Số hóa bởi Trung tâm Học liệu

1 ĐẠI HỌC THÁI NGUYÊN
TRƯỜNG ĐẠI HỌC KỸ THUẬT CÔNG NGHIỆP

NGUYỄN VĂN CƯỜNG
THIẾT KẾ BỘ ĐIỀU KHIỂN CÓ SỬ DỤNG
GIẢM BẬC MÔ HÌNH ỨNG DỤNG CHO BÀI
TOÁN ĐIỀU KHIỂN CÂN BẰNG

Chuyên ngành: Kỹ thuật điều khiển và tự động hóa
Mã số: 60520216
 
ii




TS. Nguyễn Văn Chí, 
 “Thiết kế bộ điều khiển có sử dụng giảm bậc mô hình ứng dụng
cho bài toán điều khiển cân bằng 
Tôi 
TS. Nguyễn Văn Chí 
tôi 

 tôi 
TS. Đào Huy Du 



tôi 


Thái Nguyên, ngày 15 tháng 7 4

 

3.1  35
3.2  41
3.3  42
3.4  44
 46
 48


iv



Hình1. 1: Phân chia mô hình   8
Hình1. 2: Phân  8
 9
 23
Hình 2. 2: Mô hình hóa X2T hai bánh. 24
Hình  40
Hình 3. 2. X2T 
 41
Hình 3. 3. X2T ng hai
 41

 43

 43

 44

nhân, xe nà              

 
cho X2T,  X2T v


2
 


 

 
 
H


 


             
MATLAB/SIMULINK
 



 


H



 

  

cách khác, các 




4

      

 , 

1.2. -LTI
ng (Linear Time Invariant) 


(
) ( ) ( )
( ) ( ) ( )
dx t
E Ax t Bu t
dt
y t C x t Du t
(1.1)
 


E = I, LTI 
(
) ( ) ( )
( ) ( ) ( )
dx t
Ax t Bu t
dt
y t C x t Du t
(1.2)
m = p = 1 
    > 1 và            
(MIMO).
  

      -    



B + D (1.3)
 là:


B + D (1.4)


5
1.3. Các  

). Tuy

1
, t
2


1
, t
2
], 
n
, S


 

 M: R
k
 R
n

k


n
 
R
kxm
 
 
k

), M
2

 , v 
gian Eculid R
n
.
1.3.2 














R
, B
R
, C
R

Sai 
()



p


0
T
At T A t T
Ce BB e C dt

tro
1/2
0
2
( ) ( ) 1
T
ee
H t H t dt
(1.6)
Khử hệ con



1 11 1
2 21 22 2 2
1
2
2
()
()



Hình 1. 2: 


-




     

A
r
, B
r
, C
r

A
r

) c

1
, x
1


2
, x
2
.

 
1 1 1 2 2 2
( ) ( ), ( ) ( )x t T x t x t T x t
,





1 1 1 2 2 2
( ) ( ), ( ) ( )x t T x t x t T x t

+
+
+
+
+
+

y(t)
(t)


10
1 1 1
1 1 1 1 11 2 1 1
1 1 1
12
2
2
2 21 1 2 22 2 2 2
1
1 2 2
2
ˆˆ
0
ˆˆ
( ) ( ) ( )
ˆ
0
ˆ
ˆ
()
ˆ
R R k
nk
R
x T A T T A T x T B I
t d t d t

V
0
2

(t), d
1
(t) cho ra
1
1 1 1 1 1 1
ˆˆ
( ) ; ( )
At At
X t T Ve B Y t Ce VT


12
1 1 1 1 1 1
0
ˆˆ
( ) ( ) ( )
T T T
c
X t X t dt T V W V T

2
1 1 1 1 1 1
0
ˆˆ
( ) ( ) ( )
T T T

00
ˆ ˆ ˆ ˆ
( ) ( ) ( ) ( )
TT
X t X t dt Y t Y t dt
(1.8)

2

2
2 2 2 2 2
00
ˆ ˆ ˆ ˆ
( ) ( ) ( ) ( )
TT
X t X t dt Y t Y t dt
(1.9)
Định nghĩa 1.1: 
1


2
.
 mô hình

1
, X
2

















k
ki
i
k
i
i
1
4
1
4



2
i



2
2
1
4
1
42
1




n
ki
i
k
i
i



CBA



,,

1
,
X

tx
PPtx

)(
)(

)(

2
1
2
1
tx
Q
Q
tx
tx
T
T












12
P
1
Q
1
T
 









n
ki
i
F
T
QP
1
4
22


d
F
T






 
21
2
0
2
1


QQ
Q
Q
dteCCe
T
T
tATtA
T











QQPP
QQPP
TT
TT




222222111111

,

,

,

WQUPWQUP
TT


U
1
, W
1
, U
2
, W
2


m



 



13

K
0)
T

toán cho X
co
.



e

 

1.3.3 
1. -Matching

pháp moment- 
 
1

dt
y C x D u
(1.11)

1
ˆ
ˆ ˆ ˆ ˆ
( ) ( )
k
G s C sI A B D
(1.12)


14
              
.10) và (1.12
0

2
0 0 1 2
( ) Gs
    
    
(1.13)
2
0 0 1 2

  
( ) Gs
     


ln
.

      

u t

        -Order

Padé via Lanczos (PVL)
2


= (E, A, B, C, D), 

1
0
1
0
(( ) ) ,
(( ) ) W W ,
T
k
T T T
k
A s E E V VT fe
A s E E T ge

 

Algorithm) 4
  

=             



1
0
(( ) ) ,
T
k
A s E E V VT fe

 
1
0
(( ) )
T
H V A s E E V
    
T
, V 0,
T
k
V V I f

, f và H
n k n m k k
V







 

              

             




17
2. 
 (SVD)
Ta 
AB
CD
(1.15)
l 
nn
AR

nm
BR
,
pn

P và Q là  Hermitian 
0
0
TT
TT
AP PA BB
A Q QA C C

g
)(
i



l

)()( PQ
ii



a. Gim mô hình cân bng

T
và Q= LL
T


T
L=ZSY

1
bbbb
1
bbb
CTC,BTB,ATTA


.










2
1)(
i
diagS


2




11 1
k
1
A B
C 0






11


H


k 1 n
k
2( )



   

(1.17)
b. ng xp x







  






.
             
T
và
2
ii


( PQ) ( PQ) ( X )




X




T

X
 
*
k k k k

X Z D W

*
k k k
W Z I

k

X


**
k k k k k
k
k
W A Z W B
CZ





.







)(
~
1



k
L

.

~

chính xác. Phân tích

thàn   


   


20



:

E Ax t Bu t
dt
y t Cx t Du t

v tính

 



     

()Gs
   


:
-1
ˆ
ˆ ˆ ˆ ˆ
( ) ( - )
k
G s C sI A B D


()Gs



ˆ