otomatik kontrol - sakarya Üniversitesi vizeler
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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler
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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
HsR
RHs +
-
m6
sR a
s
u A 6
T sJlt6
C I
4
( ) I s
Ms Ds H
S(s)yr (t) 6
d) m(hR)= 7a(hR)-4aX(h-6)R]+6ltmX(h-6)R]+mX(h-2)R]
4
4
6) ( ) ( )
( )4) ( ) ( )
7) ( ) lt6 ( )
2) ( )
a t H u t
bc t a t Tc t J
bt
I t c t
b x bx M I Hx D
bt bt
M
4
4
b x M
bt
Hx bx
Dbt
I
) ( ) ( )
) ( ) ( )
) ( ) ( ) ( )
rai s r
s
`ftf rai
c P t H y t
cc x t H y t
ccc a t P t x t
4
4
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( )4) ( ) ( ) ( ) ( )
7) ( ) lt6 ( )
( )2) ( ) X ] ( ) ( )
A s H u s
A s A s T C s sJ C s C s
T sJ
I s C s
I s I s Ms Ds H S s S s
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( )
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)
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
-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
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
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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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∕
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g) ( )lt1
lt1 lt3lt1 6b
b
zH
G H
z z
z z z=
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4
6( ) ( )
lt1jcm( 6)
lt1 lt3lt1b
zb
zH
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z z G
z zharr
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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
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t I I I = +
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lt1
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b b b
b b b
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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
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+
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( ) ( ) ( ) ( ) 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
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6 lt4446
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lt4446 63 lt0063 lt00 lt006
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z
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H
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4
4
4
lt4446lt4446 63 lt00
63 lt00 lt( )
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zH
z z z
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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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NRNMFRļH HNERTNJ SCJļIumlļ WCEFYC GAYFJFT lt0lt24ltlt3
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R
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m(h)
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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler
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G-4)
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0
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G(t)
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6 lt lt2( )
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s
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6( ) lt lt2
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va frf cŞjamjara bavfm abcjcr csa
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z
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Wnru 7-
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Baehjamcece hugravehjarc hftjĶ va raaj njmfjĶbĶr
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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
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HO
6 HO O
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46
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HOO
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HO 66 O
6 HO O O
T(s) G(s)
HfpfjĶ-iumlavrcm trfesiar
inehscyneu ajba abcecz
G(s)gt
T(s)
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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
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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
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G6-d
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t s lt s ltg( ) jcm g(t) g( ) jcm sG(s) jcm sR(s)T s
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s ltjcmsR(sg( )) 6T s
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g( ) jcm s
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lt
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7
W^4
G4-f
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bt
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C s A sJs T
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m m4 i t h c t I s h C s
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bt bt
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6P s I s
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Js T
C(s)hm
I(s) P(s)4
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A(s)
m
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P(s)
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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
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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler
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2
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s 6 Baragabae mnbajce pfrfmatrajarc baeaysaj ynj cja ajba abcjagahtcr
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iumlĶhĶŞ
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v
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1
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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler
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9
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g 1 lt177
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T(s)[N
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6
Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664
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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
= =
+
∔ =+ ∔
+∔
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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
= =
∔ =
+
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
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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
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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
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z
z
4lt
z 4lt
6
z
z
4lt 4lt
6lt0 6
R R
z
z a z a
lt621( )
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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
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Wnru 7-
kw
k0292
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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
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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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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
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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
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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
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6lt4
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6
66
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c
me
m
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c s s
b z P z s s P sm bs z a
6lt01 6 lt01 66
6lt 6 6lt lt6
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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
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s lt
lt6 sR
s
z
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lt64 lt4
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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
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z
z
lt060
z
z
6 lt060 6lt01 6 lt01
6 lt060 lt060
z z z
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lt6126
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6(z
s
z
z
dujueur
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T z
[NG z RO z T z
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9
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h lt6126 lt6lt060 6lt060
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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
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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
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zn` s
zn` s
G z O O z
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6
Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664
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W4)
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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
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( )lt1
6
lt1 lt16 lt1
6 lt3lt1sR R s
zO [ s
z z zs
s z a z a z∔
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+
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d) ( ) ( )lt1
lt1 lt3lt1b
b
z zH
G TH
z
z z=
+ ∔ ( ) ( ) ( )
6t t zr u T
z
zhArr= =
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4
( )lt1
( 6)(61 lt3lt1) zG
z
z z=
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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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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
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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
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+
6
( 6) lt00( ) ( )O
s [ [
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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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+
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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
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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( )
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6
4lt
sR
s
z
z a
6ltlt2
z
z
4lt
z 4lt
6
z
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z
z a z a
lt621( )
lt060O z
z
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6 lt060
z G z T z O z
z z
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z G z z z
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( 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
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Wnru 7-
kw
k0292
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6ltlt( )6
6262
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s s H s s
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H
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6262 6ltlt lt s s H
Baehjamcece hugravehjarc hftjĶ va raaj njmfjĶbĶr
4
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d f g
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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
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lt
lt
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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
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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
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c
me
m
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z z z z z z RO z
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9
66
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z lt060
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h 6
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z
h h
h lt6126 lt6lt060 6lt060
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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
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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
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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
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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
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6
lt1 lt16 lt1
6 lt3lt1sR R s
zO [ s
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s z a z a z∔
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+
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+ ∔ ∔ ∔
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lt1 lt3lt1b
b
z zH
G TH
z
z z=
+ ∔ ( ) ( ) ( )
6t t zr u T
z
zhArr= =
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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
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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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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
( )( ) ( ) ( ) ( )
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HBO sG s B s O s O s
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( )( ) ( ) ( )
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+ 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
= =
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4
lt( ) ( ) ( )
4446
( 6) 63 lt 0(
0)
H z [ H
sHBO z [ HB s O s
zs
s z
= =
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( 6) lt
( ) ( 0
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( 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
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∔ + ∔+
+
∔
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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
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Wnru 7-
kw
k0292
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4
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6262
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H T s
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4 4626 2 6ltlt 626 2 6ltlt 646 96
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s s H s s
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Baehjamcece hugravehjarc hftjĶ va raaj njmfjĶbĶr
4
4
lt 2
626 2 2 6 6ltlt lt 2330
d f g
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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
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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
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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
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6
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c
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m
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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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z a
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
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8102019 Otomatik Kontrol - Sakarya Uumlniversitesi Vizeler
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9
66
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c
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h lt6126 lt6lt060 6lt060
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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
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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)
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6
Ntnmftch Hnetrnj Ycza WĶefvĶ 4lt74lt664
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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
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( )lt1
6
lt1 lt16 lt1
6 lt3lt1sR R s
zO [ s
z z zs
s z a z a z∔
= =∔
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+
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+ ∔ ∔ ∔
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lt1 lt3lt1b
b
z zH
G TH
z
z z=
+ ∔ ( ) ( ) ( )
6t t zr u T
z
zhArr= =
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4
( )lt1
( 6)(61 lt3lt1) zG
z
z z=
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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
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lt1 lt3lt1b
zb
zH
gH
z z G
z zharr
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lt1lt0
6 lt1 lt3lt1b
b
H
H = hArr
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H H + = hArr 9b H =
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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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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
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+ 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
= =
∔ =
+
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
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
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6
H1lt6
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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
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
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z
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s
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s lt
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z z z z z z RO z
z z a z a z z z
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lt060
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6 lt060 6lt01 6 lt01
6 lt060 lt060
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6(z
s
z
z
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T z
[NG z RO z T z
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z ltG z RO z T z
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z
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9
66
66
6( ) ( ) ( )
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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
= =
+
∔ =+ ∔
+∔
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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
= =
∔ =
+
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
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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
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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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
= =
∔ =
+
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
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
= =
+
∔ =+ ∔
+∔
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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
= =
∔ =
+
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
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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
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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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
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
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
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
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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
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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
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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
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
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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
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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 RO z
z
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6 lt060 6lt01 6 lt01
6 lt060 lt060
z z z
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z
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z ltG z RO z T z
060
z
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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
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 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
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
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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 1420
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
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
( 6) 63 lt( ) ( ) 0) 0( BO z [ B
z
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4
lt( ) ( ) ( )
4446
( 6) 63 lt 0(
0)
H z [ H
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( 6) lt00( ) ( )O
s [ [
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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
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4
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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 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
= =
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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
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z
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∔ + ∔+
+
∔
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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