automatic control response of dynamic systems
DESCRIPTION
Automatic ControlTRANSCRIPT
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72 fo 1 egaP
smetsyS scimanyD fo esnopseR
.
" .
. . ")egnahC petS( " " " )pmaR( " " )eslupmI( "
" " . " )diosuniS( " " .
" " . .
.
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72 fo 2 egaP
yS redrO tsriF a fo esnopseRsegnahC eslupmI na ot met
:
sT ==+1 ) () ( ) (K
Us GsYs
Us=1 ) ( : 1 :
) ( ) () (
1
11
=+==+
sTYsK
sTGsYsK
. 5 .
:
etT ) (T= ytK
0 . t
)t(y . T/K )t(y T2 )1-e001(T/K T/K %8.63 T .
" T4 . T/K %2 T4 T/K %5 T3 %5.31 .
:
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72 fo 3 egaP
.
( ) yS redrO tsriF fo esnopseRsegnahC petS a ot met
: .
) (s
=1 Us :
) ( ) () (
1
1
=+=+
sTTK
sYsK
ssTYsK
1 = ytKetT) ( ) ( : 0 )t(y 0
T )t(y. " " K. K %59 T2 K %5.68 K )1-e-1( 001 %2.36
. T4 K %89 T3 K :
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72 fo 4 egaP
u y
" )t(y 5 .
. 5+K
noitacifitnedI metsyS redrO tsriF
. ( )
. .
%05 %03 . ( %02 )
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72 fo 5 egaP
)niaG( . ( ) tupni ni egnahc/tuptuo ni egnahC
:.
0.50503= 0403
K= . %36
01 . 01 " 3.6
: 01
0110.5 s+
2( )
redrO dnoceS fo esnopseR cimanyDsmetsyS )repmaD(
. ( ) . n) (
:
yKutdyd
tddy
nnn22
2
2
++= 2 )oitar gnipmad(
y u K : .
22 ) () ( ) (2
nn 2n
ssK
Us GsYs
==++
esnopseR petS :
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72 fo 6 egaP
:
:
)selop( 2p 1p : ssnn ++= 22 20
: 2A 1A
212
212
22
12
AKK
AKK
=
=
. 2 3 )t(y . 2p 1p
depmad revo .
depmad yllacitirc .
depmad rednu ro yrotallicso .
. 2p 1p
) (22) ( ) (
2
2
1
nn
n
sssYsK
sUs
=++
=
) (2
2
1
11sp
Asp
As
=++ Ys
=++ 112 12 ytAeAe ptpt ) (
12
244
2
222
12
=
=
nn
pdnapnnn
>1=1
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72 fo 7 egaP
>1:
:
n nntn YsK ssytKet] [) ( ) ( ) ( ) (=+=+
211 2
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72 fo 8 egaP
.
eR eslupmIesnops
) ( 22 ) (
2
2
1
nn
n
ssYsK
Us
=++=
:
) (2
2
1
1
spA
sp =+ YsA
=+ 12 12 ytAeAe ptpt ) ( : :
sucoL tooR
. 0 n : 0 ( 1p 2p) .
ssnn ++= 22 20
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72 fo 9 egaP
ppnn = 122 &1 1p 2p 0
1p 2p 1 . 1 j jn ... n
ppnn = 122 &1 0 == pj in
pj inn
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72 fo 01 egaP
:
= sjd
n " dn = 12 " " = 11
. " " " n
. n . . =soc1
esnopseR metsyS dna seloP neewteB snoitaleR : .
. / +
=+ 12 12 ytAeAe ptpt ) ( . .
.
. )selop tnanimod(
: snoitseuQ lairotuT
. R .1
. .2
.a2
1 01)s(G
s + =
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72 fo 11 egaP
2 .b51 2
)s(Gs s
+ + =2 .c
18 2
)s(Gs s
+ + =
.3 .
: .4
Gsss ssss =++ ++++ 22 0512 5040.300.60) () () () ( ) ( .
ytuKt) ( ) ( ) ( : .5
td += Tydt
) )t(y )t(u K T )t(y. )0 = t( . (
.
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72 fo 21 egaP
scitsiretcarahC esnopseR gninimreteD
: .
0 : rt ,emiT esiR %01 depmad revo .
. %59 %5 %09
: pt ,emiT kaeP . toohsrevo ( )
: pM ,toohsrevO mumixaM ( ) 1
) ( ) ( : 1 %001% ) (
=c
ctc Pp M
: st ,emiT gniltteS
. ( %5 %2" )
:
.
: 2
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72 fo 31 egaP
emiT kaeP ,tp: : ydtd=0:
) (
++
=+
ett
Ketttdydt
dd
ddt
ddt
n
n
n
soc1
nis
nis1
soc
2
2
) ( ) (
nis00,,2,3
01
nis2
==
==
=
dpdp
ntdp
tt
tt
Ktetdnp ydt
p
: ( toohsrevo) (pt ,emiT kaeP )
d tt dpp
==
: pM ,toohsrevO mumixaM
) ( : ) (
2
1
2
11
001%
nis001%1
soc
001%
2
==
=+
=
nd
p
p
pp
Me
Me
KytK
M
nd
: rt ,emiT esiR
:.
) (
==+
drdrt
nr ytKKett rnis
11soc
2
: etnr 0
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72 fo 41 egaP
nis01
soc2
=
tt drdr +
: soct dr
=
+=
21
2
11nat
nat01
1
dr
dr
t
t
%09 %01 .
: st ,emiT gniltteS
. . "
:
:.
.
yrammuS
+ot /25%) (K
%001= toohsrevoytK< toohsrevox %%
nis0011
soc2
=+
dsds ns xett t
t ds
) (n
s
t
tx
ds xe
nl001001
=
=
x=2%n
ts=3.9
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72 fo 51 egaP
noitseuQ lairotuT )emit esir( .6
.
) (n
ss
dr
dr
r
p
p
p
dpp
gniltteSemiTttx
trot
esiRemiTt
roMrof
Me
mumixaMtoohsrevOM
kaePemiTtt
:nl001
21
1nat
:
00.60.6
1
001
:
:
21
2 1
=
=
=
=
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72 fo 61 egaP
: -1 (
. (
)nosaM( .
:
H2
G2
G3
+++ +
++
Y R _ +
H3
G1
G1
H2
G2
H3
G3
+++ +
++
Y R _ +
XY
33
3GH 1 3
= GG
22
2GH 1 2
= GG
G122
2
GH 1G
33
3
GH 1G
+ + Y R _ +
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72 fo 71 egaP
R
22 +2
1 11
GH GG
33
3
GH 1G
Y _ +
(
++
=+
33
3
22
21
22
21
1111
11
GHG
GHGG
GHGG
R Y
) ( ) () ( 22331322123 ) ( ) () (
122331233
111111
GHGHGGGHGGGGGHGHGGGH
RY
++ =+
(
:
21
112
6432165321
pGpGG
==
:
2123
113
75327432
LGGGLGG
==
11 12 1212 132) () ( :
1GGG 1
GGLLpp
RY
++++=+
=+11 12 132) () ( . G3 G2
1GGG
GGRY
++ =+
-2 Tt) (
:. : (
=2 GssTs) ( ) ( ) ( )st ;emit gnilttes( )pM ;toohsrevO%( (
2t) ( )pt ;emit kaep(
G122
2GH 1 2
= GG
33
3GH 1 3
= GG
+ +Y R _ +2 1
3
4
6 5
7
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72 fo 81 egaP
. : . .
:
:
21 1
2 1
2 2
0sJ T )s(T
T T
k T
= = =
2 1 1) (2 2
sD T
k T
= =
) () (
21 2 1
2 2 1
sJ sD )s(T
k sD
= =
22 1 1
02 1 2sD sD sJ )s(T
k sD sD
+ = + =
) ( ) ( ) ( ) ( : sDssDsKs) ( ) ( ) (
TssJssDssDs
212
1122
0
=+=+
:
) ( ) ( ) ( ) (s) ( ) ( ) (
sss
Tssssss
12
122
1
=+=+
:
) ( ) ( ) ( ) ( ) (1
1()()()
1
22
222
==++
=++
TsssGss
ssss
Tssss
(
. n
J k D
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72 fo 91 egaP
:
2
2
2()
nn
n
ss GsK
=+++ :
0.511
===
nK
: :
%00161.3% === 12
P SOMe :
== 48n
Ts :
3.362 1
==
n
TP
-
. cd
K2 K1 PO (.). 0.5ces
(PO
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72 fo 02 egaP
) ( : 2 ) ( ) ( ) (
1
1212112
121222
21
2211
21
KKdnaKKKKKK
sssKKsK
nnn
nn
==+=+=+++=+++
: PO< ..2% 0.5 PTs:
0.201
pxe
0.51
2
2