Pemodelan dan Identifikasi Sistem

N a m a : M u h a m a d F a d h i l H e n d r a w a n N i m : 3 3 3 2 2 1 0 0 5 9

K e l a s : P e m o d e l a n d a n I d e n t i f i k a s i S i s t e m ( A )

U T S P e m o d e l a n d a n I d e n t i f i k a s i S i s t e m 1 .

A . T e n t u k a n a m p l i t u d e p u n c a k d a n f r e k w e n s i d a r i 1 0 h a r m o n i k g a n j i l p e r t a m a b i l a 2 a n g k a t e r a k h i r n i m m a s i n g m i s a l n y a 3 3 3 2 2 1 0 0 5 9 m a k a n i l a i

f r e k w e n s i n y a 1 0 … …

B . G a m b a r k a n s p e k t r u m f r e k u e n s i

C . H i t u n g t e g a n g a n s e s a a t t o t a l b e r b a g a i n i l a i t ( p e r i o d e T = 2 0 1 0 S ) b e r d a s a r k a n c o n o t h N I M d i a t a s d e n g a n d a n s k e t s a b e n t u k g e l o m b a n g D . H i t u n g H a r g a T e g a n g a n ( V t ) d a n W a k t u ( t )

J a w a b :

M u h a m a d F a d h i l H e n d r a w a n ( 3 3 3 2 2 1 0 05 9) m a k a n i l a i f r e k u e n s i a d a l a h 5 9 h a r m o n i k g a n j i l p e r t a m a

A . D e r e t f o u r i e r u n t u k g e l o m b a n g t e r s e b u t a d a l a h s e b a g a i b e r i k u t : v(t)=4V

π (sinωt+sin 3ωt

3 +sin 5ωt

5 +sin 7ωt

7 +sin 9ωt 9 +…) M e n e n t u k a n n i l a i f r e k u e n s i d a s a r g e l o m b a n g :

f=1

t= 1

1x10⁻³s=1kHz

S e h i n g g a , d i d a p a t i n i l a i d a r i d e r e t f o u r i e r d i a t a s :

fn=n x f dan Vn=4V nπ

 n = 1 , m a ka :

f1=1x1000=1000Hz danV1= 4x4

1x3,14=5,095V

 n = 3 , m a ka :

f3=3x1000=3000Hz dan V3= 4x4

3x3,14=1,698V

 n = 5 , m a k a :

f5=5x1000=5000Hz dan V5= 4x4

5x3,14=1,019V

 n = 7 , m a k a :

f 7=7x1000=7000Hz danV7= 4x4

7x3,14=0,7279V

B e r i k u t i n i m e r u p a k a n n i l a i f r e k u e n s i y a n g d i h a s i l k a n s e r t a n i l a i t e g a n g a n p u n c a k s a m p a i 5 9 h a r m o n i k g a n j i l :

n H a r m o n i k F r e k u e n s i ( H z ) T e g a n g a n P u n c a k

1 P e r t a m a 1 0 0 0 5 , 0 9 5

3 K e - d u a 3 0 0 0 1 , 6 9 8

5 K e - t i g a 5 0 0 0 1 , 0 1 9

7 K e - e m p a t 7 0 0 0 0 , 7 2 7

9 K e - l i m a 9 0 0 0 0 , 5 6 6

1 1 K e - e n a m 1 1 . 0 0 0 0 , 4 6 3

1 3 K e - t u j u h 1 3 . 0 0 0 0 , 3 9 1

1 5 K e - d e l a p a n 1 5 . 0 0 0 0 , 3 3 9

1 7 K e - s e m b i l a n 1 7 . 0 0 0 0 , 2 9 9

1 9 K e - s e p u l u h 1 9 . 0 0 0 0 , 2 6 8

2 1 K e - s e b e l a s 2 1 . 0 0 0 0 , 2 4 2

2 3 K e - d u a b e l a s 2 3 . 0 0 0 0 , 2 2 1

2 5 K e - t i g a b e l a s 2 5 . 0 0 0 0 , 2 0 3

2 7 K e - e m p a t b e l a s 2 7 . 0 0 0 0 , 1 8 8

2 9 K e - l i m a b e l a s 2 9 . 0 0 0 0 , 1 7 5

3 1 K e - e n a m b e l a s 3 1 . 0 0 0 0 , 1 6 4

3 3 K e - t u j u h b e l a s 3 3 . 0 0 0 0 , 1 5 4

3 5 K e - d e l a p a n b e l a s 3 5 . 0 0 0 0 , 1 4 5

3 7 K e - s e m b i l a n b e l a s 3 7 . 0 0 0 0 , 1 3 7

3 9 K e - d u a p u l u h 3 9 . 0 0 0 0 , 1 3 0

4 1 K e - d u a p u l u h s a t u 4 1 . 0 0 0 0 , 1 2 4

4 3 K e - d u a p u l u h d u a 4 3 . 0 0 0 0 , 1 1 8

4 5 K e - d u a p u l u h t i g a 4 5 . 0 0 0 0 , 1 1 3

4 7 K e - d u a p u l u h e m p a t 4 7 . 0 0 0 0 , 1 0 8

4 9 K e - d u a p u l u h l i m a 4 9 . 0 0 0 0 , 1 0 3

5 1 K e - d u a p u l u h e n a m 5 1 . 0 0 0 0 , 0 9 9

5 3 K e - d u a p u l u h t u j u h 5 3 . 0 0 0 0 , 0 9 6

5 5 K e - d u a p u l u h d e l a p a n 5 5 . 0 0 0 0 , 0 9 2

5 7 K e - d u a p u l u h s e m b i l a n 5 7 . 0 0 0 0 , 0 8 9

5 9 K e - t i g a p u l u h 5 9 . 0 0 0 0 , 0 8 6

6 1 K e - t i g a p u l u h s a t u 6 1 . 0 0 0 0 , 0 8 3

6 3 K e - t i g a p u l u h d u a 6 3 . 0 0 0 0 , 0 8 0

6 5 K e - t i g a p u l u h t i g a 6 5 . 0 0 0 0 , 0 7 8

6 7 K e - t i g a p u l u h e m p a t 6 7 . 0 0 0 0 , 0 7 7

6 9 K e - t i g a p u l u h l i m a 6 9 . 0 0 0 0 , 0 7 3

7 1 K e - t i g a p u l u h e n a m 7 1 . 0 0 0 0 , 0 7 1

7 3 K e - t i g a p u l u h t u j u h 7 3 . 0 0 0 0 , 0 6 9

7 5 K e - t i g a p u l u h d e l a p a n 7 5 . 0 0 0 0 , 0 6 9

7 7 K e - t i g a p u l u h s e m b i l a n 7 7 . 0 0 0 0 , 0 6 6

7 9 K e - e m p a t p u l u h 7 9 . 0 0 0 0 , 0 6 4

8 1 K e - e m p a t p u l u h s a t u 8 1 . 0 0 0 0 , 0 6 2

8 3 K e - e m p a t p u l u h d u a 8 3 . 0 0 0 0 , 0 6 1

8 5 K e - e m p a t p u l u h t i g a 8 5 . 0 0 0 0 , 0 5 9

8 7 K e - e m p a t p u l u h e m p a t 8 7 . 0 0 0 0 , 0 5 8

8 9 K e - e m p a t p u l u h l i m a 8 9 . 0 0 0 0 , 0 5 7

9 1 K e - e m p a t p u l u h e n a m 9 1 . 0 0 0 0 , 0 5 5

9 3 K e - e m p a t p u l u h t u j u h 9 3 . 0 0 0 0 , 0 5 4

9 5 K e - e m p a t p u l u h d e l a p a n 9 5 . 0 0 0 0 , 0 5 3

9 7 K e - e m p a t p u l u h s e m b i l a n 9 7 . 0 0 0 0 , 0 5 2

9 9 K e - l i m a p u l u h 9 9 . 0 0 0 0 , 0 5 1

1 0 1 K e - l i m a p u l u h s a t u 1 0 1 . 0 0 0 0 , 0 5 0

1 0 3 K e - l i m a p u l u h d u a 1 0 3 . 0 0 0 0 , 0 4 9

1 0 5 K e - l i m a p u l u h t i g a 1 0 5 . 0 0 0 0 , 0 4 8

1 0 7 K e - l i m a p u l u h e m p a t 1 0 7 . 0 0 0 0 , 0 4 7

1 0 9 K e - l i m a p u l u h l i m a 1 0 9 . 0 0 0 0 , 0 4 6

1 1 1 K e - l i m a p u l u h e n a m 1 1 1 . 0 0 0 0 , 0 4 5

1 1 3 K e - l i m a p u l u h t u j u h 1 1 3 . 0 0 0 0 , 0 4 5

1 1 5 K e - l i m a p u l u h d e l a p a n 1 1 5 . 0 0 0 0 , 0 4 4

1 1 7 K e - l i m a p u l u h s e m b i l a n 1 1 7 . 0 0 0 0 , 0 4 3

B . D i b a w a h i n i a d a l a h g a m b a r d a r i g r a f i k p e r b a n d i n g a n s p e k t r u m f r e k u e n s i d e n g a n t e g a n g a n p u n c a k

C . B e r i k u t i n i m e r u p a k a n n i l a i t e g a n g a n s e s a a t d a r i 9 n i l a i h a r m o n i k d a r i t a b e l d i a t a s ( N i m : 3 3 3 2 2 1 0 0 59)

J a w a b :

V ( t ) = 5 , 0 9 s i n ( 2 π 1 0 0 0 t ) + 1 , 6 9 ( 2 π 3 0 0 0 t ) + 1 , 0 2 s i n ( 2 π 5 0 0 0 t ) + 0 , 7 3 s i n ( 2 π 7 0 0 0 t ) + 0 , 5 7 s i n ( 2 π 9 0 0 0 t ) + 0 , 4 6 s i n ( 2 π 1 1 0 0 0 t ) + 0 , 3 9 s i n ( 2 π 1 3 0 0 0 t ) + 0 , 3 3 s i n ( 2 π 1 5 0 0 0 t ) + 0 , 2 9 s i n ( 2 π 1 7 0 0 0 t )

 T = 2 0 1 0 µ s / 1 6

= 1 2 5 , 6 µ s

V ( t ) = 5 , 0 9 s i n ( 2 π 1 0 0 0 ( 1 2 5 , 6 µ s ) + 1 , 6 9 ( 2 π 3 0 0 0 ( 1 2 5 , 6 µ s ) + 1 , 0 2 s i n ( 2 π 5 0 0 0 ( 1 2 5 , 6 µ s ) + 0 , 7 3 s i n ( 2 π 7 0 0 0 ( 1 2 5 , 6 µ s ) + 0 , 5 7 s i n ( 2 π 9 0 0 0 ( 1 2 5 , 6 µ s ) + 0 , 4 6 s i n ( 2 π 1 1 0 0 0 ( 1 2 5 , 6 µ s ) + 0 , 3 9 s i n ( 2 π 1 3 0 0 0 ( 1 2 5 , 6 µ s ) + 0 , 3 3 s i n ( 2 π 1 5 0 0 0 ( 1 2 5 , 6 µ s ) + 0 , 2 9 s i n ( 2 π 1 7 0 0 0 ( 1 2 5 , 6 µ s )

V ( t ) = 2 , 4 V o l t

D . U n t u k h a r g a v ( t 0 d a n w a k t u ( t ) d a p a t d i l i h a t s e b a g a i b e r i k u t :

W a k t u ( µ s ) V ( t ) ( v o l t )

0 0

1 2 5 , 6 2 , 4

2 5 1 , 2 5 1 , 5 5

5 0 2 , 5 1 , 1 3

1 0 0 5 0 , 2 5

5 0 2 , 5 - 3 , 2 8

2 5 1 , 2 5 - 1 , 2 4

1 2 5 , 6 - 1 , 0 8

2 0 1 0 - 0 , 2 5

2 . P a d a s i s t e m k e n d a l i d i g a m b a r k a n

P e r u m u s a n f u n g s i h a l i h d i g a m b a r k a n d a l a m s e b u a h m o d e l d a l a m p r o g r a m m a t l a b

B u a t l a h r e s p o n b e r u p a g r a f i k c o n t o h d i a t a s p ( s ) = 1 + 1 5 + 3 . R u b a h l a h m a s i n g m a s i n g n i l a i p ( s ) d a n q ( s ) s e s u a i N I M m a s i n g m a s i n g n i l a i p ( s ) a n g k a a k h i r N I M d a n d a r i k a n a n d a n n i l a i q ( s ) a d a l a h a n g k a s a t u d i g i t d a r i b e l a k a n g d a n n i l a i 2 a n g k a d a r i b e l a k a n g b e r u r u t

J a w a b :

N i m ( 3 3 3 2 2 1 0 05 9) p(s)

q(s)= 9 s²+9s+59 O u t p u t :

%Muhamad Fadhil Hendrawan

%Nim (333220059)

% Definisikan fungsi p(s) dan q(s) numerator = 9;

denominator = [1, 9, 59]; % koefisien untuk s^2, s, dan konstanta

% Buat model sistem menggunakan fungsi tf() G = tf(numerator, denominator);

% Plot diagram Bode figure;

bodeplot(G);

title( 'Bode Plot of p(s)/q(s) = 9/(s^2 + 9s +

59)' );

3 . B u a t l a h p e m o d e l a n t e m p e r a t u r e d i r u a n g a n r u m a h t e m p a t t i n g g a l m a s i n g 2 t e r d i r i d a r i ( s u h u d i n d i n g , s u h u l a n t a i , s u h u a t a p , s u h u u d a r a , s u h u l u a r , d a n i n t e n s i t a s c a h a y a )

J a w a b :

M o d e l t e m p e r a t u r e d i r u a n g a n r u m a h y a n g d a p a t d i d e f i n i s i k a n s e b a g a i b e r i k u t :

 S u h u d i n d i n g ( T d )

 S u h u a t a p ( T a )

 S u h u l a n t a i ( T l )

 S u h u u d a r a d i d a l a m r u a n g a n ( T c )

 S u h u l u a r r u a n g a n ( T o )

 S u h u I n t e n s i t a s c a h a y a ( T c d )

 S u h u k i p a s a n g i n ( T k )

 S u h u p r o y e k t o r ( T p )

U n t u k m e n g g a m b a r k a n m o d e l d i a t a s , d a p a t m e n g g u n a k a n r u m u a t a u

p e r s a m a a n d i f e r e n s i a l u n t u k m e n g h i t u n g p e r u b a h a n s u h u d a r i w a k t u k e w a k t u d e n g a n m e n g a c y p a d a p e r t u k a r a n p a n a s a n t a r a e l e m e n e l e m e n t e r s e b u t .

P e r s a m a a n d i f e r e n s i a l b e r i k u t a d a l a h y a n g p a l i n g s e r i n g d i g u n a k a n u n t u k m e n g g a m b a r k a n p e r u b a h a n s u h u d a l a m r u a n g a n :

 dTd

dt =K1x(¿−Td)

 dTd

dt =K2x(¿−Td)

 dTd

dt =K3x(¿−Td)

 dT c

dt =K4x(T l+Td+Ta

3 )−Tc¿+k5x Tcd

P a d a n i l a i K 1 , K 2 , K 3 , K 4 , K 5 m e r u p a k a n k o e f i s i e n p e r p i n d a h a n p a n a s y a n g a k a n m e n g g a m b a r k a n s e t i a p n i l a i d e n g a n k o n d u k t i v i t a s p a n a s

4 . B e r d a s a r k a n n o m o r 3 d i a t a s b u a t l a h m o d e l d i m a t l a b d i s e r t a d e n g a n s i m u l a s i ( m - f i l e ) c o d i n g d i s e r t a k a n

% M u h a m a d F a d h i l H e n d r a w a n

% N i m ( 3 3 3 2 2 1 0 0 5 9 )

% D e f i n i s i k a n p a r a m e t e r A = 1 0 ; % A r e a p e r m u k a a n

k = 0 . 1 ; % K o e f i s i e n t r a n s f e r p a n a s T _ l u a r = 2 8 ; % S u h u l u a r r u a n g a n I _ c a h a y a = 5 0 ; % I n t e n s i t a s c a h a y a

% D e f i n i s i k a n w a k t u s i m u l a s i

t = 0 : 0 . 1 : 1 0 ; % W a k t u s i m u l a s i d a r i 0 h i n g g a 1 0 j a m

% I n i s i a l i s a s i s u h u a w a l T _ d i n d i n g = z e r o s ( s i z e ( t ) ) ; T _ l a n t a i = z e r o s ( s i z e ( t ) ) ; T _ a t a p = z e r o s ( s i z e ( t ) ) ; T _ u d a r a = z e r o s ( s i z e ( t ) ) ;

% A s s i g n i n i t i a l t e m p e r a t u r e s T _ d i n d i n g ( 1 ) = 1 9 ;

T _ l a n t a i ( 1 ) = 1 8 ; T _ a t a p ( 1 ) = 2 8 ; T _ u d a r a ( 1 ) = 2 0 ;

% S i m u l a s i m o d e l f o r i = 2 : l e n g t h ( t )

% H i t u n g p e r u b a h a n s u h u b e r d a s a r k a n t r a n s f e r p a n a s

d T _ d i n d i n g = k * ( T _ u d a r a ( i - 1 ) - T _ d i n d i n g ( i - 1 ) ) ;

d T _ l a n t a i = k * ( T _ u d a r a ( i - 1 ) - T _ l a n t a i ( i - 1 ) ) ;

d T _ a t a p = k * ( T _ u d a r a ( i - 1 ) - T _ a t a p ( i - 1 ) ) ;

d T _ u d a r a = ( k * A * ( T _ l a n t a i ( i - 1 ) - T _ u d a r a ( i - 1 ) ) + I _ c a h a y a ) / A ;

% U p d a t e s u h u

T _ d i n d i n g ( i ) = T _ d i n d i n g ( i - 1 ) + d T _ d i n d i n g ;

T _ l a n t a i ( i ) = T _ l a n t a i ( i - 1 ) + d T _ l a n t a i ; T _ a t a p ( i ) = T _ a t a p ( i - 1 ) + d T _ a t a p ; T _ u d a r a ( i ) = T _ u d a r a ( i - 1 ) + d T _ u d a r a ; e n d

% P l o t h a s i l s i m u l a s i f i g u r e ;

p l o t ( t , T _ d i n d i n g , ' r ', t , T _ l a n t a i , ' g ', t , T _ a t a p , ' b ', t , T _ u d a r a , ' m ') ;

x l a b e l (' W a k t u ( j a m ) ') ; y l a b e l (' S u h u ( \ c i r c C ) ') ;

t i t l e (' S i m u l a s i T e m p e r a t u r d i R u a n g a n R u m a h ') ;

l e g e n d (' S u h u D i n d i n g ', ' S u h u L a n t a i ', ' S u h u A t a p ', ' S u h u U d a r a ') ;

g r i d o n

O u t p u t :