Page 79 - MODUL DARING SISTEM PENGATURAN_Neat

2 1  2 − 2 0 1  
1 1     
* a = − ( APt ) = − t r  1 1 1   1 − 2 0  
0
3 r 0 3
3 2 4   1 1 −1    

 
−1 0 0 
1  
= − t 0 −1 0
3 r  
 0 0 −1 


1
= − (-1-1-1)
3

= 1
maka :

2
adj (s I – A) = P 2 s + P 1 s + P
0
1 0  0 3 0  1 2 1  2
2      
= s  0 1 0 + s 1 3 0 + 1 1 1





0 0  1  1 1  4  3 2  4 



s 2 + 3s + 2 1 s + 2 
 
=  s +1 s 2 + 3s +1 1 
 s + 3 s + 2 s 2 + 4s + 4 
 
2
2
3
3
7
det (s I – A) = s + a 2 s + a 1 s + a = s + 5s + s + 1
0
maka :
Y (s ) adj (sI − ) A
-1
G(s) = = C (s I – A) B = C B
U (s ) det(sI − ) A
s
s 2 + 3 + 2 1 s + 2 
 2 
s
 s + 1 s + 3 + 1 1 
 s + 3 s + 2 s 2 + 4 + 4  1 
s
0
= 2 1 −  1    


s
s 3 + 5s 2 + 7 + 1
1 


s
s 2 + 4 + 4
 
 s + 2 
 s 2 + 5 + 7 
s
= 2 1 −  1  
s 3 + 5s 2 + 7 + 1
s
s 2 + 4 + 3
s
=
s
s 3 + 5s 2 + 7 + 1
Metode Ruang-Keadaan
78