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1.1 JIntroduction
אאF(Automatic Control systemsאאאאאאאאאאאKאKאאאא
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Kא אאאאאKא
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אאאאFComputersEאא)Robot (אאא
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FאEnvironmentKEאא
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١- ١(א( Eאא FKאא
אא אא אאאאWא
(1-1)
אאאאא
(controlled variable)
عناصر التحكم
+
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אא)Controlled Variable (
K אאאא א א אK א א אא א א א
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א א אאא א א א Kא א W א א
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א(Controller)
אאאאאאאאאאאאאאאאאאאKא
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3.1א(Illustrative Examples) א א אא
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4.1Laplace Transformation
Laplace Transformations א אאאאאאאאאאא
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1.4.1אא אאאאא
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1
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16
15
e-atcos ωt14
e-atsin ωt13
12
11
10
t n e-at (t=1,2,3,…)9
t n (n=1,2,3,…)8
cos ωt7
sin ωt6
te-at5
e-at4
t3
Unit step 1(t)2
1 unit impulse δ(t)1
F(s) f(t)
17
16
15
e-atcos ωt14
e-atsin ωt13
12
11
10
t n e-at (t=1,2,3,…)9
t n (n=1,2,3,…)8
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sin ωt6
te-at5
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t3
Unit step 1(t)2
1 unit impulse δ(t)1
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s
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5.1אInverse Laplace Transformation
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6.1אאClassification of Control Systems
אW אאאאOpen loop control system
אאאאClosed loop control systemK
1.6.1אאאאOpen Loop Control Systems אאאאאKא
אאאאאאאKא
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Actuating signal
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األمر
المشغل الحاكمالنظام المحكوم
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א)10-1 (אאאאאK
אאאאאאאאאאאא
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2.6.1אאאאClosed-loop Control Systems
אאאאאאאאאאאאF
אאEאKאאאאאKא
אאאאאFeedback Control SystemK
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אאאאא
(controlled variable)
عناصر التحكم النھائي
+
-
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)11-1 (אאblock diagram،
אEאאאאאאאcontrollerאא
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אאאאאKאאאOperational Amplifier K
3.6.1אאאאא
J אאאאאאאאאאאאאאאאאKא
אאאא،אאאאאא
J אאאאאאאאאא،אאאא
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35
7.1אאTransfer Function
אאאTransfer Function אאאאאאאאInitial Conditions
EFKWאאEאFאאאא
1.7.1אאאא אא
m)(ntrbdt
tdrb
dt
trdb
dt
trdb
dt
trdb
tcadt
tdca
dt
tcda
dt
tcda
dt
tcda
o
m
m
m
mm
m
m
on
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1
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W א c = output of the system
א r = input of the system
אאאאאאאאאW
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mm
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8-1
אאאאאWא
0.1 c"(t)+2c'+c(t) = 4r(t)
אאWאאאאאאא
0.1S2C(s)+2SC(s)+C(s)=4R(s)
אWאC(s)אאא )0.1S2+2S+1)C(s)=4R(s(
W א אא א C(s) R(s) K
121.0
4
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(12-1 )
H(s)
C(s) R(s) E(s)
B(s)
G(s)
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37
אWאא
C(s) = E(s)G(s) I E(s) = R(s) - B(s) II B(s) = C(s)H(s) III
אIIIאIIאאI C(s) = [R(s) - C(s)H(s)]G(s)
אא
C(s)[(1+G(s)H(s)] = R(s)G(s)
C(s) R(s)אאאא
)24-1( )()(1
)(
)(
)()(
sHsG
sG
sR
sCsTF
אאאאW J
אא
G(s)אאאforward path transfer functionא
E(s)
C(s)G(s)
H(s)אאאfeedback transfer functionא
C(s)
B(s)H(s)
)()(1
)(
sHsG
sG
R(s) C(s)
EFאא
אאאא
38
8.1אאBlock Diagram
אאBlock diagramאאאאאFאאאאאE
אאאאאאאאKאאא
blocksאאאאtransfer functionאאK
אאאאאאאאאK13-1( א(אאאK
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א א א א Kאאא אא
אKאא א א אKאא
)13-1(אא
Y1(s )X1(s) )s(G1
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39
1.8.1אאElements of Block Diagram
אאאKא
E אBlocksWאא E אBranch pointsWאאא
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)15-1(K א א א א Kאאא
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C(s )C(s )
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40
א א E Straight Line WאאאאאאאאאK
אEArrows WKאאאא Wאאאאא
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Y(s)
X1(s)
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(s)X(s)X(s)XY(s) 321
EFאא
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41
2.8.1אאאBlock Diagram Simplifications
אאאאאאאאאEאאFא
אאאאאאאאאא؛אאאא
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אא X,Y,ZאאHאאאSK
EFאא
אאאא
42
אאאEF
Y = G 1(X G 2)Y 5
Y = G 1(X G 2 4
Y = G 1X
± G 2Xحذف مستطيل (عنصر) من
أحد المسارات األمامية
3
Y = G 1X
± G
عنصران متصالن
على التوازي
2
Y = (G G )X
عنصران متصالن
1 على التوالي
المكافيالمخطط المخطط األصلي
العالقة الرياضية التي اإلجراء تربط الدخل بالخرج
1 25
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±
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X
± 2X
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1
G 1 G2X Y1 2X Y G1 G2X Y
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2
Y+
±
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X
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نظام تحكم ذو حلقة
تغذية مغلقة
حذف مستطيل (عنصر) من
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EFאא
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43
G1 G4 G2 C R
H1
G3
H2
אאא
: 9-1
אאאKאאאא
9
8
7
Z = GX ± Y نقل وصلة تجميع
أمام صندوق
6
Y = GXY =
Y = GXY =
Z = G(X± Y)Z = ± Y)
Z = ± Y
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X ZG
Y
X ZX Z
Y
X Z G
1G
Y
X Z
1 Y
X Z
111
Y
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Y
X Z
Y
X YG
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X Y
X Z
G
YG
X Z
Y
X
XY
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X
XY YX
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1 G 1 1
نقل وصلة تجميع
خلف صندوق
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نقل نقطة تفريع
خلف صندوق
Y
X Y
GY
X Y
EFאא
אאאא
44
Wא ١ JאאאG1,G4W
٢ JאאאG3,G2W
٣ JWאאאא
٤ Jאא
٥ Jאאאאא
G1 G4 G1G4 =
141
41
1 HGG
GG
141
41
1 HGG
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G2+G3
R C
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= G2+G3
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)(
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R
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EFאא
אאאא
45
אאאאא
141
23241
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3241
1
)(1
1
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HGG
HGGGGHGG
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R
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23241141
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א :אאאאאא
) أ (
R
H
G1G2 G3 C
G1 G2 G3 CR
H
EFאא
אאאא
46
אEFWאא
HGG1
GGG1
HGG1
GGG
R(s)
C(s)
21
321
21
321
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11-1
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321
1
(ب)
(ج)
(د)
32121
321
1 GGGHGG
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C R
G3 C R
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21
21
1
C(s)
G1
H2
G3 R(s)
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G2
EFאא
אאאא
47
א: אאאאאאא
אאאאG1W
E
E
E
E
232121
321
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21
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321
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48
Wאא
321232121
321
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9.1אSignal Flow Graph
KאאאאאEFאאאא
KאאאאאאEFאאאאאK
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d
1
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دخل عقدة
(Source)خرج عقدة
(Sink)
(Source)دخل عقدة
EFאא
אאאא
49
אאאא
אאאאאKאאאאאא
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Mason's ruleK
1.9.1אאBasics of Signal Flow Graph אאאא
KאאאאאאאאאK
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X 1
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a
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a
b
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X 1 X2
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a
c
X1 X 3
ab
X1 X 3
ab(b)
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a + b=(c)
=X1
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ac
bc
X 4(d)
c
X 2 X 1
a b =
X3
X1
ab
bc
X1 X3
ab1 -bc ab
1 -
EFאא
אאאא
50
Fאא17-1אEW
١ Jא2XFאa17-1E12 aXX ٢ Jאאאאאא
F17-1bKE
٣ JאאאאאאFc 17-1E
٤ JאאFd 17-1E
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x : أنأي
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13
313
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bcxabx
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א)18-1(אאאאK
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R(s)
G(s)
R(s)
R(s)G(s)
C(s)R(s)G(s)
C(s)
R(s)G(s)
C(s)E(s) G(s)
H(s)
R(s)
1
E(s) C(s)
-H(s)
R(s)
G1 (s)G1 (s)
N(s)
E(s)
H(s)
G2(s)G2(s)C(s) G1(s)
R(s)
1
E(s)
G2(s)
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1
N(s)
C(s)
EFאא
אאאא
51
2.9.1Mason's Rule
אאGEאFאאאאאאא
אאאKאאאאW
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1
אאKpath forwardth ofgain path kpk
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cb
cb LL,
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fed LLL,,
=א
k=אאאאא k
אאאאא
Kא
EFאא
אאאא
52
12-1
אאאאאאאאאאאאאא Kא
אאא)(
)(
sR
sCK
Wא ١ JאW
3211 GGGP ٢ JאW
3213
2322
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HGGL
HGGL
R(s) C(s) 1 1 G1 1 G2 G3
C(s)
-H2
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G1 G2 G3 C(sR(s)
H1
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EFאא
אאאא
53
٣ JאאאאW
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321
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)LL(L1Δ
٤ Jאאאאא1P1אאאW
1Δ1 אאאאאאאא
)(
)(
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321
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P
GsR
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אא
13-1
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R(s) C(s) G1 G5 G3G2 G4
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אאאא
54
Wא
אאW ١ JאW
7213
54612
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254324
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HGGGGGGGGGGGGGGGG
R(s)
C(s)
pPP
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sCG
EFאא
אאאא
55
؟אאאאאא -١
אאאאאא -٢
٣- אאאאא
٤- אאאא؟אא א؟
אאאאאאאא -٥
٦- Wאאאא
u(t)2cos2sing(t) (d) u(t)2sin2g(t) )(
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2
25
tttec
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t
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2
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sss
ss
se
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s
ssc
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1G 2G 3G C(s)
1H
EFאא
אאאא
56
Y5 Y2 Y3
Y4 Y5 -H1 -H2
٩- אאאאאא
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١٠- אאאאא
)(
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٩ J אאאאKא
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5
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Y
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G1
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G1
H5
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G2
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H1
H4
EFאא
אאאא
57
Y5
G3
Y2 Y3 Y4 Y5 -H1 -H2
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Y5
G1 G3
Y2 Y3 Y4 Y5 -H1 -H3
-H2
Y5
G1 G3
Y2 Y3 Y4 Y5 -H1
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G4
1 G2G1
Y1
1 (b)
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G4
1 G2
Y1
1 (c)
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1 G2
Y1
1 (d)
EFאא
אאאא
58
אאאאאאאאאא
EFאא
אאאא
59
אאW
א EאF אאאKא
אאאW ١K אKא
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EFאא
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60
1.2
אאאאאאאError SignalKאאא
אאאאאאא
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61
2.2אאאMathematical Modeling
א א א א א א א אאאאא
אאאאאאאKאאאאא
א א אא אאאאאK
אאאאאאא א א א אא אא
Kא 1-2
אא אאRCאאאאKאאאאאא
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)1-2( אאRC series circuit
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Wאא )1-2 ( )()()( tvtvte cr
אאאאW
R
C e(t)
Vr(t)
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EFאא
אאאא
62
)()( tRitvr אאאאK
dt
tdvCti c )(
)((
אאW
dt
tdvRCtv c
r
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אא)١-٢( )2-2( )()(
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dt
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c
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c
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אאאאW
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1
)(
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SRCsE
sVsG c
EFאא
אאאא
63
אWאאאא
אאאא،אאאאאאאKאאsאא 2-2
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64
א4-2) (W
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c
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tetvdt
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cc
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2
tetvdt
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65
3-2 אאאTypes of Industrial Controller
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אאאאW ١ Jאא Discontinuous controllers ٢ JאאProportional Controller (P-Controller) ٣ JאאIntegral Controller (I-Controller) ٤ JאאDifferential Controller (D-Controller) ٥ JאאאPI-Controller ٦ JאאאאPID-Controller אאאא
אאאאאאK
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66
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67
2.3.2אאContinuous Controllers אאא
KאאאאאאאWאאאP-ControllerאאI-
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C
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א
p
B=C
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Kp
א
א
P(s)E(s)
א
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EFאא
אאאא
68
אאאאPKאאKPK א
אאאאKאאPKאאאEאFאאאאKא
א W e(t)Kp(t) P
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t t
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a
aKp
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EFאא
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69
2.2.3.2אאI-Controller
אאאאF7-2EKאאאאאא
אFR=CEאאK
אאאאW
2)-(7 )(
1
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s
K
E(s)
P(s)sG
E(s)s
KP(s)
dtteKp(t)
IC
I
t
I
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e(t) = aEאא
א
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KI
S
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א
א
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אאאא
70
אF7-2EW
C a t Kp(t)
adtKp(t)
I
t
I
2)-(8 0
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אאאKאאאאאאאאאא
IKK אIKאreset rateאאאאCאRKאאאIK
א،אאאאאאאאאאאIKKא
אאאאאIK.
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0
e(t)
א
t t
p(t)א
a
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71
3.2.3.2אאD-Controller
אאאא
F9-2KEאאFאrate controllerEאK
אאFאEאKאאאאאאא
אאאאאאאאFK9-2אאEאאאאUnit Step FunctionK
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אאאאFאאKEאFא EאאKאאאא
אאאאא
א
E(s)
א
אKDS
אאא
p(s)
א
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0
e(t)
t 1 t
p(t) א
0
EFאא
אאאא
72
אאאא
אאאKאא
4.2.3.2אאאPI-Controller אאאאא
אאPKאאאאF10-2Eאא
אאאPKאאאIKאאKאאאIK1TI
אאאFאSTI1KEאאאאIIP Tأو ,K ,Kאאא
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K(K
E(s)s
KE(s)KP(s)
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א
P(s)E(s)
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K P
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+
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73
F10-2E
s
KK
E(s)
P(s))( I
P SGC
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F11-2E e(t)dt
dKe(t)dtKe(t)Kp(t) D
t
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0
e(t )
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t t
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א
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EFאא
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74
PKאאIKאאDKאאאאאאא
אא(11-2) אאאאW
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K PK P
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AC Motor
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Control system
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אא א Modern Control System, Edison Wesley,
1990 R. C. Dorf
Control System Design, Saunders College
Publishing, 1993. C. T. Chen
Feedback Control System, Prentice Hall,
1990. John Van De Vegta
Automatic Control Systems, Prentice Hall B. Kuo Process Control Instrumentation Technology,
Prentice Hall, 2002 Johnson, C. D
Introduction to Control Systems Technology,
Prentice Hall, 2002 Bateson, R. N.
Modern control Engineering, Prentice Hall,
1997 Ogata, K.
Modern Control Systems, Addison Wesley,
1998 Dorf, R. C. and Bishop, R. H.
Introduction to control system technology;7th
edition1993 Robert N. Bateson
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