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F e e d b a c k l i n e a r i z a t i o n c o n t r o l f o r U A V a t t i t u d e c o n t r o l b a s e d o n E x t e n d e d s t a t e o b s e r v e r
Jiang Hongru, Qiu Lingcun, Li Di, Wu Kai, Dong Shiyin
Shanghai Electro-Mechanical Engineering Institute, Shanghai 201109
E-mail: darcy_jhr@163.com
Abstract: With the development of integrated electronic technology, unmanned aerial vehicle (UAV) has been widely concerned and applied. High response speed, coupling dynamics and nonlinearities of Unmanned earial vehicles makes the attitude control a significant technology. In view of this research direction,this paper proposes a feedback linearization control scheme based on backstepping technology design for attitude tracking control of UAV in the presence of disturbances. In the proposed control design scheme, the back stepping technology is designed to split the simplified model and feedback linearization to reduce the adjustment parameters. Meanwhile,the extended state observer (ESO) is adopted to estimate and compensate for the disturbances. At the same time, the convergence of ESO and the stability of closed-loop system are given to prove the feasibility of the method Then the convergence of ESO and stability of closed-loop system are presented. Finally, simulation results are given to illustrate the effectiveness of the proposed method.
Key Words: UAV , Backstepping technology , Feedback linearization , Extended state observer
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up, u, Ğ_lAm, 4Nяzz*Y3eN:g(WsNbN-Nv^(u[ J ] , zz)Y2_, 2 0 2 0 , V o l . 3 , I s s u e ( 2 ) : 8 5 - 9 0
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N F a v a l o r o , G P e z z e l l a , V C a r a n d e n t e , D e s i g n A n a l y s i s o f t h e H i g h - S p e e d E x p e r i m e n t a l F l i g h t T e s t V e h i c l e H E X A F L Y - I n t e r n a t i o n a l [ C ] , A I A A I n t e r n a t i o n a l S p a c e P l a n e s a n d H y p e r s o n i c S y s t e m s a n d T e c h n o l o g i e s C o n f e r e n c e , 2 0 1 5 .
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S B i , H J i , S C h e n , R o b u s t A t t i t u d e C o n t r o l o f A i r c r a f t B a s e d o n P a r t i t i o n e d B a c k s t e p p i n g [ C ] , C o n t r o l a n d A u t o m a t i o n , 2 0 0 8 , 1 0 0 0 - 1 3 2 8 .
R Z h a n g , C S u n , J Z h a n g , S e c o n d - o r d e r t e r m i n a l s l i d i n g m o d e c o n t r o l f o r h y p e r s o n i c v e h i c l e i n c r u i s i n g f l i g h t w i t h s l i d i n g m o d e d i s t u r b a n c e o b s e r v e r [ J ] , J o u r n a l o f C o n t r o l T h e o r y a n d A p p l i c a t i o n s , 2 0 1 3 , 2 9 9 - 3 0 5 .
W W Q i n , Z Q Z h e n g , G L i u , R o b u s t v a r i a b l e g a i n c o n t r o l f o r h y p e r s o n i c v e h i c l e s b a s e d o n L P V [ J ] , S y s t e m s E n g i n e e r i n g a n d E l e c t r o n i c s , 2 0 1 1 , 6 : 1 3 2 7 - 1 3 3 1 .
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T A l s u w i a n , C o m p a r i s o n o f P I D a n d n o n l i n e a r f e e d b a c k l i n e a r i z a t i o n c o n t r o l s f o r l o n g i t u d i n a l d y n a m i c s o f h y p e r s o n i c v e h i c l e a t s u b s o n i c s p e e d s [ C ] , e r o s p a c e a n d E l e c t r o n i c s C o n f e r e n c e ( N A E C O N ) a n d O h i o I n n o v a t i o n S u m m i t ( O I S ) , 2 0 1 6 .
X i n D o n g L i , B i n X i a n , C h e n D i a o , O u t p u t f e e d b a c k c o n t r o l o f h y p e r s o n i c v e h i c l e s b a s e d o n n e u r a l n e t w o r k a n d h i g h g a i n o b s e r v e r [ J ] , S c i e n c e i n C h i n a . S e r i e s F : I n f o r m a t i o n S c i e n c e s , 2 0 1 1 V o l . 5 4 , N o . 3 : 4 2 9 - 4 4 7 .
hTm, OfU, sQ. ؚX ޘLhVhߍ*vSekn!jc6R[ J ] , {:gKmϑNc6R. , 2 0 1 4 , 2 2 ( 7 ) : 2 0 6 3 - 2 0 6 6 , 2 0 7 5 .
G a o D a o - x i a n g , S u n Z e n g - q i , F u z z y a d a p t i v e c o n t r o l f o r h y p e r s o n i c v e h i c l e v i a b a c k s t e p p i n g m e t h o d [ J ] , C o n t r o l T h e o r y a n d A p p l i c a t i o n s , 2 0 0 8 , V o l . 2 5 , N o . 5 : 8 0 5 - 8 1 0 .
W H C h e n , D i s t u r b a n c e o b s e r v e r b a s e d c o n t r o l f o r n o n l i n e a r s y s t e m s [ J ] , I E E E / A S M E t r a n s a c t i o n s o n m e c h a t r o n i c s , 2 0 0 4 , 9 ( 4 ) : 7 0 6 - 7 1 0 .
l^ O, hg OY, [Sf Z, RR, B T T [9_WNib _r`KmhVvn!jc6R_[ J ] , {:gKmϑNc6R, 2 0 1 4 , 2 2 ( 1 1 ) , 3 6 3 3 - 3 6 3 5 , 3 6 3 8 .
S u J i n y a , C h e n W e n - H u a , H i g h o r d e r D i s t u r b a n c e O b s e r v e r D e s i g n f o r L i n e a r a n d n o n l i n e a r S y s t e m s [ C ] , I n f o r m a t i o n a n d A u t o m a t i o n , 2 0 1 5 I E E E I n t e r n a t i o n a l C o n f e r e n c e , 2 0 1 5 .
G o d b o l e , A . A . , K o l h e , J . P . , T a l o l e , S . E , P e r f o r m a n c e a n a l y s i s o f g e n e r a l i z e d e x t e n d e d s t a t e o b s e r v e r i n t a c k l i n g s i n u s o i d a l d i s t u r b a n c e s [ J ] , S C o n t r o l S y s t e m s T e c h n o l o g y , I E E E T r a n s a c t i o n s , 2 0 1 3 , V o l . 2 1 , N o . 6 : 2 2 1 2 - 2 2 2 3 .
J i n g q i n g H a n , F r o m P I D t o a c t i v e d i s t u r b a n c e r e j e c t i o n c o n t r o l [ J ] , I n d u s t r i a l E l e c t r o n i c s , I E E E T r a n s a c t i o n s , 2 0 0 9 , V o l . 5 6 , N o . 3 : 9 0 0 - 9 0 6 .
Hl[ ~? u[[ st WNib _r`KmhVv gPe6e[e6R[_[ J ] zz)Y2_, 2 0 1 9 V o l . 2 , N o . 3 : 9 0 0 - 9 0 6 .
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c
F MathType 6.0 Equation MathTy O l e
n C o m p O b j o i O b j I n f o q E q u a t i o n N a t i v e r pe EF Equation.DSMT4 9q D( T L( DSMT6 WinAllBasicCodePages Times New Roman Symbol Courier New MT Extra WinAllCodePages !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
g _ 1 6 5 0 1 9 1 9 1 8 F Pdl`el O l e
w C o m p O b j x i O b j I n f o z
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d , t , W E E q u a t i o n N a t i v e { 6 _ 1 6 5 0 1 9 1 9 7 0 ' F `el`el O l e
C o m p O b j i
F MathType 6.0 Equation MathType EF Equation.DSMT4 9q ( T ( DSMT6 WinAllBasicCodePages Times New Roman Symbol Courier New MT Extra WinAllCodePages !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
O b j I n f o ! E q u a t i o n N a t i v e _ 1 6 5 0 1 9 2 0 1 2 $ F `el`el O l e
a , b , m
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p , q , r
F MathType 6.0 Equation MathType EF Equation.DSMT4 9q 5 ( T ( DSMT6 WinAllBasicCodePages Times New Roman Symbol Courier New MT Extra WinAllCodePag O l e
C o m p O b j ( * i O b j I n f o + E q u a t i o n N a t i v e Q es !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
M x
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, M z
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C o m p O b j - / i O b j I n f o 0 E q u a t i o n N a t i v e g _ 1 6 5 0 1 9 2 1 2 2 h 3 F p=elp=el O l e
C o m p O b j 2 4 i K ( T ( DSMT6 WinAllBasicCodePages Times New Roman Symbol Courier New MT Extra WinAllCodePages !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
f 1
, f 2
, f 3
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I x x
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, I z z O b j I n f o 5 E q u a t i o n N a t i v e v _ 1 6 5 0 1 9 2 1 5 4 8 F elel O l e
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C o m p O b j 7 9 i O b j I n f o : E q u a t i o n N a t i v e _ 1 6 5 7 5 5 7 5 3 8 @ = F deldel X , Y , Z
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C o m p O b j < > i O b j I n f o ? E q u a t i o n N a t i v e A @AHA*_D_E_E_A
a = ="- p c o s ( a ) t a n ( b ) + + q "- r s i n ( a ) t a n ( b ) b = = p s i n ( a ) "- r c o s ( a ) m = = p c o s ( a ) s e c ( b ) + + r s i n ( a ) s e c ( b ) _ 1 6 5 7 5 5 7 5 6 8 0 B F deldel O l e
C o m p O b j A C i O b j I n f o D
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E q u a t i o n N a t i v e V _ 1 6 5 0 1 9 2 3 3 7 6 O G F elel O l e
C o m p O b j F H i p = = I y y
"- I z z
I x x
q r + + M x
I x x
+ + d 1
q = = I z z
"- I x x
I y y
p r + + M y
I y y
+ + d 2
r = = I x x
"- I y y
I z z
p q + + M z
I z z
+ + d 3
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d 1
, d 2
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C o m p O b j K M i O b j I n f o N E q u a t i o n N a t i v e _ 1 6 5 0 1 9 2 4 6 7 J Q F elel W
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C o m p O b j P R i O b j I n f o S E q u a t i o n N a t i v e A @AHA*_D_E_E_A
w
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C o m p O b j U W i O b j I n f o X E q u a t i o n N a t i v e _ 1 6 5 0 1 9 2 6 0 1 [ F elel O l e
C o m p O b j Z \ i ! " # $ % & ' ( ) * + , - . / 0 1 2 5 8 9 : ; < = > ? @ A B C F I J K L M P S T U V Y \ ] ^ _ ` a b e h i j k l m p s t u v w x y | es !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
W= = a b m [ ] , w= = p q r [ ] , u = = M x
M y
M z
[ ] , d = = d 1
d 2
d 3
[ ]
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E q u a t i o n N a t i v e _ 1 6 5 0 1 9 2 6 6 3 Y c ` F elel O l e
es !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
W = = F 1
( W ) w w = = F 2
( w ) + + G u + + d
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F 1
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( w ) = = I y y
"- I z z
I x x
q r I z z
"- I x x
I y y
p r I x x
"- I y y
I z z
p q [ ] , G = = 1 I x x
0 0 0 1 I y y
0 0 0 1 I z z
[ ]
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3 C o m p O b j d f 4 i O b j I n f o g 6 E q u a t i o n N a t i v e 7 % Times New Roman Symbol Courier New MT Extra WinAllCodePages !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
W c
= = a c
b c
m c
[ ] , w c
= = p c
q c
r c
[ ] , u c
= = M x c
M y c
M z c
[ ]
F MathType 6.0 Equation MathType EF Equation.DSMT4 9q _ 1 6 5 0 1 9 4 5 0 5 T | j F elel O l e
D C o m p O b j i k E i O b j I n f o l G E q u a t i o n N a t i v e H i _ 1 6 5 0 1 9 4 5 6 6 o F fl fl O l e
N C o m p O b j n p O i M ( T ( DSMT6 WinAllBasicCodePages Times New Roman Symbol Courier New MT Extra WinAllCodePages !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
W c
, w c
, u c
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W c O b j I n f o q Q E q u a t i o n N a t i v e R _ 1 6 5 0 1 9 4 6 0 4 m w t F fl fl O l e
W C o m p O b j s u X i O b j I n f o v Z E q u a t i o n N a t i v e [ _ 1 6 5 0 1 9 4 6 3 5 y F fl'fl
F MathType 6.0 Equation MathType EF Equation.DSMT4 9q ¬ 4( T $( DSMT6 WinAllBasicCodePages Times New Roman Symbol Courier New MT Extra WinAllCodePages !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
V 1
= = 1 2 ( W c
"-W ) T
( W c
"-W )
F MathType 6.0 Equation MathType EF Equation.DSMT4 9q \( T D( DSMT6 WinAllBasicCodePages O l e
c C o m p O b j x z d i O b j I n f o { f E q u a t i o n N a t i v e g Times New Roman Symbol Courier New MT Extra WinAllCodePages !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
V 1
= = ( W c
"-W ) T
( W c
"-W )
F MathType 6.0 Equation MathTy_ 1 6 5 0 1 9 4 6 7 0 r ~ F 'fl'fl O l e
n C o m p O b j } o i O b j I n f o q pe EF Equation.DSMT4 9q ( T l( DSMT6 WinAllBasicCodePages Times New Roman Symbol Courier New MT Extra WinAllCodePages !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
w= = F 1
( W ) "- 1
[ W c
E q u a t i o n N a t i v e r _ 1 6 5 0 1 9 4 7 5 7 F 'fl'fl O l e
z C o m p O b j { i + + k ( W c
"-W ) ]
F MathType 6.0 Equation MathType EF Equation.DSMT4 9q ( T ( DSMT6 WinAllBasicCodePages Times New Roman Symbol Courier New MT Extra WinAllCodePag O b j I n f o } E q u a t i o n N a t i v e ~ _ 1 6 5 0 1 9 4 8 1 4 F 'flNfl O l e
es !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
k = = d i a g ( k a
, k b
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F MathType 6.0 Equation MathType EF Equation.DSMT4 9q t ( T ( DSMT6 WinAllBasicCodePages Times New Roman Symbol Courier New MT Extra WinAllCodePages !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
d e t ( F 1
) = ="-s e c b`" 0 , F 1
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C o m p O b j i O b j I n f o E q u a t i o n N a t i v e Y es !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
e W
= =W c
"-W
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C o m p O b j i O b j I n f o E q u a t i o n N a t i v e a _ 1 6 5 0 1 9 4 9 0 4 F Nflufl O l e
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e W
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W
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