Soalan dan Jawapan frekuensi harmonik berdasarkan NIM

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 33 2 2 1 0 0 5 9

K e l a s : P em 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 em od e l a n d a n Id e n t i f i k a s i S i s t e m

1 .

A . Te nt u k a n a m p l i t u d e p un c a k d an f r e k w en 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 am 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 ni l a i f r e k w e n s i n y a 1 0 … …

B . G a m b a r ka n s p e k t r u m fr 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 an 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 rg a Te g a n g an (V t ) d a n Wa kt u ( t )

J a w a b :

M u h a m a d F a d h i l H e n dr 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 al a h 5 9 h a r m o n i k g a nj i l p e r t am a

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

𝜋 (𝑠𝑖𝑛ω𝑡 + 𝑠𝑖𝑛3𝜔𝑡

3 + 𝑠𝑖𝑛5𝜔𝑡

5 + 𝑠𝑖𝑛7𝜔𝑡

7 + 𝑠𝑖𝑛9𝜔𝑡 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 om b an g :

𝑓 =1

𝑡 = 1

1 𝑥 10 𝑠 = 1 𝑘𝐻𝑧 S e h i n g g a , d i d a p at 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 k a :

𝑓1 = 1 𝑥 1000 = 1000 𝐻𝑧 𝑑𝑎𝑛 𝑉1 = 4 𝑥 4

1 𝑥 3,14= 5,095 𝑉

 n = 3 , m a k a :

𝑓3 = 3 𝑥 1000 = 3000 𝐻𝑧 𝑑𝑎𝑛 𝑉3 = 4 𝑥 4

3 𝑥 3,14= 1,698 𝑉

 n = 5 , m a k a :

𝑓5 = 5 𝑥 1000 = 5000 𝐻𝑧 𝑑𝑎𝑛 𝑉5 = 4 𝑥 4

5 𝑥 3,14= 1,019 𝑉

 n = 7 , m a k a :

𝑓7 = 7 𝑥 1000 = 7000 𝐻𝑧 𝑑𝑎𝑛 𝑉7 = 4 𝑥 4

7 𝑥 3,14= 0,7279 𝑉

B e r i k u t i n i m e r up a k a n n i l a i f r e ku 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 ) Te g a n g an 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

11 K e - e n a m 11 . 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 bi 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 el 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 el a s 3 1 . 0 0 0 0 , 1 6 4

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

3 5 K e - d e l a p a n b el 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 , 11 8

4 5 K e - d u a p u l u h t i g a 4 5 . 0 0 0 0 , 11 3

4 7 K e - d u a p u l u h em 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 en 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 em b i l a n 5 7 . 0 0 0 0 , 0 8 9

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

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

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

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

6 7 K e - t i g a p ul u h em p a t 6 7 . 0 0 0 0 , 0 7 7

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

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

7 3 K e - t i g a p ul 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 ul u h d e l ap a n 7 5 . 0 0 0 0 , 0 6 9

7 7 K e - t i g a p ul 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

111 K e - l i m a p u l u h e n a m 111 .0 0 0 0 , 0 4 5

11 3 K e - l i m a p u l u h t u j u h 11 3 . 0 0 0 0 , 0 4 5

11 5 K e - l i m a p u l u h d el ap a n 11 5 . 0 0 0 0 , 0 4 4

11 7 K e - l i m a p u l u h s e m b i l a n 11 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 ar d a r i g r a f i k p e r b a n d i n g an s p e k t r um f r e k u e n s i d e n g a n t e g a n g a n pu n c a k

C . B e r i k ut i n i m e r u p ak a n n i l a i t eg 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 ni 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 00 t ) + 1 , 6 9 ( 2 π 3 0 0 0 t ) + 1 , 0 2 s i n ( 2π 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 11 0 0 0t ) + 0 , 3 9 s i n ( 2 π 1 3 0 00 t ) + 0, 3 3 s i n ( 2 π 1 5 0 0 0 t ) + 0 , 2 9 s i n ( 2 π 17 0 0 0 t )

 T = 20 1 0 µ s / 1 6

= 12 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 25 , 6 µ s ) + 0 , 5 7 s i n ( 2 π 9 0 0 0 ( 1 25 , 6 µ s ) + 0 ,4 6 s i n ( 2 π 11 0 0 0 ( 1 2 5 , 6 µ s ) + 0 , 3 9 s i n ( 2 π 1 3 0 00 ( 1 2 5 , 6 µ s ) + 0 , 3 3 s i n ( 2 π 1 5 0 0 0 ( 1 25 , 6 µ s ) + 0 , 2 9 s i n ( 2 π 1 7 00 0 ( 1 2 5 , 6 µ s )

V ( t ) = 2 , 4 Vo l t

D . U n t u k h a r g a v ( t 0 d a n w a kt 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 : Wa 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 em 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 al a m s e b u a h m o d e l d al a m p r o g r am m a t l a b

B u a t l a h re s p o n b e r u p a g r a f i k co n t oh d i at 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 as i n g n i l a i p ( s ) a n g k a a kh 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 da 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 𝑠 + 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 at l a h p em o d e l a n t em p e r a t u r e d i r u a n g an r u m ah t e m p a t t i n gg a l m a s i n g 2 t e r d i r i d a r i ( s u hu d i nd i n g, s u hu 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 ar, d a n i nt en s i t a s c a ha y a )

J a w ab :

M o d e l t em p e r a t u r e d i r u a n g a n ru m a h y a n g d a p at d i d e f i ni 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 ( Ta)

 S u h u l a n t ai ( T l )

 S u h u u d a r a d i d a l a m r u an g a n ( Tc )

 S u h u l u a r r u a n g a n ( To )

 S u h u I n t e n s i t as c ah a y a ( Tc 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 or ( 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 at a s , d a p a t m e n g g u n ak 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 ru 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 er 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 an g p a l i n g s e ri n g d i g u n ak a n u n t u k m e n g g a m ba 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 an :

 = 𝐾1 𝑥 (𝑇𝑜 − 𝑇𝑑)

 = 𝐾2 𝑥 (𝑇𝑜 − 𝑇𝑑)

 = 𝐾3 𝑥 (𝑇𝑜 − 𝑇𝑑)

 = 𝐾4 𝑥 ( ) − 𝑇𝑐) + 𝑘5 𝑥 𝑇𝑐𝑑

P a d a n i l ai K 1 , K 2 , K 3 , K 4 , K 5 m e r u p a k a n k o e fi s i e n p e r p i n d a h a n p an as y a n g ak a n m e n g g a m b a r k an s e t i ap n i l ai 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 el d i m a t l a b d i s e r t a d en 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 ak a n

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

% N i m ( 33 3 2 2 1 0 0 5 9 )

% D e f i ni s i k a n p a r a m e te r A = 1 0 ; % A r e a p e r m u ka 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 ya = 5 0 ; % I n t en s i t a s c a h a y a

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

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

% I n i s ia l i s a s i s u h u aw a l T _ d i n d in g = z e r o s ( s i ze ( t ) ) ; T _ l a n t ai = 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 gn i n i t i a l t e m pe r a t u re s T _ d i n d in g ( 1 ) = 1 9 ;

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

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

% Hi t u n g p e r u b a h an s u h u b e r d a s ar k a n t r a n s f er p a n a s

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

d T _l a n t a i = k * (T _ u d a ra ( i - 1 ) - T _ l a n t ai ( 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 ha y a ) / A ;

% Up d a t e s u h u

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

T _ la n t a i ( i ) = T _ la n t a i (i - 1 ) + dT _ l a n ta i ; T _ a t a p ( i ) = T_ a t a p (i - 1 ) + dT _ a t a p;

T _ ud a r a ( i ) = T _ u da 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 er a t u r d i R u a n ga 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 uh u A t a p ', ' S u h u U d a r a ') ;

g r i d o n

O u t p ut :