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MODELING CONTROL
SYSTEMS
ELECTRIC NETWORK
&OPERATIONAL AMPLIFIER
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OBJECTIES
• F!n" a #a$%#a$!'a( #)"(* 'a((" a$+an,-+ -un'$!)n -)+ (!na+* $!#!n.a+!an$ ('$+!'a(* #'%an!'a( an"('$+)#'%an!'a( ,/,$#,
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ELECTRIC NETWORK
• A(/ $+an,-+ -un'$!)n $)#a$%#a$!'a( #)"(!n )- ('$+!'a('!+'u!$ !n'(u"!n a,,!. N$)+ an"
O4A# '!+'u!$
• E6u!.a(n$ '!+'u!$, -)+ $% ('$+!'n$)+, $%a$ )+ !$% 7+,$
')n,!,$ )- $%+ a,,!. (!na+')#)nn$,8 resistors, capacitorsand inductors.
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ELECTRIC NETWORK
• Ta9( :1 ,u##a+!z, $% ')#)nn$, an"$% +(a$!)n,%!, 9$n .)($a an"'u++n$ an" 9$n 'u++n$ an" '%a+
un"+ z+) !n!$!a( ')n"!$!)n,• F+)# $%, +(a$!)n,%!,* 'an +!$ $%
"!;+n$!a( 6ua$!)n, -)+ $% '!+'u!$ u,!nK%!+'%%);
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ELECTRIC NETWORK
• O+ 'an u, transform methods: – loop or mesh analysis – Kirchhof’s
voltage law
– nodal analysis – Kirchhof’s 'u++n$ law
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ELECTRIC NETWORK
Ta9( :1
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ELECTRIC NETWORK
• S!#(* S!n( L)) E('$+!' N$)+ – M,% ana(/,!,
• !a $% "!;+n$!a( 6ua$!)n
• !a $+an,-)+# #$%)"
– N)"a( ana(/,!,• !a $+an,-)+# #$%)"
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ELECTRIC NETWORK
• E=a#( 184 F!n" $% $+an,-+-un'$!)n +(a$!n $% 'aa'!$)+.)($a* C>,? $) $% !nu$ .)($a*
>,?* !n F!u+ :1
F!u+ :1
LC s
L
R s
LC sV sV C
1/1
)()(
2++
=
An,+,84
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ELECTRIC NETWORK
• Ra$ $% =a#( u,!n #,%ana(/,!, an" $+an,-)+# #$%)",!$%)u$ +!$!n a "!;+n$!a(
6ua$!)n
• Ra$ $% =a#( u,!n n)"a(ana(/,!, an" $+an,-)+# #$%)",
!$%)u$ +!$!n a "!;+n$!a(6ua$!)n
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ELECTRIC NETWORK
• C)#(= C!+'u!$ – #,% ana(/,!,
• .!a $+an,-)+# #$%)"
– n)"a( ana(/,!,• .!a $+an,-)+# #$%)"
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ELECTRIC NETWORK
• E=a#( 284 G!.n $% n$)+ )-F!u+ :2* 7n" $% $+an,-+ -un'$!)n*I2>,? @ >,?
F!u+ :2
121
2
21
2
2
)()()(
)()(
R s LC R R LCs R R
LCs
sV
s I sG
++++
==An,+84
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ELECTRIC NETWORK
• N)$!' $%a$ 'an u, $%,6ua$!)n,8Sum ofImpedances
around Mesh 1 I1>,
?
_Sum of
Impedances
common to the
two meshes
I2>,
?
=
Sum of applied
voltages around
Mesh 1
Sum of
Impedances
around Mesh 1 I1>,?
_Sum of
Impedances
common to thetwo meshes
I2>,?
=
Sum of applied
voltages around
Mesh 1
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ELECTRIC NETWORK
• E=a#( 384 F!n" $% $+an,-+-un'$!)n* C>,?@>,?* -)+ $% '!+'u!$ !n
F!u+ :2
• An,+,84
• %+ G1 1@R1 an" G2 1@R2
LC
G s
LC
C LGG sGG
sC
GG
sV
sV C
2212
21
21
)()(
)(
++
++
=
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ELECTRIC NETWORK
• N)$!' $%a$ 'an u, $%,6ua$!)n,8Sum of
admittances
connected toNode 1 L>,
?
_Sum of
admittances
common to thetwo nodes C>
,?
=Sum of applied
currents at
Node 1
Sum ofadmittances
connected to
Node 2
C>,
?
_ Sum ofadmittances
common to the
two nodes
L>,
?
=Sum of appliedcurrents at
Node 2+
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ELECTRIC NETWORK
• E=a#( :84 W+!$ $% #,%6ua$!)n, -)+ $% n$)+ ,%)n !nF!u+ :3
F!u+ :3
An,+ 8>2,2?I1>,? >2,1?I2>,?
I3 >,? >,?>2,1? I1>,? >,1?
I2>,? :, I3 >,? 0
I1>,? :, I2>,?
>:,11@,? I3 >,? 0
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OP4AMP
F!u+ ::Sazuan BEKC 3533 120112012
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OP4AMP
• Ba,!' O4A#8 O a# >F!u+ ::>a??%a, $% -)(()!n '%a+a'$+!,$!',84
– D!;+n$!a( !nu$* 2 >$? 1 >$?
– !% !nu$ !#"an'* ! >!"a(?
– L) )u$u$ !#"an'* ) 0 >!"a(?
– !% ')n,$an$ a!n a#(!7'a$!)n* A >!"a(?
• T%+-)+* $% )u$u$* )>$? A2>$?
1>$?HSazuan BEKC 3533 120112012
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OP4AMP
• In.+$!n O4A#8 I- 2>$? !,
+)un""* $% a#(!7+ !, 'a((" an!n.+$!n )4a# a, ,%)n !n F!u+::>9?
• T%+-)+* )>$? A1>$?
•
I- $) !#"an' a+ ')nn'$" $)$% !n.+$!n )4a# a, ,%)n !nF!u+ ::>'? * an" !- $% !nu$!#"an' !, %!%* Ia>,? 0 an" I1>,?
I , Sazuan BEKC 3533 120112012
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OP4AMP
• S!n' A >a!n? !, (a+* 1>$? 0 T%u,
I1>,? !>,?@1>,? an"
•
I2>,? )@2>,? E6ua$!n $)'u++n$ an" $ $% $+an,-+-un'$!)n )- !n.+$!n )4a# !,
)>,?@!>,? 2>,?@1>,?
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OP4AMP
• N)n4In.+$!n O A#8 F+)# F!u+
:5* $ )>,?A>!>,? 1>,??• ,!n .)($a "!.!,!)n*
F!u+:5
)()()(
)(
21
11 sV
s Z s Z
s Z V
o
+
=
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OP4AMP
•
F)+ (a+ A* "!,+a+" un!$/ !n"n)#!na$)+* $%u,
))()(/()(1)(
)(
211 s Z s Z s AZ
A
sV
sV
i
o
++
=∴
)(
)()(
)(
)(
1
21
s Z
s Z s Z
sV
sV
i
o +
=∴
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OP4AMP
• E=a#( 58 4 F!n" $% $+an,-+-un'$!)n* ) >,?@! >,?* -)+ $% '!+'u!$
!.n !n F!u+ :
F!u+ : s
s s
sV
sV
i
o 55.2295.45
232.1)(
)( 2 ++−=∴
An,+84
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OP4AMP
• E=a#( 8 4 F!n" $% $+an,-+-un'$!)n* )>,?@!>,? -)+ $% '!+'u!$
!.n !n F!u+ :
F!u+ :
An,+84
1)(
1)(
)(
)(
1122
2
1212
112122
2
1212
+++
++++=
s RC RC s R RC C
s RC RC RC s R RC C
sV
sV
i
o
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TOGT OF TE DAY
• W%a$ !, /)u+ ')n$+!9u$!)n $)a+",n+/ ')n,+.a$!)n
4TE
END4
Sazuan BEKC 3533 120112012