3-modeling control systems

8/18/2019 3-Modeling Control Systems

1/24

MODELING CONTROL

SYSTEMS

ELECTRIC NETWORK

&OPERATIONAL AMPLIFIER

Sazuan BEKC 3533 120112012


2/24

OBJECTIES

• F!n" a #a$%#a$!'a( #)"(* 'a((" a$+an,-+ -un'$!)n -)+ (!na+* $!#!n.a+!an$ ('$+!'a(* #'%an!'a( an"('$+)#'%an!'a( ,/,$#,

Sazuan BEKC 3533 120112012


3/24

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.

Sazuan BEKC 3533 120112012


4/24

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%!+'%%);


5/24

ELECTRIC NETWORK

• O+ 'an u, transform methods: – loop or mesh analysis – Kirchhof’s

voltage law

– nodal analysis – Kirchhof’s 'u++n$ law

Sazuan BEKC 3533 120112012


6/24

ELECTRIC NETWORK

Ta9( :1

Sazuan BEKC 3533 120112012


7/24

ELECTRIC NETWORK

• S!#(* S!n( L)) E('$+!' N$)+ – M,% ana(/,!,

• !a $% "!;+n$!a( 6ua$!)n

• !a $+an,-)+# #$%)"

– N)"a( ana(/,!,• !a $+an,-)+# #$%)"

Sazuan BEKC 3533 120112012


8/24

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

Sazuan BEKC 3533 120112012


9/24

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

Sazuan BEKC 3533 120112012


10/24

ELECTRIC NETWORK

• C)#(= C!+'u!$ – #,% ana(/,!,

• .!a $+an,-)+# #$%)"

– n)"a( ana(/,!,• .!a $+an,-)+# #$%)"

Sazuan BEKC 3533 120112012


11/24

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

Sazuan BEKC 3533 120112012


12/24

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

Sazuan BEKC 3533 120112012


13/24

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

)()(

)(

++

++

=

Sazuan BEKC 3533 120112012


14/24

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+

Sazuan BEKC 3533 120112012


15/24

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

Sazuan BEKC 3533 120112012


16/24

OP4AMP

F!u+ ::Sazuan BEKC 3533 120112012


17/24

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


18/24

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


19/24

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>,?

Sazuan BEKC 3533 120112012


20/24

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

+

=

Sazuan BEKC 3533 120112012


21/24

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 +

=∴

Sazuan BEKC 3533 120112012


22/24

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

Sazuan BEKC 3533 120112012


23/24

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

Sazuan BEKC 3533 120112012


24/24

TOGT OF TE DAY

• W%a$ !, /)u+ ')n$+!9u$!)n $)a+",n+/ ')n,+.a$!)n

4TE

END4

Sazuan BEKC 3533 120112012

3-modeling control systems

Documents