التحكم الآلي

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אאאW

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אאWאאאאאאאאאאK אאאWאאאאאאאא

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אאאאאאאאK

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אאW


- ٢ -

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F١ J١WEאFE

برغي تعديل


- ٣ -

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الهدف

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- ٤ -

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א،אאאאאאא،אאא،אאא

א،אאאאאאאKKKKאK אאאאBiological systemsא

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אאאאK


- ٦ -

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א אא

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- ٢٣ -

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- ٢٥ -

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491.670

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- ٢٦ -

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KאאאאאאאאאאאK

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ethanol -110 →100

toluene -90 →100

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א


- ٢٧ -

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- ٢٩ -

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א

א

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- ٣٠ -

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0 25 50 75

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א -250 → 1100


- ٣١ -

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א

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- ٣٤ -

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- ٣٥ -

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א

mV


- ٣٦ -

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- ٣٨ -

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- ٣٩ -

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- ٤٠ -

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- ٤١ -

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- ٤٣ -

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- ٥٠ -

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hgP ..ρ= WPWאאFPascalE،ρWאFkg/m3E،hWאFmE،

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٢ J٣ J١אאאאW אאאאאאאאאאאאאאאאא

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٢ J٢٨Wאאאא

א،אאאאאאW

א אא

א


- ٥١ -

hAggMf .... ρ−=

WƒWאאאאאFNE،MW،אאgWאא

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٢ J٣ J٢אW

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٢ J٢٩Wא

א420mA0%100%K

אאאאאאאאאאאאKאאאאאאא

א

א


- ٥٢ -

אKאאאאאאאאK

٢ J٣٠Wאאאא

٢ J٣ J٣אאcapacitance probeW

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٢ J٣١WאאF70E

אא

א

אא

א

א

א


- ٥٣ -

G١W אאאאאאאאW

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אאאאWkeroseneρ=800kg/m3 אאאƒאאאאאK

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אאKאρ=1000kg/m3g=9.81m/sec2K אW

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٢ J٣ J٤אGamma radiationW

א،אאאאאאאאאאK


- ٥٤ -

W W

٢ J٣٢Wא

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א،א،א،אאאK אאאאאאKאאאא

K אאאאאK

٢ J٣٣W


- ٥٥ -

٢ J٤אW ،אאא،אא

Kאאא אאFm3/secWE

tVQ∆∆

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אאאאאOrificeא∆P،אא

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PKQ ∆= . א،אאאאא

אאאא،אאKאאאאא،אא

אKאאאאאאאKאאאאאKאאאא

אאKאאאKאאאאK


- ٥٦ -

٢ J٣٤Wאא

٢ J٤ J٢אאW

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אא

אא

א אא

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- ٥٧ -

٢ J٣٥WF

אE

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א

אא א

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- ٥٨ -

אאא

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אא،אאK אאאאא

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- ٥٩ -

٢ J٥אאאW ٢ J٥ J١אאאW

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א א

א א


- ٦٠ -

JאאאFLVDTELinear Variable Differential TransformersW אאאאאאא

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אאא

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code diskKאאאKא،

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א:X


- ٦١ -

٢ J٣٩Wאincremental encoder

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א

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- ٦٢ -

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x=(π.d.NT)/NR WxWאאא،dW،אNTW،אאNRWא

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אאא

אא

א


- ٦٣ -

FbFEaE

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אKא5.91cmאא180אא180אאKאאא

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٢ J٥ J٢אW

א

א אא


- ٦٤ -

א،אאאאKאאאKאאאאאא،א

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GאאW Jאאdc tachometerW

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- ٦٥ -

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אאthree-phaseFErectifierאK،אאא

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- ٦٦ -

0.7VKEאאא100110001אאKאאbrushesK

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2000K


- ٦٧ -

Jאאא1200Lאאא5msK

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٢ J٥ J٣אW

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F = m.a W

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- ٦٨ -

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2

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א

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Force א

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- ٦٩ -

S=אFN/mE F=אאאאFNE L=אאאאFmE b=אFmE h=אFmE

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- ٧٠ -

JW אא،אאאאאKא

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א

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- ٧١ -

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W WA=2.1 in2א،K

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٣ JאTransducerW ٣ J١אW

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G

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4-20 mA


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24V


- ٧٤ -

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- ٧٥ -

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א

א


- ٧٦ -

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אאאElectro-pneumaticאאElectro-

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אאEאאאאאאאאאServomotorאאאאאK

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- ٧٧ -

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א

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- ٧٨ -

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- ٧٩ -

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٤W

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- ٨٠ -

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050lb015psiKאאאK

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- ٨٢ -

WE0،a1a2אאאא Firon-constantanEאאאאאW

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50 100 150 200

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25 50 75

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sp=אאF%E אKאאאא13KKא

אאאspK ١٦W


- ٨٣ -

K=34.1cm3/pulseKאאW

J8200 J32060 J680

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אאא050N/cm2K ٢٠W

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- ٨٤ -

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2550 75

100

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- ٨٥ -

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אאאא

אא

אא

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- ٨٦ -

אא Jאא J

אאW אאW

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אאW


- ٨٧ -

אאWאא אאאאא،

אאKאאאאDifferential equationאאKאאאאא

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אאFQin>QoutKEאאKאאאFQin<QoutKEאK

QinW

QoutW

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- ٨٨ -

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⎠

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אאאW


- ٨٩ -

inGqh

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١ J٢אאאRCW

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- ٩٠ -

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- ٩١ -

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GW אאW

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אא

אRm

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- ٩٢ -

dtetf st∫∞ −

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Differential equation

Algebric equation

א

Time domain

Frequency domain


- ٩٣ -

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٢ J٥אאאW

אאf(t) אf(t) F(s) ١אא δ(t) 1

٢אאFKE K sK

٣אא tK 2s

K

٤אאa>0 ateK −.

asK+

٥אאτ>0 τt

eK −. 1. +s

Kτ

٦אאאאa>0

ate −−1

)( assa+


- ٩٤ -

٧אאאאτ>0

)1( τt

eK −− )1.( +ss

Kτ

٨אאsinא،ω )sin(. tK ω 22 ω

ω+s

K

٩אאcosא،ω )cos(. tK ω 22 ω+s

Ks

١٠אאאsin teK at ωsin.. −

22)( ωω++ as

K

١١אאאcos teK at ωcos.. −22)(

)(ω++

+as

asK

١٢אאא atetK −.. 2)( as

K+

٣ JאאW

אאאאאאאאאאאאאKא

אאW ١ JאאK ٢ JאWאאW،،،אאK

א

א

א v

א y

e


- ٩٥ -

אאאאאאא

אKKKK אאאאאW

אאאFאEאW

אאK

٣ J١אאאW אא،אא

אאאאאK

HHאH

א

א v אy

G(s)

دخلE(s)

خرجU(s)

عنصر

HHאHאH

א

v ye


- ٩٦ -

אאW)()()( sG

sEsU=

GW אאאאאא tetU −−= 1)(

אK אאW

JאW

stesE 1]1[£)]([£)( ===

]1[£)]([£)( tetesU −−==

W1

11+

−=ss

U(s)

אW)1(

1)(+

=ss

sU

JאאאאW

11

1.

)1(1

)()()(

+=

+==

ss

sssEsUsG

אאאW1

1)(+

=s

sG

٣ J٢אאאW ٣ J٢ J١אאאW

? tetU −−=1)(E(t)=1

)(1 sG )(2 sG

)().( 21 sGsG

E(s) U(s)

E(s) U(s)


- ٩٧ -

٣ J٢ J٢אאאאאW

Wאאאא

אW

GאאH(s) =1אאW

W

GאאאW

G(s)

H(s)

v ye

)()(1)(

sHsGsG

+

v y

אאאאא

G(s) v ye

)(1)(sG

sG+

v y

G(s

H(s

v(s) y(s)e

z-


- ٩٨ -

W : eאWe = v-z

G(s)WאאאאאW)()()(

sesysG =

H(s)WאאאאאW)()()(

syszsH =

G(s).H(s)WאאאאאW)()()()(

seszsHsG =

)()(1)(

sHsGsG

+WאאאאאW

)()(

)()(1)(

svsy

sHsGsG

=+

٣ J٢ J٣W אאאאאא،W?

)()(=

svsy

אW אאאאW

ss 1+

121+s

K2

K1 v(s) y(s)

v1 e1 e2

e2

K2

)12(1++ss

sK1 v v1 e1 y


- ٩٩ -

אאאאאאGHG

ey

+=

11

W)12(

1++

=ss

sGH(s)=K2K

W)12()1(21

)12(1

.11

++

+

++

=+

=

sssK

sss

HGG

ey

W)1(2)12(

11 +++

+=

sksss

ey

אW2)12(2

11 2 kkss

sey

++++

=

אאW

אאאאאWGHG

vy

+=

11

W22

2 )1(21

kksssG

++++

=H=1

W22

2

222

)1(211

)1(21

11kkss

skkss

s

GG

vy

++++

+

++++

=+

=

W1)1(2

1

222

1 ++++++

=skkss

svy

אW1)2(2

1

222

1 +++++

=kkss

svy

אאW

2)11(21

2 kksss

++++

K1 v v1

e1 y

K1 1)2(21

222 ++++

+kkss

s v v1 y


- ١٠٠ -

אאאאאאW

21.GGvy=

אאאאאK

אאאאאאאאאאא٢

٣ J٢ J٤W GW

אאאאאאW

inGqhdtdh

=+τ

W

)(£

)]([£)(

ssHdtdh

thsH

=⎥⎦⎤

⎢⎣⎡

=

אW

[ ]

1)()(

)(1

)(

)(1)()()()(

+=

+=

=+=+

sG

sQsH

sQsGsH

sGQssHsGQsHssH

in

in

in

in

τ

τ

ττ

1)2(2)1(

222

1

+++++

kksssk

v y


- ١٠١ -

)()(

sQsH

in

אאK

GאW אאאאאאW

inoutout EE

dtdE

=+τ

אאאW

sEE

in

out

τ+=

11

GW אאאאאאW

xCdt

dxRdt

xdmAPm

min

12

2

++=

אאאW

21 smCsCRAC

Px

mmm

m

in ++=


- ١٠٢ -

J٣ J ١W

אאאW ١ Jƒ(t)=12 ٢ J tetf 22)( −+= ٣ Jttf 4sin2)( = ٤ Jttf 377cos120)( = ٥ Jƒ(t)=27t ٦ Jtetf t 1000sin.89)( 2−= ٧ Jf(t)=12.3+t+5e-4t

GאW ١ JF(s)=12/sK ٢ JF(s)=2/s+1/(s+2) ٣ J

168

2 +sF(s)=

٤ J22 )377(377120

+×

sF(s)=

٥ JF(s)=27/s2 ٦ J

1000000)2(890002 ++s

F(s)=

٧ J4

513.12)( 2 +++=

ssssF

٢W אאאאW

١ JS

sF 5.27)( =

٢ J5

8)(+

=s

sF

٣ J25006.19)( 2 +

=s

ssF

٤ J128322

4.17)( 2 ++=

sssF


- ١٠٣ -

٥ J10000)2(

350)( 2 ++=

ssF

٦ J2

212 )2(2)2()1(8)(

++

+=

++

=s

KsK

sssF

GאW ١ JאWf(t)=27.5 ٢ JאWf(t)=8e-t ٣ JאWf(t)=19.6cos50t ٤ J22 )8(

7.86416

7.8)(+

=++

=sss

sFא،Wf(t)=8.7te-8t

٥ J22 )100()2()100)(5.3()(

++=

ssFא،Wf(t)=3.5e-2tsin100t

٦ J١Wא2)2( +sW21 )2()1(8 KsKs ++=+ ٢Ws-2אאWK2=-8 ٣WK2אאWK1=8

W2)2(

82

8)(+

−+

=ss

sF

אא١٢Wtt teetf 22 88)( −− −=

٣W אאאאאW

J)(7)(12)(8)( 2

2

txdt

tdxdt

txdtf ++=אאW ١ Jx(0)=0 ٢ Jx(0)=64)0(

−=dt

dx

J∫++= dttxtxdt

tdxtf )(8.4)(2.24)(5.5)(אWx(0)=0 GאW

אWF(s)=8s2.X(s)+12s.X(s)+7.X(s) ٤W

אא-א -אPID ControllerאW


- ١٠٤ -

∫++= dteTK

dtdeKTKei

id .

W iWאFmilliampereKE eWאFvoltKE

KWאK TdWאK TiWאK

אאW،אאI(s)/E(s)א،W K=3.6 ،Td=0.008 ،Ti=2.2.

GאW אW

ssE

TKsEsKTsEKsI

id

)(.)(..)(.)( ++=

W).

1.1()(/)(sT

sTKsEsIi

d ++=

אאW)2.21008.01(6.3)(/)(

sssEsI ++=

٥W

אא)()(

sIsXא

אW

ixdtdx

dtXd 3.002.00001.02

2

=++

Wx = אאFinchE،i=אFmAKE

אW102.00001.0

3.0)()(

2 ++=

sssIsX

٦W אאאאאאW


- ١٠٥ -

GאW

100520

)()(

2 ++=

sss

sRsC

٧W אאאאאאW

GאW24120

)2(10)()(

23 ++++

=sss

ssRsC

R(s) C(s)

ss 20+

21

++

ss

+

- s1

s1

20

10

R(s) C(s)

520+s

s5

+

-

אאאאאאאאאא

אאאא

אא

א

א

א

٤

א ٢٥٤ אאא אאFE אאאאא

- ١٠٦ -

אאא Jאאאאא J

אאW אא

אאאאאW GאאאאK GאאK GאאאאK GאאK Gאאאא


אאW٤K


אאW


- ١٠٧ -

אאאWאאאאא א،אאאאאאא

אאאאK ١ JאאאW ١ J١אאW

אאאאאW

)()()( tbxtaydt

tdy=+א،t=0y(0)=y0F4 J1E

אאאW

)()()( tGxtydt

tdy=+τא،t=0y(0)=y0F4 J2E

abW،א

τWאFa1

=τE

GWאאאFabG =E

y0Wאאאא אאF4 J1Eא،W

)()()()()()(

0

0

sbXysYassbXsaYyssY

+=+⇔=+−

אas +אW)(11)( 0 sXas

bas

ysY+

++

=

Wy0=0אW

אW

asabE

sabE

assbEsY

+−=

+=

//)(

)(

אאY(s)אtW

asb+

sEsX =)(

X(s) )(

)(ass

bEsY+

=


- ١٠٨ -

)1()( /τteGEtY −−= אאאאאאW

אt τ 2τ 3τ 4τ 5τ אY(t) 0.63GE 0.86GE 0.95GE 0.98GE 0.99GE

אאFW4.1،4.2،4.3EW

JאFτETime constantWאWτ=1/aאאאאאא63%א

אK JאאF(TrRise TimeW

אאאאא10%90%אאאא)(∞yK

τ×==−= 2.22.211.031.2aaa

Tr

٤ J١Wאאa=5אτ=1/5=0.2sec

TsTr

0.63GE

τ=1/a

0.98GE Yss=GE


- ١٠٩ -

JאFTsESettling TimeW אאאאאא

אאאFא2%±KE

τ44==

aTs

GW

אאאאאאאאא

אאאW)(10)(2)( txtydt

tdy=+

אτאא،Trא،TsK אW

אאW

15.05

210

)()(

)(10)(2)(

+=

+=

=+

sssxsy

sxsyssy

אWs

sX 1)( =Wss

sY)15.0(

5)(+

=

Wtt eety 5.05.0 55)1(5)( −− −=−= אאאW5)( ==∞= ssyty

אאWtety 5.05)( −−= אWτ=0.5s،Ts=2s،Tr=1.1sK

١ J٢אאאW אאW

GאאאWτ=1/a GאאאאאF٩٨٪EאאWTs=4 τ GאאאWGEy

ss=


- ١١٠ -

GאFgain coefficientEאאאאWG=yss/EK

١ J٣W

אא،אאאאאWA=1m2אא،WR=500s/m2K

אW Jא

Jאτ JאG JאאWQin(t)=2×10-4m3/sא،אאא

אאK אW

JאאW)()()( tRQthdt

tdhAR in=+ARW

)(500)()(500 tQthdt

tdhin=+

Jאאאאאא

)()()( tGxtydt

tdy=+τ،Wτ=500s

JאאWG=500 JאאW)1(500)1()( 002.0/ tt eeGEth −− −=−= τ

א،אh(t=∞)=hss=500K


- ١١١ -

0 500 1000 1500 2000 2500 30000

50

100

150

200

250

300

350

400

450

500Step Response

Time (sec)

Ampl

itude

٤ J٢Wא


- ١١٢ -

٢- אאאW אאאא

אאאא،אאK אאאאאא

אאK ٢ J١אאW

אאאאאאאאW

bassbsG

++=

2)(،bn =

2ωna ξω2=

אאאאאאW

)()()(2)( 22

..

2

2

txtydt

tdydt

tydnnn ωωξω =++

WξאDamping ratio ωn א frequency

אאW Jξ<1אUnderdamped systemK

Jξ≥1 א Critically damped system. Jξ=0א

0 1 2 3 4 5 60

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08Step Response

Time (sec)

Ampl

itude

٤ J٣Wאאξ<1


- ١١٣ -

0 0.5 1 1.5 2 2.50

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05Step Response

Time (sec)

Ampl

itude

٤ J٤Wאאאξ≥1

٤ J٥Wאξ=0

٢ J٢אאW אאאאW


- ١١٤ -

אIndex אאAnalytical expression ١ JMaximum overshoot δ 10%100.

21/ <<= −− ξδ ξξπe ٢ Jאtp

21 ξωπ−

=n

pt

٢ JאאDelay time Td

1,15.06.01

10,7.01

2

≥++

≈

<<−

≈

ξω

ξξ

ξω

ξ

n

d

n

d

T

T

٣ JאאRise time Tr

1,4.11.11

10,5.28.0

2

≥++

≈

<<+

≈

ξω

ξξ

ξω

ξ

n

r

n

r

T

T

٤ JאSettling time Ts τ

ξω44

=≈n

sT

٥ JאDamping index ψ 21/2(

1

21 1 ξπξψ −−−=−

= eA

AA

٤ J٦Wאאא

A1 A2


- ١١٥ -

٢ J٣אאאW אא

אאm kc K

אm fאאא

mK

אאW אא..

. xmFאEאאאK אאאאFWאאKE

(1)0ftkxdt

tdxcdt

txdm =−++ )()()(2

2

F1EאאאאאW

0)()()()(2 =−++ sfskxsCsxsxms

)()()( 2 sfsxkCsms =++

mks

mcs

mkCsmssf

sx

++=

++=

22

11

)()(

m

k C

f

X א

+

-


- ١١٦ -

Wmk

=0ωCcC

=ξ

WkmCc 2=

ξWאK

0ωWאאאK Cc WאאK

W200

2

20

200

2 21

2

1

)()(

ωξωω

ωξω ++=

++=

sskssm

sfsx

אאW 200

2

20

2 ωξωω

++ ss،אאאאאאK

GאאאאW

אאאאאf(t)K

אאx(s)W)2(

)(200

2

20

ωξωω

++=

ssssx

אאאx(s)٣

אאx(t)אξK 2

020

2 ωωξ −=∆

W)1( 220 −=∆ ξω

200

2

20

21

ωξωω

++ ssk

x(s)خرج f(s)الدخل

s1 f(s)= x(t)=?


- ١١٧ -

JאאW0>∆1>ξWא(over damped system) אאW2

002 2 ωξω ++ ss،W

)1(1 20

2001 −+−=−+= ξξωξωξωs

1(1 20

2002 −−−=−−−= ξξωξωξωs

2121

20

))(()(

ssC

ssB

sA

ssssssx

−+

−+=

−−=

ω

tsts CeBetx 211)( ++=

W A=1 ،21

2

sss

B−

=،21

1

sss

C−−

=

JאאW0=∆1=ξ،(critically damped system)

אאW002 2 ωξω ++ ss،W

021 ξω−== ss

200

20

20

)()()(

ξωξωξωω

++

++=

+=

sC

sB

sA

sssx

F1=ξE)1(1)( 00 tetx t ωω +−= −

JאאW0<∆1<ξא(Under damped system)

אאW002 22 ωξω ++ ssW

2001 1 ξωξω −+= js

2002 1 ξωξω −−−= js

[ ] )1()()1()()(

220

20

220

20

20

ξωξωξωξωω

−+++

+=−++

=s

cBssA

sssx

)1( <ξ[ ]Qtetx t +−−

−= −

02

21sin.

111)( 0 ωξξ

ω


- ١١٨ -

Wξξ 21−

= arctgQ

אאאאאאאW

• אFrtEWאא0100 00א

אאאW2

0 1 ξωπ

−−

=Qtr

• א)( pM،אאאW

21 ξ

πξ

−

−

= eM p

• א)( ptWאאאאאW

20 1 ξωπ−

=pt

• א)( st،אאאא±50

0

אאאאאW0

3ξω

=st

٢ J٤אW

٤ J٧W

אאאW

e


- ١١٩ -

• אאWeKRidtdiL e =Ω++F1E

• אאWא=Ω+Ω B

dtdJF2E

• אאWא=iKtF3E

אF2EF3EWtK

BdtdJ

iΩ+

Ω

=

אאאאW

Gedtda

dtda =Ω+

Ω+

Ω12

2

2

WBJ

m =τאאK

RL

e =τאאK

RBKK

KGRBKKRBa

RBKKRBa

te

t

te

em

te

em

+=

++

=+

= ,)(,12

ττττ

JWאFkg.m2E BWאFN.m.s/radE LWאאאFHE RWאאאFΩE KtWאFN.m/AE EWאFVE ωWאאאFrad/sE KeWאאFV.s/radE

אאW

2

1

2

1

2

0 2,

2,1

aa

aa

a=== ξαω


- ١٢٠ -

GW אאאW

radVsKAmNKRHLradsmNBmkgJ

et /043.0,/.043.02.1,02.0,/..100.1,.102.6 424

==Ω==×=×= −−

אW Jאא

Jאא Jאא Jאא JאאאK

אW Jτm=J/B=6.2×10-4/1.0×10-4=6.2s

Jτe=L/R=0.02/1.2=0.0167s JאW8.21,379.0,0063.0 12 === Gaa

אאW)(8.21)()(379.0)(0063.02

2

tetdt

tddt

td=++ ωωω

JאאW

387.20063.02

379.02

0794.00063.011

2

1

2

0

===

===

aaa

ξ

ω

JאאW ،אאאא

W 01379.00063.0 2 =++ ss

אW∆=(0.379)2-4×0.0063×1=0.137>0א،W


- ١٢١ -

765.20063.02

)137.0379.0(

393.570063.02

)137.0379.0(

1

1

−=×+−

=

−=×−−

=

r

r

אאאFξ>1EאאW

⎥⎦

⎤⎢⎣

⎡×

−−×

−+= trtr e

rrre

rrrbEty 21

21

1

21

220

1)(ω

אאאω(t)א،r1r2ω0E=5VFאאEb=21.8אW

[ ]tt eet 76.239.57 05.105.0127.137)( −− −+=ω

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

20

40

60

80

100

120

140Step Response

Time (sec)

Ampl

itude

٤ J٨Wא


- ١٢٢ -

J٤ J ١W

אאW

אW אאאא

)()(

svsyאτאא،Tr،

אTsK GאW

)10297.0

1(99.010297.0

99.01013

100

131001

13100

)()(

+=

+=

+=

++

+=sss

s

ssvsy

Wτ=0.0297،Tr=2.2×0.0297=0.065،Ts=4×0.0297=0.118K ٢W

אאאאKW

2

100S

KS

v(s) y(s)

- -

13100+s

v(s) y(s)e(s)


- ١٢٣ -

אWאאאאאW)()(

svsyא،K

GאW

אאאאאאW2

100S

KSאאW

KSS

S

.1 2

2

100

100

+=

KSS .100100

2 +=

)100(100

KSS +

אאאאאW)100(

100KSS +

1אאW

)()(

svsy =

)100(1001

)100(100

KSS

KSS

++

+ =100)100(

100++ KSS

=100100

1002 ++ KSS

אאאK ٣W

١ Jξωn אאאאאאאW

362.436)(

2 ++=

sssG

٢ Jאδאא،Tdא،Trא،TsאψK GאW ١ J362 =nω6=nω،2.42 =nξωξ=0.35<1K ٢ Jאאא٢١Wδ=36%،Td=0.125،Tr=0.279،

Ts=1.42،ψ=0.178K ٤W

ξאאאאאאW

١ J128

12)(2 ++

=ss

sG

٢ J168

16)(2 ++

=ss

sG


- ١٢٤ -

٣ J208

20)(2 ++

=ss

sG

GאWאאאאW200

2

20

2)(

ωξωω

++=

sssG

W ١ J ξ=1.155ξ>1 ٢ J ξ=1

ξ=0.894ξ<1

٥W אאW

50)(10)(=+ ty

dttdy،t≥0

W ١ Jאτ ٢ Jא ٣ Jאאא

אWτ=0.1،G=5،tety 1.01)( −−=

٦W

אאW

2)(2)(3)(2

2

=++ tydt

tdydt

tyd،t≥0

W ١ Jאאא ٢ JאG 3 JאK

אW


- ١٢٥ -

١ Jξ=1.06،ω0=1.414אא ٢ JאWG=1 ٣ Jtt eety −− +−= 21)(

٧W אאאאאאW

W

١ JאאTr ٢ JאTs ٣ JMpא ٤ Jאאא

אW١ JTr=0.28sec،٢ JTs=0.9sec،٣ JMp=16%،٤ JG=1K

אאאאאא

אאאא

א

א

א

٥


- ١٢٦ -

אא Jאאא J

אאW

אאW אאאאW

GאאאאK GאאאאאK Gאאאאא Gאאאאא Gאאאאאא Gאאאאאאא

Gאאאאא


אאW٤



- ١٢٧ -

אאWאאא אאאאאFאאEא

אאKאאאאאאאאאאאאPאא،I،אא

אPIאא،DאאאאPIDאאאK

١ J אאאAstatic and Static systemsW אאא

אWאאAstatic systemsאאStatic systemsא٥ J١ אאK

٥ J١ W


- ١٢٨ -

אאאQFאאאאE

אאאאאאאאאאאKQ

אאאאאאאFhEאאQא،

hאQKאאאאאאStatic systemsא،Degree of statism

אW

min

minmax

hhh −

=δ

אאאאKאאאא

אA,Bאאאאא،אאhאh0א،Astatic systemאhאQאאא

FאאSteady stateEאאK אאאאאאא

k/sאאאאאאOrder of astatismאאIntegratorsא

אאאאאKאאאאאאאאא

אK אאאClassical controllersW

GStatic controllersאאP-controllersא

א JאPD-controllersK


- ١٢٩ -

GAstatic controllersאאI-controllersא،א JאPI-controllersאא Jא JאPID-

controllersאאFirst order astatismK אאאא

אאאK

٢ JאאW אאאאFאאEא

אאKאאאKאאאFSteady state

errorKE GWאאאאאאאאאK

אאאאאאאאאאאאW

)()(11

)()(

sHsGsse

+=

υ

אאW)()(1

)()(sHsG

sse+

=υ

e(s)אK

אאאאW

G(s)

H(s)

Wv(s) e(s) y(s)خرج


- ١٣٠ -

)()(1)(.lim)(.lim

0 sHsGsssese

ssss +==

→→

υ

א)(tυ،s

s 1)( =υW

)()(1

1.lim

0 sHsGs

se

sss +=

→

Wp

ss koHoGe

+=

+=

11

)()(11

WKp= G(o). H(o) KpWא (Position error constant)

٣ JW ٣ J١אאW

אאW

١K אאτאאK ٢K אאאאאא)(tvK

GאW ١K אאאאאW

13100+S

Wv(s) e(s) y(s)خرج

-


- ١٣١ -

1013100

)()(

131013

13100

131001313

100

13100

1313

13100

131001

13100

)()(

+=⇒

+++=

++++=

++

++

+=

++

+=

sssy

sss

ss

s

sss

s

s

sssy

υ

υ

אτאאא)()(

ssy

υאאW

1+stkK

אאאW101 W

110297.099.0

)()(

+=

+=

stk

sssy

υ

אאאW τ = 0.0297 ٢ Jאאsse،W

)(11

)()(11

oGoHoGess +

=+

=

WH(s)=1אאW13

100)(+

=s

sG

W100)( =oG،Wkp=100

אW0099.010011

=+

=sse

٣ J٢אאW

אאאאW

2

100S

KS

v(s) e(s) y(s)

- -


- ١٣٢ -

WkK GאW

١E Jאאאאא)()(

ssy

υK

٢E JאאאאאאW)(tv ٣E JאkאאFovershootE

K GאW

١K אאאאאאאאאאאאאW

אאאאאאW

ksss

ksss

sks

ssesy

100100

100

100

1001

100

)()(

2

2

2

2

2

2

+=

+=

+=

אאW

אאW

ksskss

kss

kss

kssssy

100100100

100100

1001001

100100

)()(

2

2

2

2

+++

+=

++

+=υ

KSS 100100

2 +

v(s) e(s) y(s)

-


- ١٣٣ -

W

100100100

)()(

2 +=

kssssy

υ

אאאאאK

٢K אאאאאאאאKאאאאאK

אאW

100100)100(

1001001

1)()(

2

2

+++

=

++

=kss

kss

ksssse

υ

א

2

1)(s

s =υW

100100()100(

100100)100(.1)(

222 +++

=++

+=

kssks

ksskss

sse

אאאW

)(.lim0

sesesss →

=

)100100()100.(lim

20 +++

=→ ksss

ksss

100

100k=

אאWess= k


- ١٣٤ -

٣ JאאאW ٣ J١אW

אאאאאאאt ى K∞إلא،אאאאא

אאאאאאKאאאאאא

אאאא،אאW

אא Time function

אא Physical

interpretation

א Name

א Waveform

s1

1

א Constant position

Unit Step

2

1s

t א

Constant velocity Unit Ramp

3

1s

2

21 t

א Constant acceleration

אא Parabola


- ١٣٥ -

٣ J٢אאW אאאאאא

אא،אאW

Gkpאאאא،Fv(t)=1 :()(0

sGLimksp →

= Gkvאאאאא،Fv(t)=t :()(.

0sGsLimk

sv →=

Gka ،אאאאאF2

21 tv(t)= :()(.2

0sGsLimk

sa →=

٣ J٣אאאאאW

JstepאאאW

ps

step ksGLimee

+=

+=∞=∞

→1

1)(1

1)()(0

JrampאאאW

vs

ramp ksGsLimee 1

)(.1)()(

0

==∞=∞→

JparabolaאאאW

as

parab ksGsLimee 1

)(.1)()(

0

2 ==∞=∞

→

G(s)V(s) E(s) Y(s)


- ١٣٦ -

אאא،א،אאאאאW אType 2 אType 1 אType 0 א

אError

אStatic error

constant

אאError

אStatic error

constant

אאError

אStatic error

constant

אא

א Input

0 ∞kp= 0 ∞kp= pk+1

1kp= pk+1

1W1

0 ∞kv= vk

1 kv= ∞ kv=0 vk

1 Wt

ak1 ka= ∞Ka=0 ∞ Ka=0

ak1

W2

21 t

٤ JאאאW

אאאאאא،אW

GGp(s)אאאאא GGc(s)אא

٥ J٢Wאא

אאאאW


- ١٣٧ -

G(s)=Gc(s)×Gp(s) אאW

)()(1)()(

)()(

sGsGsGsG

sRsC

pc

pc

×+×

=F٥ J١E

אאאW

)()(1)()(

sGsGsRsE

pc ×+=F٥ J٢E

٤ J١אאאאאאP-controllerW אאאW)()( teKtp p=

אW)()( sEKsP p=

אאאWpc KsGsEsP

== )()()(F٥ J٣E

،אאאאR0אאW

GאWsRsR 0)( =

GאW1

1)(+

=s

sGp τ

אF٥ J٢EאW

)1(1

111

1)( 00

pp

KsssR

sR

sK

sE+++

=×

++

=ττ

τ

אאאW

ppssss K

RKss

ssRssEe+

=+++

==→→ 1)1(

1lim)(lim 0000 τ

τ

،אאאאאאאאא،אKpא

אאאK


- ١٣٨ -

GWאW1

1)(+

=s

sGpאאW1)( =tr،

אאW10,5,2 === ppp KKKאאא،אאW

٥ J٣Wאאאא

٤ J٢אאאאאאI-controllerW

אאאW∫= t

IdtteKtp 0 )()(

אאאWs

KsG Ic =)(

،אאאאR0אאW

GאWsRsR 0)( =

0.66

0.830.91


- ١٣٩ -

GאW1

1)(+

=s

sGp τ

אאW

)()1(

111

1)(20

0

II KsssssR

sR

ssKsE

+++

=×

+×+

=τ

τ

τ

אאאW

0)(

)1(lim)(lim2000

=+++

==→→

Issss Ksss

sssRssEeτ

τ

אא،אאאאאאאאאK

GWאW1

1)(+

=s

sGpאאW1)( =tr،

אאW2,3.0,2.0,1.0 ==== IIII KKKK،אאאאאW

٥ J٤Wאאאא


- ١٤٠ -

٤ J٣אאאאאאאPI-controllerW אאאאW∫+= t

Ip deKteKtp0

)()()( ττ

אאאאWs

KsKsG Ip

c

+=)(

،אאאאאR0אאW

iK אWsRsR 0)( =

iiK אW1

1)(+

=s

sGp τ

אאW

])1([)1(

111

1)(20

0

IpIp KKsssssR

sR

ssKsKsE

++++

=×

+×

++

=τ

τ

τ

Wאאא

0])1([

)1(lim)(lim2000

=+++

+==

→→Ip

ssss KKssssssRssEe

ττ

אאאא،אאאאאK

GWאW1

1)(+

=s

sGpאאW1)( =tr،

אאאW

2,1 == pI KK 1,1 == pI KK 1,2 == pI KK

אאאאאW


- ١٤١ -

٥ J٥Wאאאאא

٤ J٤אאאאאאאאPID-controllerW

אאאאW

dttdeKdtteKteKtp

D

t

Ip

)()()()( 0 ++= ∫

אאאאאWs

KsKsKsG IpD

c

++=

2

)(

،אאאאאאR0אאW

GאWsRsR 0)( =

GאW1

1)(+

=s

sGp τ

אאW


- ١٤٢ -

])1()[()1(

111

1)(20

02

IpDIpD KsKsKsssR

sR

ssKsKsK

sE++++

+=×

+×

+++

=τ

τ

τ

אאאW

0])1()[(

)1(lim)(lim2000

=++++

+==

→→IpD

ssss KsKsKssssRssEe

ττ

אאא،אאאאאאאK

GWאW1

1)(+

=s

sGpאאW1)( =tr،

،אאאאאאאאאW

2,1,1 === DpI KKK1,1,1 === DpI KKK 2.0,1,2 === DpI KKK

0 5 10 15 20 25 30

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05Step Response

Time (sec)

Ampl

itude

0 5 10 15 20 25 300.5

0.6

0.7

0.8

0.9

1

1.1

1.2Step Response

Time (sec)

Ampl

itude

0 5 10 15 20 25 300.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1Step Response

Time (sec)

Ampl

itude

٥ JאאאאW

sK

sKKsU

dtdeKdteKeKu D

IpDIp ++=⇒++= ∫ )(.

א א


- ١٤٣ -

،אאאאWאאאא

א אאא

אאא

אא

Kp א Ki א א א Kd

אאאאW PIDאאאאאא،W

אאאאאאK אאK K אאאK אWKp،KiKdאא

GW،אאW

٥ J٦W،

JאאWFkxdtdxb

dtxdM =++2

2

JאW)()()()(2 sFskXsbsXsXMs =++

JאאאאאX(s)אF(s)WkbsMssF

sX++

=2

1)()(


- ١٤٤ -

W אWM=1kg אWb=10N.s/m אWk=20N/m אWF(s)=1

אאאאאW2010

1)()(

2 ++=

sssFsX

אאאWKp،KiKdW Gאא G Gאא

JאאאW2010

1)()(

2 ++=

sssFsX

٥ J٧Wאאא

JאאProportional controlW

אאאאFKpE،אאאאK

אאאאאW


- ١٤٥ -

)20(10)()(

2P

P

KssK

sFsX

+++=

אWKp=300אאאW

٥ J٨Wאאאא

אאאאאא،אK

Jאא JאProportional-Derivative controlW

אאאא،אאאאאאW

)20()10()()(

2PD

PD

KsKsKsK

sFsX

+++++

=

WKp=300Kd=10אאאW


- ١٤٦ -

٥ J٩Wאאאא J

،אאאאאאא

J אאאPI controlW אאאPID אאW

IP

IP

KsKssKsK

sFsX

+++++

=)10(10)(

)(23

WKp=350Ki=300Kd=50אאאW

٥ J١٠Wאאאא J J

אאאK


- ١٤٧ -

J٥ J ١W

אאאאאאW

١ JאFkp,kv,ka(אK ٢ Jא؟ ٣ JאאאK

GאW

١ JאW208.512108

52500)(0

=××××

==→

sGLimksp

אW0)(.0

==→

sGsLimksv

אW0)(.2

0==

→sGsLimk

sa ٢ JאאאF٣ J٣Eאtype 0. ٣ J،،W

161.01

1)(1

1)()(0

=+

=+

=∞=∞→ ps

step ksGLimee

∞===∞=∞→ vs

ramp ksGsLimee 1

)(.1)()(

0

∞===∞=∞→

as

parab ksGsLimee 1

)(.1)()(

0

2

)12)(10)(8()5)(2(500

+++++sss

ssV(s)

E(s)Y(s)


- ١٤٨ -

٢W

אאאאאאW

١ JאFkp,kv,ka(אK ٢ J؟א ٣ JאאאK

GאW

١ JאW3

100532

1000)(0

=××

==→

sGLimksp

אW0)(.0

==→

sGsLimksv

אW0)(.2

0==

→sGsLimk

sa ٢ JאאאF٣ J٢ J٣Eא0. ٣ J،،W

0291.01

1)(1

1)()(0

=+

=+

=∞=∞→ ps

step ksGLimee

∞===∞=∞→ vs

ramp ksGsLimee 1

)(.1)()(

0

∞===∞=∞→

as

parab ksGsLimee 1

)(.1)()(

0

2

)5)(3)(2(1000

+++ sss

V(s) E(s)

Y(s)


- ١٤٩ -

٣W אKאא،אאאא

١٠אK٪ GאW

אType1W ∞==

→)(

0sGLimk

sp

8765)(.

0 ×××

==→

KsGsLimksv

0)(.2

0==

→sGsLimk

sa ١٠٪W

1.01)(.

1)()(0

===∞=∞→ vs

ramp ksGsLimee

W10876

5)(.0

=×××

==→

KsGsLimksv

אWK=672K ٤W

אאאW

)8)(7)(6()5(

++++

sssssK

V(s) E(s)

Y(s)

)10(100+ss

V(s) E(s)

Y(s)

51+s


- ١٥٠ -

١ J אK ٢ J אאאK ٣ J אאאK

GאW ١ Jאאאא

אאאK אאאאאW

4005015)5(100

)10(100

)5(1

)10(1001

)10(100

)()().(1)()( 23 −++

+=

+−

+++

+=

−+=

ssss

sssss

sssGsHsG

sGsG e

אאW

אType 0אW

45

4005100)(

0

−=

−×

==→

sGLimk esp

Wkv=0ka=0K אאאW

4

451

11

1)()( −=−

=+

=∞=∞p

step kee

אאאאאK

4005015)5(100

23 −−++

ssss

V(s) E(s)

Y(s)


- ١٥١ -

٥W

،אאאאאK

W1000)(1 =sG)25(

1)(2 +=

sssGK

WY(s)=E(s)G1(s)G2(s)+D(s)G2(s)،WY(s)=V(s)-E(s)،

Y(s)،אאאW)()()(1

)()(

)()(11)(

21

2

21

sDsGsG

sGsV

sGsGsE

+−

+=

E(s)אאK GאW

אאאאW )()()(

)()(1)(

lim)()()(1

lim)(lim)(21

2

021

00∞−∞=

+−

+==∞

→→→ DVssseesD

sGsGssG

sVsGsG

sssEe

Wev،אאאeDאאאK אאאא،א

D(s)=1/s،W

10001

100001

)(lim)(

1lim

1)(10

20

−=

+−

=+

−=∞

→→sG

sG

e

ss

D

٦W

V(s) E(s)

Y(s)

1000 )25(1+ss

D(s)


- ١٥٢ -

אF٣ J٥EאאאאאאFAntenna azimuth position controlKE

אאאאאW Kpot=0.318،K1=100،a=100،Km=2.083،am=1.71،Kg=0.1K

١ J אאאK،W،K

٢ J א؟אKא،١٠K٪

٣ J٥Wאאא

GאW ١ Jאאאאא

אאאG(s)W

אאא אא

אא

אאא

אא


- ١٥٣ -

)100)(71.1(63.6)(

++=

sssKsG

אאאW

)(1)(lim)(lim)(

00 sGssVssEe

ss +==∞

→→

G،WV(s)=1/sאאW

0)0(1

1)(1

1

lim)(lim)(00

=+

=+

==∞→→ GsG

ss

ssEess

G،V(s)=1/s2אאW

KsGssGs

sssEe

sss

79.25))(1(

1lim)(1

1

lim)(lim)(0

2

00=

+=

+==∞

→→→

G،V(s)=1/s3אאW

∞=+

=+

==∞→→→ ))(1(

1lim)(1

1

lim)(lim)(20

3

00 sGssGs

sssEe

sss

٢ Jא١(Type1) אאאאא،אאא

١٠אK٪

9.25779.251.0)( =⇒==∞ KK

e

١٥٤

אאאאאאאא

אא

א

א

א

א

٦

א ٢٥٤ אא אאFE אאאא

١٥٤

אא Jאאאא J

אאW

אאW אאאאW

GאאאאאK GאאאK GאאאאK GאאאK


אאW٤

אאW ٤ J אאאאK ٥ J אאאאK ٦ J K

אאW


١٥٥

אאWאאאא ١ JאאאW

אאאאאFאאEאאאKאאא

،אאאאאאאK

٢ JאאאאאW אאא٦ J١אW

٦ J١Wאאאא

PlantControllerReference

signalאSet point deviceKאאאאאאExternal disturbance أوא

؟אאאאאאאK

אאאאאאאאאא،אאאא

א،אאאאא،אאאא

אאאKאאאאאאאאstable equilibriumא،

אStableאאאא


١٥٦

אKאאאאאאאאאUnstableאא،

אאאאאOn the boundary of stabilityאאNeutralOn the brink of stabilityKאא

אאאאK

אאא٦ J٢FEא ٦ J٢FEאK

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6Step Response

Time (sec)

Ampl

itude

٦ J٢ FWE


١٥٧

0 5 10 15 20 25 30-3

-2

-1

0

1

2

3

4Step Response

Time (sec)

Ampl

itude

٦ J٢FWE

אאאאאאאאאאאLyapunov's theory of stabilityא،

אאאאKKאאאאאאאאאאאאKאא

אאאאReal time domainK אאאאאאאא

אאאאאאW

)...(.....1 011

1

1101

1

1 xbdtdxb

dtxdb

dtxdbkya

dtdya

dtyda

dtyda

m

m

mm

m

mn

n

nn

n

n +++=++−

+−

−

−

−

−

אאאאλiKא٦ J٣אאאאK


١٥٨

٦ J٣W אאאא

אאאWאאאStable processes؟אא

אאProcess y(t)אאאW

0)( =∞→t

tyLimK

אאאאאאאאאCharacteristic equationאאComplex

rootsאאNegative real partאאאאPositive real partאא

KאאאאStable processesאאאUnstable processesK


١٥٩

W אאא א

121+S

21−

=S

)1)(1(2

−+ SS S=1

)2(1+SS

א

11

2 ++ SS אW

23

21

2,1 jS ±−=

kS +21 k

אאאאאאאא

אאImpulse responseאאאRoots of the characteristic equationK

אאאאאאProcess stabilityאאאא

אאאאא،אאאאK

אאאאאאW

١ J אאAlgebric criteriaאאאאWW

Routh criteriaHurwitz criterionK ٢ J אאFrequency criteriaWNyquist

criteriaMichailov criterionTsypkin's ruleK ٣ J D،D-partition methodK

אאK


١٦٠

٣ JאאW אאאאאאאאא

אאאאאCharacteristic equationאStableאאNeutralUnstableK

٣ J١Routh criterion W אאW

0... 011

1 =++++ −− asasasa n

nn

n אאאTwo strokes

אאאan,an-2,an-4,…אאan-1,an-3,an-5,…אW 3…. 2 1

an-4…. an-2an sn an-5… an-3 an-1 sn-1

......33 =a 1

54132

−

−−− −=

n

nnnn

aaaaa

a1

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−

−−− −=

n

nnnn

aaaaa

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......43 =a 31

33453142 a

aaaaa nn −− −

=31

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aaaaa nn −− −

=sn-3

......53 =a 41

3431334152 a

aaaaa

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41

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−=sn-4

אאאאאאאאאאאאRight half of the complex

planeKאאאNecessary and sufficient conditionא،אאאאאאאאא

אאאאאאK אאאאאא،

אאאאאאK


١٦١

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אW ٢ J אאאεא،

אεK ٣ J ε+→ 0εא،

אאאאאאאאאאK

J אאאW אאאאאאW

١ J אאאsi،אAuxiliary equationFאאKE

٢ J אאאsאא،אאאאאK

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٣ J٢Hurwitz criterionW

אאאnnW


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n

n

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אאאאאאDiagonal minorsאא∆n،אW

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אאאאאאאאאאאאFאאאEאK

٤ JW ٤ J١١W

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113

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א،אאאאאאאא،א

3js ±=K ٤ J٣٣W

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3 0 s2

،אאאא

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١٦٥

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012 =++ bss b>0 0123 =+++ csbssbc-1>0 01234 =++++ dscsbssbcd-d2-b2 >0 012345 =+++++ esdscsbssbcd+b-d2-b2e >0 0123456 =++++++ fsesdscsbss (bcd+bf-d2-b2e)e+b2c-bd-bc2f-f2+bfe+cdf >0


١٦٧

J٦ J ١W

אאW 633244)( 2345 +++++= ssssssq

١ JK ٢ J؟א

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163131

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20020631

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אא א

א אא


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1)1(

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+=

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)(1)(1+++

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+=+ssss

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Ka11 1 s4 (K+6) 6 s3 Ka

Ka

=6

061

6

606

66111

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+

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0

660

660

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אK ٢ JK


١٧٠

٣ JKaאאאess24%Wr(t)=At

GאW

١ J0)5)(2)(1(

)()( =+++

+=

ssssasKsG

W

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)()5)(2)(1()5)(2)(1(

)(1)(1+++

+++++=

++++

+=+ssss

asKssssssss

asKsG

אאW0)10(178 234 =+++++ KasKsss ٢ JW

Ka17 1 s40 (K+10) 8 s3 Ka

Ka

=6

061

8

1268

108171

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+

s2

0

8126

8126

8126

8126 8)10(

108

K

K

K

K KaKKaK

−

−

−

− −+×=

+s1

Kas0

)1()(

++

sas

)5)(2( ++ sssK

R(s) Y(s)

אא

א


١٧١

٣ JאW

W12608

126≤⇒≥

− KK

W0≥Ka W064)126()10( ≥−−×+ KaKK

אessWess=A/Kv،10

)(lim0

KassGKsv ==→

،W

KaAess

10=K

אW%24=sseA42=Ka،F6.0,70 == aKEF84.0,50 == aKEאאא

24%K ٤W

אא،W 04)2(3 23 =++++ sKKss

KאאK GאWK>0.53 ٥W

אאאאאאאאW

אא אא 0152 =++ ss b>0

……………………………………………...012

413 =+++ sss bc-1>0

……………………………………………...01102 234 =++++ ssss bcd-d2-b2 >0

……………………………………………...01325 2345 =+++++ sssss bcd+b-d2-b2e >0

……………………………………………...0132 23456 =++++++ ssssss (bcd+bf-d2-b2e)e+b2c-bd-bc2f-f2+bfe+cdf >0

……………………………………………...


١٧٢

GאW אא אא

0152 =++ ss b=5>0 א

012413 =+++ sss bc-1=0.25×1-1=-0.75 <0

א 01102 234 =++++ ssss bcd-d2-b2=1×2×10-102-12= -81 <0

א 01325 2345 =+++++ sssss bcd+b-d2-b2e=30+5-32-52×1=1 >0

א 0132 23456 =++++++ ssssss (bcd+bf-d2-b2e)e+b2c-bd-bc2f-f2+bfe+cdf >0

(2+2-1-12)×3+4-2-2-1+6+1=-19<0 א

א ٢٥٤ א

אאFE

- ١٧٣ -

AC Motor Actuator

Analog Automatic Control

Block Diagram אאCharacteristic Equation

Characteristics אClosed Loop

Control System Control Valve

אאControlled variable Controller

Critical damping Damping

DC Motor אDelay time

Derivative Derivative controller

Design Digital

Disturbance Dynamic

Error Feedback

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א ٢٥٤ א

אאFE

- ١٧٤ -

אאFinal control element אFlow meter

אFlow rate Forward path

Frequency Gain

Input Integral

Integral controller Laplace transform

Level Manual control

Motor אOn-off controller

אOpen loop Output

אOver damping Over shoot

אPeak time אPerformance

אאPermanent response א،Pneumatic אPolynomial

אPotentiometer Process

Proportional Proportional Controller

א ٢٥٤ א

אאFE

- ١٧٥ -

Reference input אResponse

אResponse curve אאRise time

Root Sensor

אSeries אSet point

אSettling time אSignal transducer

אאStability אאStability criteria

Step input System

א،Tachometer אTime constant

אTime response Transducer

אאTransfer function אTransient response

Under damping Unit step

Unity feedback

א ٢٥٤ אא

אאFE

אא

١ Jאא JLא Jא J١٩٨٩א

٢ JIntroduction to control system technology- fifth editionאWRobert- N.BatesonWPrentice HallK

٣ JFeed back Control systemsא،WBruns and saundersWMc Graw-Hill 1995K

٤ JControl systems Engineering-third editionא،WNorman S.NiseWJohn Wiley & Sons, IncK

٥ JModern Control systemsא،WRICHARD C.DORF ROBERT H.BISHOP،WAddison-Wesley

א ٢٥٤ א

אאFE

א

אאWאאא

١ JKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٢ ٢ JאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٦ ٣ JאאאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١١ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٦ ١KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٧

אאWאא ١ JאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٢٣ ٢ JאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٢٤ ٢ J١אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٢٤ ٢ J٢אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٤١ ٢ J٣KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٥١ ٢ J٤אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٥٦ ٢ J٥אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٦٠ ٣ JאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٧٣ ٣ J١אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٧٣ ٣ J٢אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٧٣ ٣ J٣אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٧٤ ٣ J٤אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٧٥ ٣ J٥אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٧٦ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٧٩

٢KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٨٠

א ٢٥٤ א

אאFE

אאWאא ١ JאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٨٧ ٢ JKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٩١ ٣ JאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٩٤

٣KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٠٢ אאאWאאאאא

١ JאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٠٧ ٢ JאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١١٢

٤KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٢٢ אאWאאא

١ JאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٢٧ ٢ JאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٢٩ ٣ JאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٣٤ ٤ JאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٣٦ ٥ JאאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٤٢

٥KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٤٧ אאWאאאא

١ JאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٥٥ ٢ JאאאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٥٥ ٣ JאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٦٠ ٤ JKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٦٢ ٥ JאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٦٥

٦KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٦٧ אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٧٥

אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٧٦

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