)T s

bcr

ļstaeae

s ltjcmsR(sg( )) 6T s

s lt 4

6ltH s 1 6

6ltH 6 s 66H

g( ) jcm s

s 1H

6

9 1 s

s ltjcm s

4

lt

lt

6ltH 1 6

6ltH 6 66H 9 1 1 slt H

6

H1lt6

1 1H

6

H 3

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7

W^4

G4-f

Wb6 a t Tc t J c t A s TC s JsC s

bt

6

C s A sJs T

W

m m4 i t h c t I s h C s

mI s h C s

4

W 4

4

b b7 i t hx t D x t M x t I s hP s DsP s Ms P s

bt bt

4

6P s I s

Ms Ds h

djnh bcyforfm

A(s) 6

Js T

C(s)hm

I(s) P(s)4

6

Ms Ds h

A(s)

m

4

h

Js T Ms Ds h

P(s)

m

4

P s h

A s Js T Ms Ds h

Sfebf varcjae huacutetja yfy va ajahtrnmĶheftĶs scstamceba ajahtrn

mĶheftĶs huvvatc mI(t) h c(t) njfrfh varcjmahtabcr

f- Wcstama fct bcefmch baehjamjarc yfzĶeĶz Hnetrnj djnh

bcyforfmĶeĶ ajba abcecz ( xy x(t) ugravejiumluacutejae hneum)

d-

r y raiarfes hneum ocrcŞc njmfh uacutezara fyrĶh-zfmfe sfyĶsfj

hfpfjĶ iumlavrcm hnetrnj djnh bcyforfmĶeĶ iumlczcecz

Ent Huacutetja yfy baeoaba

T J c(t)

a(t)Ajahtrn

mĶheftĶs

M

D h+ Y

x

yx

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

G4-d

A(s) P(s)sR6 a

s

[NBFG

B(z)P(z)

FBG

R

R

m

4

h

Js T Ms Ds h

W^7

FyrĶh zfmfe fiumlĶh-iumlavrcm trfesiar inehscyneu O(z) ajba abcecz ([Nndash ju)

g) Dcrcm dfsfmfh ocrcŞ ciumlce g(h) ndash yĶ ajba abcecz va h=1 ciumlce g(h) yĶ `asfpjfyĶeĶz

G7-f

6

H

s 6 Baragabae mnbajce pfrfmatrajarc baeaysaj ynj cja ajba abcjagahtcr

FiumlĶh iumlavrcm hfzfeiuml H csa

lt01

lt016

iumlĶhĶŞ

ocrc Ş

v H

v

ajba abcjcr

FiumlĶh iumlavrcm zfmfe sfdctc csa lt974 lt174iumlĶhĶŞv ndashya baeh oajae zfmfe baĞarc njup dcrcm

dfsmfh gavfp aĞrcscebae 6lt se njfrfh nhueur

6 Baragabae trfesiar inehscyneuebf pfrfmatrajar yarjarcea hneursf

lt01

6lt 6O s

s

dujueur

Sfebf C Baragabae scstama fct fiumlĶh -iumlavrcm dcrcm dfsfmfh gavfdĶ varcjmcŞtcr

f) O(s) trfesiar inehscyneueu dujueuz

d) ugravereahjama zfmfeĶ R1

njmfh uacutezara

zfmfe sfdctc

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1

G7-d

sR z a

6lt4

1 1R se

6

66

6( ) ( ) ( )( 6)

c

me

m

cm sR

c s s

b z P z s s P sm bs z a

6lt01 6 lt01 66

6lt 6 6lt lt6

Rs

[N [N

a [ R s O s RO z [ z [

s s s s

6

ltlt01 lt6 [N

z RO z s

z

6

lt6 s s

lt6

lt sR

s

z s

z a

6

s lt

lt6 sR

s

z

z a s

lt64 lt4

lt6 lt

6 6 6 6ltlt01 ltlt01 6lt 6lt

lt6 lt060 6 [N

z z z z z z RO z

z z a z a z z z

6

lt01 [N

z RO z

z

z

lt060

z

z

6 lt060 6lt01 6 lt01

6 lt060 lt060

z z z

z z z

lt6126

lt060 [N RO z

z

G7-g

OcrcŞ cŞfratc W z6r(t) u(t) T(s) T )

6(z

s

z

z

dujueur

[N

G zRO z

T z

[NG z RO z T z

[N

lt6126

z ltG z RO z T z

060

z

z 6

lt6126zG z

z lt060 z 6

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9

66

66

6( ) ( ) ( )

( 6) c

me

m h

cm z z

c

b x h z z P z z

m bz

lt6126z

z lt060 z 6g h [ G z [

g h z lt060

lt6126z

z lt060 h 6

z lt060

z z 6z 6

lt6126z

z lt060 z 6

h 6

z 6

z

h h

h lt6126 lt6lt060 6lt060

lt060 6

126g h lt01 6

6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

W^2 R= lt6 se ciumlce r(t) u(t) ciumlce G(z) ndashc ajba abcecz G( ) baĞarcec `asfp abcecz

T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

zn` s zn` s zn` sG s T s G s O s O s T s O s O s G s O s O s

zn` s zn` sG s T s O O s G s O O s

zn` s zn` sG s G s O O s T s O O s

6

zn` s

zn` s

G s O O s

T s O O s

6

zn` s

zn` s

G z O O z

T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj SĶj ļiumlc WĶefvĶ 62Ecsfe4lt66

W^6

FŞfĞĶbf varcjae Hnetrnj djnh bcyforfmĶebf6

6O (s)

s 6

4O (s) 6lt 7

sO (s)

s 1

njmfh uacutezara

varcjmahtabcr

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

G6-f

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

O (s)6

O (s)4H

O (s)7

T(s) G(s)A(s)

4

6

O

O (s)6

T(s) G(s)A(s)

4

6

O

4

4 7

HO

6 HO O

46

4 7

46

4 7 4

HOO

6 HO O

HO 66 O

6 HO O O

T(s) G(s)

HfpfjĶ-iumlavrcm trfesiar

inehscyneu ajba abcecz

G(s)gt

T(s)

d) r(t ) u(t ) ciumlce g( ) 6

njmfsĶ ciumlce H gt `asfp abcecz

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

4

6

4 7

6

HOO

G s 6 HO O

T s H O6 O

4

4 7

6

6 HO O O

4

6

4 7 6 4

4 7 6 4 7 6

4 74

HO 6O H6lt

6 HO O O HO s 6

6 HO O O H s 66 HO O O H 6 H 6lt H

s 1 s 66 HO O

6 6H 6lt H 6lt

G s H 6lt s 1s 6 s 6

s 6 s 1 s 6 H 6lt s s 6 s 1 H T s s 1 s 6 H 6lt s s 6 s 1 H6 H 6lt H

s 1 s 6 s 1 s 6

G s 6ltH s 1R s

T s s 1 s 6 6ltHs s 6 s 1 H

4 4

G s 6ltH s 1R sT s s s 1s 1 6ltHs 6ltHs Hs 1H

4

G s 6ltH s 1R s

T s 6ltH 6 s 66H 9 s 1 1H

G6-d

Wr (t ) u (t ) 6T(s)s

dujueur

W

t s lt s ltg( ) jcm g(t) g( ) jcm sG(s) jcm sR(s)T s

bcr

ļstaeae

s ltjcmsR(sg( )) 6T s

s lt 4

6ltH s 1 6

6ltH 6 s 66H

g( ) jcm s

s 1H

6

9 1 s

s ltjcm s

4

lt

lt

6ltH 1 6

6ltH 6 66H 9 1 1 slt H

6

H1lt6

1 1H

6

H 3

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7

W^4

G4-f

Wb6 a t Tc t J c t A s TC s JsC s

bt

6

C s A sJs T

W

m m4 i t h c t I s h C s

mI s h C s

4

W 4

4

b b7 i t hx t D x t M x t I s hP s DsP s Ms P s

bt bt

4

6P s I s

Ms Ds h

djnh bcyforfm

A(s) 6

Js T

C(s)hm

I(s) P(s)4

6

Ms Ds h

A(s)

m

4

h

Js T Ms Ds h

P(s)

m

4

P s h

A s Js T Ms Ds h

Sfebf varcjae huacutetja yfy va ajahtrnmĶheftĶs scstamceba ajahtrn

mĶheftĶs huvvatc mI(t) h c(t) njfrfh varcjmahtabcr

f- Wcstama fct bcefmch baehjamjarc yfzĶeĶz Hnetrnj djnh

bcyforfmĶeĶ ajba abcecz ( xy x(t) ugravejiumluacutejae hneum)

d-

r y raiarfes hneum ocrcŞc njmfh uacutezara fyrĶh-zfmfe sfyĶsfj

hfpfjĶ iumlavrcm hnetrnj djnh bcyforfmĶeĶ iumlczcecz

Ent Huacutetja yfy baeoaba

T J c(t)

a(t)Ajahtrn

mĶheftĶs

M

D h+ Y

x

yx

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2

G4-d

A(s) P(s)sR6 a

s

[NBFG

B(z)P(z)

FBG

R

R

m

4

h

Js T Ms Ds h

W^7

FyrĶh zfmfe fiumlĶh-iumlavrcm trfesiar inehscyneu O(z) ajba abcecz ([Nndash ju)

g) Dcrcm dfsfmfh ocrcŞ ciumlce g(h) ndash yĶ ajba abcecz va h=1 ciumlce g(h) yĶ `asfpjfyĶeĶz

G7-f

6

H

s 6 Baragabae mnbajce pfrfmatrajarc baeaysaj ynj cja ajba abcjagahtcr

FiumlĶh iumlavrcm hfzfeiuml H csa

lt01

lt016

iumlĶhĶŞ

ocrc Ş

v H

v

ajba abcjcr

FiumlĶh iumlavrcm zfmfe sfdctc csa lt974 lt174iumlĶhĶŞv ndashya baeh oajae zfmfe baĞarc njup dcrcm

dfsmfh gavfp aĞrcscebae 6lt se njfrfh nhueur

6 Baragabae trfesiar inehscyneuebf pfrfmatrajar yarjarcea hneursf

lt01

6lt 6O s

s

dujueur

Sfebf C Baragabae scstama fct fiumlĶh -iumlavrcm dcrcm dfsfmfh gavfdĶ varcjmcŞtcr

f) O(s) trfesiar inehscyneueu dujueuz

d) ugravereahjama zfmfeĶ R1

njmfh uacutezara

zfmfe sfdctc

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1

G7-d

sR z a

6lt4

1 1R se

6

66

6( ) ( ) ( )( 6)

c

me

m

cm sR

c s s

b z P z s s P sm bs z a

6lt01 6 lt01 66

6lt 6 6lt lt6

Rs

[N [N

a [ R s O s RO z [ z [

s s s s

6

ltlt01 lt6 [N

z RO z s

z

6

lt6 s s

lt6

lt sR

s

z s

z a

6

s lt

lt6 sR

s

z

z a s

lt64 lt4

lt6 lt

6 6 6 6ltlt01 ltlt01 6lt 6lt

lt6 lt060 6 [N

z z z z z z RO z

z z a z a z z z

6

lt01 [N

z RO z

z

z

lt060

z

z

6 lt060 6lt01 6 lt01

6 lt060 lt060

z z z

z z z

lt6126

lt060 [N RO z

z

G7-g

OcrcŞ cŞfratc W z6r(t) u(t) T(s) T )

6(z

s

z

z

dujueur

[N

G zRO z

T z

[NG z RO z T z

[N

lt6126

z ltG z RO z T z

060

z

z 6

lt6126zG z

z lt060 z 6

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9

66

66

6( ) ( ) ( )

( 6) c

me

m h

cm z z

c

b x h z z P z z

m bz

lt6126z

z lt060 z 6g h [ G z [

g h z lt060

lt6126z

z lt060 h 6

z lt060

z z 6z 6

lt6126z

z lt060 z 6

h 6

z 6

z

h h

h lt6126 lt6lt060 6lt060

lt060 6

126g h lt01 6

6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

W^2 R= lt6 se ciumlce r(t) u(t) ciumlce G(z) ndashc ajba abcecz G( ) baĞarcec `asfp abcecz

T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

zn` s zn` s zn` sG s T s G s O s O s T s O s O s G s O s O s

zn` s zn` sG s T s O O s G s O O s

zn` s zn` sG s G s O O s T s O O s

6

zn` s

zn` s

G s O O s

T s O O s

6

zn` s

zn` s

G z O O z

T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

4

6

4 7

6

HOO

G s 6 HO O

T s H O6 O

4

4 7

6

6 HO O O

4

6

4 7 6 4

4 7 6 4 7 6

4 74

HO 6O H6lt

6 HO O O HO s 6

6 HO O O H s 66 HO O O H 6 H 6lt H

s 1 s 66 HO O

6 6H 6lt H 6lt

G s H 6lt s 1s 6 s 6

s 6 s 1 s 6 H 6lt s s 6 s 1 H T s s 1 s 6 H 6lt s s 6 s 1 H6 H 6lt H

s 1 s 6 s 1 s 6

G s 6ltH s 1R s

T s s 1 s 6 6ltHs s 6 s 1 H

4 4

G s 6ltH s 1R sT s s s 1s 1 6ltHs 6ltHs Hs 1H

4

G s 6ltH s 1R s

T s 6ltH 6 s 66H 9 s 1 1H

G6-d

Wr (t ) u (t ) 6T(s)s

dujueur

W

t s lt s ltg( ) jcm g(t) g( ) jcm sG(s) jcm sR(s)T s

bcr

ļstaeae

s ltjcmsR(sg( )) 6T s

s lt 4

6ltH s 1 6

6ltH 6 s 66H

g( ) jcm s

s 1H

6

9 1 s

s ltjcm s

4

lt

lt

6ltH 1 6

6ltH 6 66H 9 1 1 slt H

6

H1lt6

1 1H

6

H 3

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7

W^4

G4-f

Wb6 a t Tc t J c t A s TC s JsC s

bt

6

C s A sJs T

W

m m4 i t h c t I s h C s

mI s h C s

4

W 4

4

b b7 i t hx t D x t M x t I s hP s DsP s Ms P s

bt bt

4

6P s I s

Ms Ds h

djnh bcyforfm

A(s) 6

Js T

C(s)hm

I(s) P(s)4

6

Ms Ds h

A(s)

m

4

h

Js T Ms Ds h

P(s)

m

4

P s h

A s Js T Ms Ds h

Sfebf varcjae huacutetja yfy va ajahtrnmĶheftĶs scstamceba ajahtrn

mĶheftĶs huvvatc mI(t) h c(t) njfrfh varcjmahtabcr

f- Wcstama fct bcefmch baehjamjarc yfzĶeĶz Hnetrnj djnh

bcyforfmĶeĶ ajba abcecz ( xy x(t) ugravejiumluacutejae hneum)

d-

r y raiarfes hneum ocrcŞc njmfh uacutezara fyrĶh-zfmfe sfyĶsfj

hfpfjĶ iumlavrcm hnetrnj djnh bcyforfmĶeĶ iumlczcecz

Ent Huacutetja yfy baeoaba

T J c(t)

a(t)Ajahtrn

mĶheftĶs

M

D h+ Y

x

yx

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2

G4-d

A(s) P(s)sR6 a

s

[NBFG

B(z)P(z)

FBG

R

R

m

4

h

Js T Ms Ds h

W^7

FyrĶh zfmfe fiumlĶh-iumlavrcm trfesiar inehscyneu O(z) ajba abcecz ([Nndash ju)

g) Dcrcm dfsfmfh ocrcŞ ciumlce g(h) ndash yĶ ajba abcecz va h=1 ciumlce g(h) yĶ `asfpjfyĶeĶz

G7-f

6

H

s 6 Baragabae mnbajce pfrfmatrajarc baeaysaj ynj cja ajba abcjagahtcr

FiumlĶh iumlavrcm hfzfeiuml H csa

lt01

lt016

iumlĶhĶŞ

ocrc Ş

v H

v

ajba abcjcr

FiumlĶh iumlavrcm zfmfe sfdctc csa lt974 lt174iumlĶhĶŞv ndashya baeh oajae zfmfe baĞarc njup dcrcm

dfsmfh gavfp aĞrcscebae 6lt se njfrfh nhueur

6 Baragabae trfesiar inehscyneuebf pfrfmatrajar yarjarcea hneursf

lt01

6lt 6O s

s

dujueur

Sfebf C Baragabae scstama fct fiumlĶh -iumlavrcm dcrcm dfsfmfh gavfdĶ varcjmcŞtcr

f) O(s) trfesiar inehscyneueu dujueuz

d) ugravereahjama zfmfeĶ R1

njmfh uacutezara

zfmfe sfdctc

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1

G7-d

sR z a

6lt4

1 1R se

6

66

6( ) ( ) ( )( 6)

c

me

m

cm sR

c s s

b z P z s s P sm bs z a

6lt01 6 lt01 66

6lt 6 6lt lt6

Rs

[N [N

a [ R s O s RO z [ z [

s s s s

6

ltlt01 lt6 [N

z RO z s

z

6

lt6 s s

lt6

lt sR

s

z s

z a

6

s lt

lt6 sR

s

z

z a s

lt64 lt4

lt6 lt

6 6 6 6ltlt01 ltlt01 6lt 6lt

lt6 lt060 6 [N

z z z z z z RO z

z z a z a z z z

6

lt01 [N

z RO z

z

z

lt060

z

z

6 lt060 6lt01 6 lt01

6 lt060 lt060

z z z

z z z

lt6126

lt060 [N RO z

z

G7-g

OcrcŞ cŞfratc W z6r(t) u(t) T(s) T )

6(z

s

z

z

dujueur

[N

G zRO z

T z

[NG z RO z T z

[N

lt6126

z ltG z RO z T z

060

z

z 6

lt6126zG z

z lt060 z 6

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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9

66

66

6( ) ( ) ( )

( 6) c

me

m h

cm z z

c

b x h z z P z z

m bz

lt6126z

z lt060 z 6g h [ G z [

g h z lt060

lt6126z

z lt060 h 6

z lt060

z z 6z 6

lt6126z

z lt060 z 6

h 6

z 6

z

h h

h lt6126 lt6lt060 6lt060

lt060 6

126g h lt01 6

6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

W^2 R= lt6 se ciumlce r(t) u(t) ciumlce G(z) ndashc ajba abcecz G( ) baĞarcec `asfp abcecz

T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

zn` s zn` s zn` sG s T s G s O s O s T s O s O s G s O s O s

zn` s zn` sG s T s O O s G s O O s

zn` s zn` sG s G s O O s T s O O s

6

zn` s

zn` s

G s O O s

T s O O s

6

zn` s

zn` s

G z O O z

T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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7

W^4

G4-f

Wb6 a t Tc t J c t A s TC s JsC s

bt

6

C s A sJs T

W

m m4 i t h c t I s h C s

mI s h C s

4

W 4

4

b b7 i t hx t D x t M x t I s hP s DsP s Ms P s

bt bt

4

6P s I s

Ms Ds h

djnh bcyforfm

A(s) 6

Js T

C(s)hm

I(s) P(s)4

6

Ms Ds h

A(s)

m

4

h

Js T Ms Ds h

P(s)

m

4

P s h

A s Js T Ms Ds h

Sfebf varcjae huacutetja yfy va ajahtrnmĶheftĶs scstamceba ajahtrn

mĶheftĶs huvvatc mI(t) h c(t) njfrfh varcjmahtabcr

f- Wcstama fct bcefmch baehjamjarc yfzĶeĶz Hnetrnj djnh

bcyforfmĶeĶ ajba abcecz ( xy x(t) ugravejiumluacutejae hneum)

d-

r y raiarfes hneum ocrcŞc njmfh uacutezara fyrĶh-zfmfe sfyĶsfj

hfpfjĶ iumlavrcm hnetrnj djnh bcyforfmĶeĶ iumlczcecz

Ent Huacutetja yfy baeoaba

T J c(t)

a(t)Ajahtrn

mĶheftĶs

M

D h+ Y

x

yx

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

G4-d

A(s) P(s)sR6 a

s

[NBFG

B(z)P(z)

FBG

R

R

m

4

h

Js T Ms Ds h

W^7

FyrĶh zfmfe fiumlĶh-iumlavrcm trfesiar inehscyneu O(z) ajba abcecz ([Nndash ju)

g) Dcrcm dfsfmfh ocrcŞ ciumlce g(h) ndash yĶ ajba abcecz va h=1 ciumlce g(h) yĶ `asfpjfyĶeĶz

G7-f

6

H

s 6 Baragabae mnbajce pfrfmatrajarc baeaysaj ynj cja ajba abcjagahtcr

FiumlĶh iumlavrcm hfzfeiuml H csa

lt01

lt016

iumlĶhĶŞ

ocrc Ş

v H

v

ajba abcjcr

FiumlĶh iumlavrcm zfmfe sfdctc csa lt974 lt174iumlĶhĶŞv ndashya baeh oajae zfmfe baĞarc njup dcrcm

dfsmfh gavfp aĞrcscebae 6lt se njfrfh nhueur

6 Baragabae trfesiar inehscyneuebf pfrfmatrajar yarjarcea hneursf

lt01

6lt 6O s

s

dujueur

Sfebf C Baragabae scstama fct fiumlĶh -iumlavrcm dcrcm dfsfmfh gavfdĶ varcjmcŞtcr

f) O(s) trfesiar inehscyneueu dujueuz

d) ugravereahjama zfmfeĶ R1

njmfh uacutezara

zfmfe sfdctc

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

G7-d

sR z a

6lt4

1 1R se

6

66

6( ) ( ) ( )( 6)

c

me

m

cm sR

c s s

b z P z s s P sm bs z a

6lt01 6 lt01 66

6lt 6 6lt lt6

Rs

[N [N

a [ R s O s RO z [ z [

s s s s

6

ltlt01 lt6 [N

z RO z s

z

6

lt6 s s

lt6

lt sR

s

z s

z a

6

s lt

lt6 sR

s

z

z a s

lt64 lt4

lt6 lt

6 6 6 6ltlt01 ltlt01 6lt 6lt

lt6 lt060 6 [N

z z z z z z RO z

z z a z a z z z

6

lt01 [N

z RO z

z

z

lt060

z

z

6 lt060 6lt01 6 lt01

6 lt060 lt060

z z z

z z z

lt6126

lt060 [N RO z

z

G7-g

OcrcŞ cŞfratc W z6r(t) u(t) T(s) T )

6(z

s

z

z

dujueur

[N

G zRO z

T z

[NG z RO z T z

[N

lt6126

z ltG z RO z T z

060

z

z 6

lt6126zG z

z lt060 z 6

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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9

66

66

6( ) ( ) ( )

( 6) c

me

m h

cm z z

c

b x h z z P z z

m bz

lt6126z

z lt060 z 6g h [ G z [

g h z lt060

lt6126z

z lt060 h 6

z lt060

z z 6z 6

lt6126z

z lt060 z 6

h 6

z 6

z

h h

h lt6126 lt6lt060 6lt060

lt060 6

126g h lt01 6

6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

W^2 R= lt6 se ciumlce r(t) u(t) ciumlce G(z) ndashc ajba abcecz G( ) baĞarcec `asfp abcecz

T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

zn` s zn` s zn` sG s T s G s O s O s T s O s O s G s O s O s

zn` s zn` sG s T s O O s G s O O s

zn` s zn` sG s G s O O s T s O O s

6

zn` s

zn` s

G s O O s

T s O O s

6

zn` s

zn` s

G z O O z

T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1820

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1920

2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 2020

1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1220

2

G4-d

A(s) P(s)sR6 a

s

[NBFG

B(z)P(z)

FBG

R

R

m

4

h

Js T Ms Ds h

W^7

FyrĶh zfmfe fiumlĶh-iumlavrcm trfesiar inehscyneu O(z) ajba abcecz ([Nndash ju)

g) Dcrcm dfsfmfh ocrcŞ ciumlce g(h) ndash yĶ ajba abcecz va h=1 ciumlce g(h) yĶ `asfpjfyĶeĶz

G7-f

6

H

s 6 Baragabae mnbajce pfrfmatrajarc baeaysaj ynj cja ajba abcjagahtcr

FiumlĶh iumlavrcm hfzfeiuml H csa

lt01

lt016

iumlĶhĶŞ

ocrc Ş

v H

v

ajba abcjcr

FiumlĶh iumlavrcm zfmfe sfdctc csa lt974 lt174iumlĶhĶŞv ndashya baeh oajae zfmfe baĞarc njup dcrcm

dfsmfh gavfp aĞrcscebae 6lt se njfrfh nhueur

6 Baragabae trfesiar inehscyneuebf pfrfmatrajar yarjarcea hneursf

lt01

6lt 6O s

s

dujueur

Sfebf C Baragabae scstama fct fiumlĶh -iumlavrcm dcrcm dfsfmfh gavfdĶ varcjmcŞtcr

f) O(s) trfesiar inehscyneueu dujueuz

d) ugravereahjama zfmfeĶ R1

njmfh uacutezara

zfmfe sfdctc

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

G7-d

sR z a

6lt4

1 1R se

6

66

6( ) ( ) ( )( 6)

c

me

m

cm sR

c s s

b z P z s s P sm bs z a

6lt01 6 lt01 66

6lt 6 6lt lt6

Rs

[N [N

a [ R s O s RO z [ z [

s s s s

6

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z RO z s

z

6

lt6 s s

lt6

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s

z s

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6

s lt

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s

z

z a s

lt64 lt4

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6 6 6 6ltlt01 ltlt01 6lt 6lt

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z z z z z z RO z

z z a z a z z z

6

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z

z

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z

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OcrcŞ cŞfratc W z6r(t) u(t) T(s) T )

6(z

s

z

z

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T z

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z ltG z RO z T z

060

z

z 6

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z lt060 z 6

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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9

66

66

6( ) ( ) ( )

( 6) c

me

m h

cm z z

c

b x h z z P z z

m bz

lt6126z

z lt060 z 6g h [ G z [

g h z lt060

lt6126z

z lt060 h 6

z lt060

z z 6z 6

lt6126z

z lt060 z 6

h 6

z 6

z

h h

h lt6126 lt6lt060 6lt060

lt060 6

126g h lt01 6

6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

W^2 R= lt6 se ciumlce r(t) u(t) ciumlce G(z) ndashc ajba abcecz G( ) baĞarcec `asfp abcecz

T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

zn` s zn` s zn` sG s T s G s O s O s T s O s O s G s O s O s

zn` s zn` sG s T s O O s G s O O s

zn` s zn` sG s G s O O s T s O O s

6

zn` s

zn` s

G s O O s

T s O O s

6

zn` s

zn` s

G z O O z

T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1320

1

G7-d

sR z a

6lt4

1 1R se

6

66

6( ) ( ) ( )( 6)

c

me

m

cm sR

c s s

b z P z s s P sm bs z a

6lt01 6 lt01 66

6lt 6 6lt lt6

Rs

[N [N

a [ R s O s RO z [ z [

s s s s

6

ltlt01 lt6 [N

z RO z s

z

6

lt6 s s

lt6

lt sR

s

z s

z a

6

s lt

lt6 sR

s

z

z a s

lt64 lt4

lt6 lt

6 6 6 6ltlt01 ltlt01 6lt 6lt

lt6 lt060 6 [N

z z z z z z RO z

z z a z a z z z

6

lt01 [N

z RO z

z

z

lt060

z

z

6 lt060 6lt01 6 lt01

6 lt060 lt060

z z z

z z z

lt6126

lt060 [N RO z

z

G7-g

OcrcŞ cŞfratc W z6r(t) u(t) T(s) T )

6(z

s

z

z

dujueur

[N

G zRO z

T z

[NG z RO z T z

[N

lt6126

z ltG z RO z T z

060

z

z 6

lt6126zG z

z lt060 z 6

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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9

66

66

6( ) ( ) ( )

( 6) c

me

m h

cm z z

c

b x h z z P z z

m bz

lt6126z

z lt060 z 6g h [ G z [

g h z lt060

lt6126z

z lt060 h 6

z lt060

z z 6z 6

lt6126z

z lt060 z 6

h 6

z 6

z

h h

h lt6126 lt6lt060 6lt060

lt060 6

126g h lt01 6

6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

W^2 R= lt6 se ciumlce r(t) u(t) ciumlce G(z) ndashc ajba abcecz G( ) baĞarcec `asfp abcecz

T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

zn` s zn` s zn` sG s T s G s O s O s T s O s O s G s O s O s

zn` s zn` sG s T s O O s G s O O s

zn` s zn` sG s G s O O s T s O O s

6

zn` s

zn` s

G s O O s

T s O O s

6

zn` s

zn` s

G z O O z

T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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9

66

66

6( ) ( ) ( )

( 6) c

me

m h

cm z z

c

b x h z z P z z

m bz

lt6126z

z lt060 z 6g h [ G z [

g h z lt060

lt6126z

z lt060 h 6

z lt060

z z 6z 6

lt6126z

z lt060 z 6

h 6

z 6

z

h h

h lt6126 lt6lt060 6lt060

lt060 6

126g h lt01 6

6 lt060

h g h lt01 6 lt060

1g lt01 6 1 lt060

g 1 lt177

W^2 R= lt6 se ciumlce r(t) u(t) ciumlce G(z) ndashc ajba abcecz G( ) baĞarcec `asfp abcecz

T(s)[N

G(s)6

6 s

G2

T(s)[N

G(s)6

6 s

A(s)

Os(s)

A s T s G s A s T s G s

zn` s zn` s zn` sG s T s G s O s O s T s O s O s G s O s O s

zn` s zn` sG s T s O O s G s O O s

zn` s zn` sG s G s O O s T s O O s

6

zn` s

zn` s

G s O O s

T s O O s

6

zn` s

zn` s

G z O O z

T z O O z

bnĞrubfe yfzĶjfdcjcr (IumlĶhfrĶm dcjoc fmfiumljĶ varcjmcŞtcr)

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

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4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1820

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1920

2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 2020

1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1520

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1620

6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1720

4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1820

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1920

2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 2020

1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1620

6

Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664

W6)

W4)

W7)

i T

i J

i c

i a (t)

fc =sdt

K

w

R y

SuhfrĶbf fjfe hnetrnjjuacute BG-mfhcea sfyĶsfj cŞjamgc ouacuteiuml huvvatjaebcrcgc H va `Ķz ugravejiumlar Hv varcjmahtabcr

fyrĶh-zfmfe sfyĶsfj `Ķz hnetrnjuacute oariumlahjaŞtcrcjmah cstaemahtabcr (Ycshnz suacutertuacuteemaD = lt

)983142) 983112983142983164983142983146Ķ 983279983137983161983156983139983149 983164983156983137983141983159983139983164 983144983150983141983154983156983150983146 983138983137983161983156983137983159983139983141983139 983279983139983163983139983141983139983163

983140) 983127983139983159983154983137983149983137 983142983139983154 983154983085983138983150983149983137983141983139 983138983137983141983144983146983137983149983146983137983156983139 983155983142983163Ķ983141Ķ983163 983104983137983156 983140983139983156 983140983146983150983144 983154983156983142983141983159983145983137983156 983145983150983141983144983159983139983155983150983141983146983142983156Ķ983141Ķ 983137983146983138983137 983137983138983137983156983137983144 983144983142983164983142983146Ķ 983279983137983161983156983139983149

983144983150983141983154983156983150983146 983140983146983150983144 983138983139983155983142983151983156983142983149Ķ983141Ķ 983279983139983163983139983141983139983163

W2)

66

66

6( ) ( ) ( )

( 6) c

mem h

cm z zc

b x hR z z P z z

m bz

∔

∔

∔ ==

= ∔ ∔

∖ 6

66

6( ) ( ) ( )

( 6)c

mem

cm sR c s s

b z P z s s P s

m bs z a

∔

∔

= =

= ∔

∔ ∔ ∖

yfebf varcjae scstam ciumlce

f)

R=lt6s

d) ( ) ( )t t r u= va Hb =6 ciumlce8 c) g(h) = g(hR) = gt

cc) ( ) ( )jcmh

h g gharr∕

∕ = va6

( ) ( )( 6)jcm z

z zg G harr

∕ = ∔ cifbajarcec `asfpjfyĶeĶz

g) g(∕) = lt0 njfdcjmasc ciumlce Hb = gt

Wuacutera 6ltltbh983108983142Ş983142983156Ķ983146983142983156991273

983106983150983279983106983156983110983155983136983142983141 983257983131983106983105983117ļ983124 983085 983123983156983138983106983150983279983106983156ļ983156983145983142983141 983123983110983131983107983111983107

yfebf varcjae scstam ciumlce

c) bcefmch baehjamjarc yfzĶeĶz

cc)

Sfebf varcjae hnetrnj scstamceba983142) 983108983150983163983153983143983153 983151983139983156983139Ş983139 983106(983159) 983139983279983139983141 983279Ķ983144ĶŞ 983143983137983161983142983140Ķ983141Ķ 983137983146983138983137

983137983138983139983141983139983163

983140) ( )6

6

O s

s

=

+ ( ) 6 s = 983161983137 ( )

6 B s

s

= 983150983146983138983153Ğ983153983141983142

983151983289983156983137 983140983150983163983153983143983153 983151983139983156983139Ş 983106(983159) 983139983279983139983141 983143983137983161983142983140Ķ983141 983159Ķ983145Ķ983156

983150983146983142983140983139983146983149983137983159983139 983139983279983139983141 983112991251983155Ķ 983136983137983159983142983164983146983142983155Ķ983141Ķ983163 983122983101lt41

4

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1720

4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1820

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1920

2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 2020

1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1720

4

G6

f) 6lt6lt6 6

( )lt1

6

lt1 lt16 lt1

6 lt3lt1sR R s

zO [ s

z z zs

s z a z a z∔

= =∔

= =

+

+ = =

+ ∔ ∔ ∔

d) ( ) ( )lt1

lt1 lt3lt1b

b

z zH

G TH

z

z z=

+ ∔ ( ) ( ) ( )

6t t zr u T

z

zhArr= =

∔ ciumlce

4

( )lt1

( 6)(61 lt3lt1) zG

z

z z=

∔ ∔

44

6 6

lt9lt7

6

( )

lt1lt77761( 6) ( lt9lt7)

lt3lt1 ( 6)( lt9lt7)

( 6)( )61

h h

z

z

h g

z z

z z z z z z

z z

∔ ∔

=

=

= ∔ + ∔∔ ∔

∔ ∔

( )lt777 lt777lt9lt7

lt9lt7 lt073 lt1lt9 lt9lt7lt73 (lt9lt7 6)

h h h g = + = ∔

∔

cc)4 4

6 6( ) ( )

lt1 lt16jcm( 6) jcm( 6) lt02

( 6)(61 lt3lt1) (616 lt3lt1) z z zg

z z G z

z zharr harr

∕ = ∔ = ∔ = =∔ ∔ ∔

( ) ( )jcm jcm(lt073 lt1lt9lt9lt7 ) lt073h

h h h g g

harr∕ harr∕

∕ = = ∔ =

g) ( )lt1

lt1 lt3lt1 6b

b

zH

G H

z z

z z z=

+ ∔ ∔

4

6( ) ( )

lt1jcm( 6)

lt1 lt3lt1b

zb

zH

gH

z z G

z zharr

∕ = ∔ =+ ∔

lt1lt0

6 lt1 lt3lt1b

b

H

H = hArr

+ ∔ lt9 lt2 lt1b b

H H + = hArr 9b H =

G4) c- Yarcjae scstamba

H6 va D6 ajamfejfrĶ haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x(t)ndashya sf`cptcrjar FyeĶ Şahcjba H4 D4 va M ajamfejfrĶ bf haebc frfjfrĶebf sarc dfĞjĶbĶr fyeĶ yar baĞcŞtcrma x6(t)ndashyasf`cptcrjar

Warc dfĞjĶ mahfech ajamfejfrf athc abae huvvat ajamfejfrĶe huvvatjarc tnpjfmfbĶr

cc- H6 D6 ajamfejfrĶ H4 D4 M mahfech ajamfejfrĶ cja pfrfjaj dfĞjĶbĶr frfjaj dfĞjĶ mahfechajamfejfrf fyeĶ huvvat athc abar

c-) va cc-) ba varcjae dcjocjar ĶŞĶĞĶ fjtĶebf fŞfĞĶbfhc cifbajar yfzĶjĶr

H6 va D6 ajamfejfrĶef athc abae huvvat 6 6

( )h D

t I I I = +

bcr

H4 D4 va M ajamfejfrĶef athc abae huvvat 4 4( ) m h Dt I I I I = + +

bcr

( )( )

( ) ( )6

lt1

lt1lt3lt1lt1 lt1 lt3lt16lt3lt1

b b b

b b b

z z

z z

H H O H G

T H O H H

z

z z z z z

z

= =

+

∔ =+ ∔

+∔

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1820

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1920

2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 2020

1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1820

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1920

2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 2020

1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

z

[ s s zO s zs

= =

+ ∔ + =

4

lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

sHBO z [ HB s O s

zs

s z

= =

+ ∔ + =

( 6) lt

( ) ( 0

) )0

( H z [ H

sHO z [ HO s s

z

= =

∔=

+

6

( 6) lt00( ) ( )O

s [ [

z z s

zO

= =

∔ =

+

4

4

lt4446

lt4446 63 lt0063 lt00 lt006

lt

( )( ) ( ) ( )6 ( )

00

HBO zG z

z

H z z z z z z z z

H

BO z O zHO

z

z

∔ +∔

∔ + ∔+

+

∔

= ∔ =

4

4

4

lt4446lt4446 63 lt00

63 lt00 lt( )

00G z

zH

z z z

z z z Hz

∔ +∔

∔ + ∔ +=

983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 1920

2

6-)( )

( ) ( ) ( ) ( ) i

i i i i i i

i i

A s A s T C s sJ C s C s

sJ T= + hArr =

+

4-) ( ) ( )a c i R s H C s=

7-)( ) ( )

( ) ( ) ( ) ( ) m y

m y

R s R sR s sK s R s s

sK

∔= + hArr =

2-) ( ) ( )a mR s R s= (suacuterahjc rakcmba)

2f) Yarcjae hnetrnj djnh bcyforfmĶ T(s)=lt ciumlce fŞfĞĶbf varcjbcĞc ocdc yaecbae buacutezaejaecr

d) SuhfrĶbf ajba abcjae hnetrnj djnh bcyforfm yfrbĶmĶ cja B(s) ocrcŞ ciumlce G(z) ajba abcjcr

6 ( ) ( ) ( ) P s B s S s= ∔

( )4 ( ) ( ) ( ) ( ) ( ) () )( G s B s O s S sG s P s O s c a r Os s bc= ∔=

7 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ s G s s csa [ s B s O s s S s O s s bcr = = ∔

va ( ) ( ) ( ) ( ) [ s BO s S r s O s bc= ∔

2 ( ) ( ) ( ) ( ) ( ) ( ) S s HBS s H[ s O s HS s O cs csa b r == ∔

Ajba abcjae cifba

( )S s ciumlce buacutezaejaecr

( )( )

6 ( )

HBO sS s

HO s=

+ va 4 enju baehjamba yarcea hnyujur

( )( ) ( ) ( ) ( )

6 ( )

HBO sG s B s O s O s

HO s= ∔

+ yĶjbĶzjfeĶr csa

( )( ) ( ) ( )

6 ( )

HBO sG s BO s O s

HO s= ∔

+ va

( )( ) ( ) ( )6 ( )HBO zG z BO z O z

HO z= ∔

+ njfrfh yfzĶjĶr

8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 2020

1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

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lt( ) ( ) ( )

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lt4446

lt4446 63 lt0063 lt00 lt006

lt

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lt4446lt4446 63 lt00

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983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler

httpslidepdfcomreaderfullotomatik-kontrol-sakarya-ueniversitesi-vizeler 2020

1

983140983075 983122983101lt41 983159983141 983161983137 983136983137983156 983140983139983156 983140983139983146983137Ş983137983141 983139983279983139983141 983163983085983138983289983141983290Ş983290983149983146983137983156983139 983136983137983159983142983164983146983142983141Ķ983156

4

6 lt4446

( 6) 63 lt( ) ( ) 0) 0( BO z [ B

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= =

+ ∔ + =

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lt( ) ( ) ( )

4446

( 6) 63 lt 0(

0)

H z [ H

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lt4446lt4446 63 lt00

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983111(983163) 983139983145983142983138983137983159983139 983149983137983161983143983153983154 983154983150983164983150983146983150983147983139 983139983146983137 983108983150983163983153983143983153 983151983139983156983139Ş983139 983112 983144983142983163983142983141983143Ķ 983139983146983137 983279Ķ983144ĶŞ983154983142 983159Ķ983145Ķ983156983146983142983141983142983149983142983163 H = ∕ 983150983146983159983142 983138983142983136983139 ( ) ltG ∕ =

983150983146983149983142983163