kuliah dasar sistem kendali 6
TRANSCRIPT
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Dasar Sistem Kontrol
06:
Steady state errors
DWI ANA RATNA WATI
Department of Electrical [email protected]
mailto:[email protected]:[email protected] -
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Isi
definisi steady state errorkonstanta static error
static errors sistem dengan pengendali
static errors sistem sero
static errors sistem dengan pengganggu
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Steady state erroradala" selisi" antara input
dan output saat
Definisi steady state error
t
Jika se#ua" sistem stabil:
tmakarespon alamianya mendekati0 saat
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Klasifikasi sistem kontrol
( ) ( ) ( )
( ) ( ) ( )111
111)(
21 ++++
++++=
sTsTsTs
sTsTsTKsG
p
N
mba
Sistem kontrol dengan umpan #alik memiliki fungsi ali"loop ter#uka G%s&
dise#ut sistem tipe N'
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Steady state error
)(sR )(sC)(sE)(sG
)(1)(
)()(
sGsG
sRsC
+
=
)()(1
1
)(1
)()()()()()( sR
sGsG
sGsRsRsCsRsE
+
=
+
==
)(1
)(lim)(lim)(lim
00 sG
ssRssEtee
sstss
+
===
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Static position error constant Kp
Steady)state error untuk input unit!stepadala"
)0(1
11
)(1lim
)(1
)(lim
00 GssG
s
sG
ssRe
ssss
+
=
+
=
+
=
Static position error constant Kpdidefinisikan :
)0()(lim0
GsGKs
p ==
p
ssK
e+
=
1
1
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Static position error constant Kp
+or a type 0 system
( ) ( )
( )( ) K
sTsT
sTsTKK ba
sp =
++
++=
...11
...11lim
210
+or a type 1 or "ig"er system
( ) ( )
( ) ( )
=
++
++=
...11
...11lim
21
0
sTsTs
sTsTKK
N
ba
sp
Kess
+
=
1
1
0=sse
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Static elocity error constant Kv
Steady)state error untuk input unit!rampadala"
)(
1lim
1
)(1lim
)(1
)(lim
0200 ssGssG
s
sG
ssRe
sssss
=
+
=
+
=
Static elocity error constant Kdidefinisikan :
)(lim0
ssGKs
v
=
v
ssK
e 1=
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Static elocity error constant Kv
.ntuk sistem tipe nol
( )( )
( ) ( ) 0
...11
...11lim
210
=
++
++=
sTsT
sTsTsKK ba
sv
.ntuk sistem tipe satu
( )( )
( ) ( ) K
sTsTs
sTsTKsK ba
sv =
++
++=
...11
...11lim
210
=sse
Kess
1=
.ntuk sistem tipe dua dan yang le#i" tinggi
( ) ( )
( ) ( ) =
++
++=
...11
...11lim
210 sTsTs
sTsTKsK
N
ba
sv
0=sse
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Static acceleration error constant Ka
Steady)state error untuk input unit!parabolicadala"
)(1lim1
)(1lim
)(1)(lim
20300 sGsssGs
sGssRe
sssss
=
+
=
+
=
Static acceleration error constant Kadidefinisikan :
)(lim 20
sGsKs
a
=
a
ssK
e 1=
2)(
2ttr =
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Static acceleration error constant Ka
.ntuk sistem tipe nol
( ) ( )( ) ( )
0...11
...11lim
21
2
0=
++
++=
sTsT
sTsTKsK ba
sa
.ntuk sistem tipe dua
( )( )
( )( ) K
sTsTs
sTsTKsK ba
sa =
++
++=
...11
...11lim
21
2
2
0
=sse
Kess
1=
.ntuk sistem tipe tiga dan yang le#i" tinggi
( ) ( )
( )( ) =
++
++=
...11
...11lim
21
2
0 sTsTs
sTsTKsK
N
ba
sa
0=sse
( ) ( )
( )( ) 0...11
...11
lim 21
2
0=
++
++=
sTsTs
sTsTKs
K
ba
sa =sse
.ntuk sistem tipe satu
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Steady)state error dalam #entuk gain
step input ramp input acc' input
type 0system
type 1system
type 2system
2)(
2ttr =1)( =tr ttr =)(
K+1
1
K
1
K1
0
0 0
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Sistem kendali proporsional
)(sR )(sC)(sE
1
1
+TsK
/entukan steady)state errors sistem ini
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Sistem kontrol integral
)(sR )(sC)(sE
1
1
+TssK
/entukan steady)state errors sistem ini
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Steady)state error sistem sero
)(sR )(sCK
s
1)(sE
BJs +1
/entukan steady)state errors system #erikut
J
Kn=JK
B
2=
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Steady)state error sistem sero
dengan kontrol proportional deriatif
)(sR )(sC
s
1)(sE
BJs +
1
/entukan steady)state errors sistem #erikut
J
Kpn=
p
d
JK
KB
2
+=
sKK dp+
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espon pengendali proporsional
ter"adap gangguan torsi
)(sR )(sCpK s
1)(sE
BJs +1
)(sD
/entukan steady)state error yang dise#a#kan ole" gangguan torsi#erupa step dengan magnitudo Td
T
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espon pengendali proporsionalintegral
ter"adap gangguan torsi
)(sR )(sC
s
1)(sE
BJs +1
)(sD
/entukan steady)state error yang dise#a#kan ole" gangguan torsi#erupa step dengan magnitudo Td
T
+
sTK
i
p
11
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Sistem Sero dengan elocity feed#ack
)(sR )(sCK
s
1
hK
)(sE
BJs +1
)(sD
/entukan error ketika input referensi dan input pengganggu muncul
di dalam sistem #erikut'
tentukan nilai steady)state error ketika sistem memiliki input
referensi unit)ramp and input pengganggu step dengan magnitud d'