6
1 No.61203091 No.61273171 No.SAST201234 (No.NS2012069) (No.kfjj120107) [1-5] [6] Yuehua 1 2 1 1 3,4 1. 210016 E-mail: [email protected] 2. 210016 E-mail: [email protected] 3. 200233 4. 200233 : : , , , Reconfigurability Analysis for Redundant Momentums Control Systems with Single Fault Qi haiming 1 , Cheng yuehua 2 Jiang bin 1 Ma yajie 1 Liu chengrui 3,4 1. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 E-mail: [email protected] 2. Academy of Frontier Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 E-mail: [email protected] 3. Beijing Control Engineering Institute, Beijing 200233, China 4. Beijing Key Laboratory of Space Intelligent Control Technology, Beijing 200233, China Abstract This paper provides an approach to evaluate and analyze the reconfigurability of redundant momentums for satellite attitude control systems with single fault. The conception of reconfigurability degree is discussed and then how to describe the reconfigurability degree is studied. Character of each actuator is described by an attribute vector with several parameters, and then the attribute matrix is built by all attribute vectors. The connection between the attribute matrix and controllability Gramian matrix of the attitude control system is analyzed. Depth-First-Search Algorithm is used to calculate the reconfigurability degree in the presence of single momentum fault. Simulations of several redundant configurations are presented to show the reconfigurability analysis result. The proposed approach provides an engineering means to evaluate the reconfigurability and it is also helpful for designing appropriate redundant actuators. Keywords Satellite attitude control systems, Reconfigurability, Character analysis, Depth-First-Search 4898 978-1-4673-5534-6/13/$31.00 c 2013 IEEE

[IEEE 2013 25th Chinese Control and Decision Conference (CCDC) - Guiyang, China (2013.05.25-2013.05.27)] 2013 25th Chinese Control and Decision Conference (CCDC) - Reconfigurability

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Page 1: [IEEE 2013 25th Chinese Control and Decision Conference (CCDC) - Guiyang, China (2013.05.25-2013.05.27)] 2013 25th Chinese Control and Decision Conference (CCDC) - Reconfigurability

1

No.61203091 No.61273171

No.SAST201234(No.NS2012069)(No.kfjj120107)

[1-5] [6]

Yuehua

1 2 1 1 3,4

1. 210016

E-mail: [email protected]

2. 210016

E-mail: [email protected]

3. 200233

4. 200233

:

: , , ,

Reconfigurability Analysis for Redundant Momentums Control Systems

with Single Fault

Qi haiming1, Cheng yuehua2 Jiang bin1 Ma yajie1 Liu chengrui3,4

1. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016

E-mail: [email protected]

2. Academy of Frontier Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016

E-mail: [email protected]

3. Beijing Control Engineering Institute, Beijing 200233, China

4. Beijing Key Laboratory of Space Intelligent Control Technology, Beijing 200233, China

Abstract This paper provides an approach to evaluate and analyze the reconfigurability of redundant momentums for satellite attitude control systems with single fault. The conception of reconfigurability degree is discussed and then how todescribe the reconfigurability degree is studied. Character of each actuator is described by an attribute vector with severalparameters, and then the attribute matrix is built by all attribute vectors. The connection between the attribute matrix and controllability Gramian matrix of the attitude control system is analyzed. Depth-First-Search Algorithm is used to calculatethe reconfigurability degree in the presence of single momentum fault. Simulations of several redundant configurations arepresented to show the reconfigurability analysis result. The proposed approach provides an engineering means to evaluatethe reconfigurability and it is also helpful for designing appropriate redundant actuators. Keywords Satellite attitude control systems, Reconfigurability, Character analysis, Depth-First-Search

4898978-1-4673-5534-6/13/$31.00 c©2013 IEEE

Page 2: [IEEE 2013 25th Chinese Control and Decision Conference (CCDC) - Guiyang, China (2013.05.25-2013.05.27)] 2013 25th Chinese Control and Decision Conference (CCDC) - Reconfigurability

Cheng[7]

Wu, ZhouSalomon[8] [9]

Frei [10]

Hao Yang[11]

; MIT Afreen Siddiqi[12] Object-Process Methodology

OPM Design Structure Matrices DSM

2

[8].

=

=

3

vv

3.1

1

am

am j

jz amj ,,1=

1 2 3 4 5 6[ , , , , , ]j j j j j j jz z z z z z z=

1 1, 2, ,j az m=

2 1,2,3, 4jz = 1 x 2

y 3 z 4 3jz , 4jz , 5jz

6 0,1jz = 1 0

am1

11 16

1 6a am m

z z

z zΖ = 1

2

11 16 17 18 19'

1 6 7 8 9a a a a am m m m m

z z z z zZ

z z z z z= 2

7jz

1 0 8jz1 0

9jz 1

0 6 7 8 9j j j jz z z z= × ×

2013 25th Chinese Control and Decision Conference (CCDC) 4899

Page 3: [IEEE 2013 25th Chinese Control and Decision Conference (CCDC) - Guiyang, China (2013.05.25-2013.05.27)] 2013 25th Chinese Control and Decision Conference (CCDC) - Reconfigurability

7jz 8jz 9jz 0 6jz 0

2

x Ax Buy Cx

= +=

2

2

0 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

0 0 0 0

0 0 0 0 0 0

0 0 0 0

y z y z xo o

x x

y z y z xo o

z z

J J J J JA

J J

J J J J J

J J

ω ω

ω ω

− − −=

− − −

[ , , , , , ]Tx ϕ θ ψ ϕ θ ψ=

1 2[ , , , ]Tmu u u u= 1B J D−= 6 6C I ×=

( , , )X Y ZJ diag J J J= B

BC

3

Z 6jzM

16

26

6am

zz

M

z

=

Z 3 4 5 N ,

13 14 15

3 4 5a a am m m

z z zN

z z z=

TN M D= 1 1( )TB J D J N M− −= =M N

2 3 4 5( , , , , , ) 6rank B AB A B A B A B A B = ,

M6 7 8 9j j j jz z z z= × ×

17 18 19

27 28 29'

7 8 9a a am m m

z z zz z z

M

z z z

× ×× ×

=

× ×

13 14 15'

3 4 5a a am m m

z z zN

z z z=

' '( )TN M D= 1 1 ' '(( ) )TB J D J N M− −= ='M 'N

2 3 4 5( , , , , , ) 6rank B AB A B A B A B A B = ,

3.2

1

1an

1aR1

1a

aa

nRm

=

0,1af = 10

1af = 0af =

1 ii

i

6 0iz =1 1=i i

ami =

4900 2013 25th Chinese Control and Decision Conference (CCDC)

Page 4: [IEEE 2013 25th Chinese Control and Decision Conference (CCDC) - Guiyang, China (2013.05.25-2013.05.27)] 2013 25th Chinese Control and Decision Conference (CCDC) - Reconfigurability

1

10a

in

==

1 1 1a an n= +

ai m≤

6 1, 1iz i i= = +

1af =

af

6 0i az f= =

1

2

iijmj a ≠= ,,1

M N B2 3 4 5( , , , , , ) 6rank B AB A B A B A B A B =

2 3

1 2

11

aa

a

nR

m=

3.3

1

a

i

m

ai

p=

iap i

1ar

'1aR

=

=a

i

m

ia

aa

p

rR

1

1'1

7jz 8jz 9jz

6r =

2 3 4 5( , , , , , )r rank B AB A B A B A B A B=

1af = 0af =

6j ijz P=

16 26 6( , , , )am

M diag z z z=

13 14 15

3 4 5a a am m m

z z zN

z z z=

1,TN M D B J D−= =

2

4

4.1

A1 A2A3

2~43

5

2013 25th Chinese Control and Decision Conference (CCDC) 4901

Page 5: [IEEE 2013 25th Chinese Control and Decision Conference (CCDC) - Guiyang, China (2013.05.25-2013.05.27)] 2013 25th Chinese Control and Decision Conference (CCDC) - Reconfigurability

5

4.2

1 3.1

1,2,3,4 1 X,Y,Z 1α , 1β , 1γ2 X,Y,Z 2α , 2β , 2γ , 3

X,Y,Z 3α , 3β , 3γ , 4

X,Y,Z 4α , 4β , 4γ1,2,3,4 1 X,Y,Z

0 ,90 , 90 2 X,Y,Z90 , 0 , 90 , 3 X,Y,Z

90 , 90 , 0 , 4 X,Y,Zα , β ,γ1,2,3,4,5 1 X,Y,Z 0 ,

90 , 90 2 X,Y,Z 90 , 0 , 90 , 3 X,Y,Z 90 , 90 , 0 4 X,Y,Z 'α , 'β , 'γ ,

5 X,Y,Z 'α , 'β , 'γ

1 1 1

2 2 2

3 3 3

4 4 4

1 4 sin sin sin 12 4 sin sin sin 1

Z13 4 sin sin sin 14 4 sin sin sin 1

α β γα β γα β γα β γ

= 3

1 1 0 1 1 12 2 1 0 1 1

23 3 1 1 0 14 4 sin sin sin 1

Z

α β γ

= 4

' ' '

' ' '

1 1 0 1 1 12 2 1 0 1 1

3 3 3 1 1 0 14 4 sin sin sin 15 4 sin sin sin 1

Zα β γα β γ

= 5

2

2

30.7 0 00 18.6 00 0 23.6

kg m= ⋅J

0.0011 /rad s=o

7 3

7 3

0 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

2 10 0 0 0 0 1.3 100 0 0 0 0 00 0 2.6 10 1.7 10 0 0

A − −

− −

=− × − ×

− × − ×

1D 2D 3D

1

3 3 3 33 3 3 33 3 3 3

3 3 3 33 3 3 3

3 3 3 3

− −

=

− −

D

2

31 0 0330 1 0

330 0 1

3

=D 3

3 31 0 03 33 30 1 0

3 33 30 0 1

3 3

=D

3.2

1 4an =4am =

11 4 / 4 1aa

a

nR

m= = =

1 12ar =12ap =

4902 2013 25th Chinese Control and Decision Conference (CCDC)

Page 6: [IEEE 2013 25th Chinese Control and Decision Conference (CCDC) - Guiyang, China (2013.05.25-2013.05.27)] 2013 25th Chinese Control and Decision Conference (CCDC) - Reconfigurability

' 11 12 /12 1aa

a

rR

p= = =

1 4an =4am =

11 4 / 4 1aa

a

nR

m= = =

1 12ar =12ap =

' 11 12 /12 1aa

a

rR

p= = =

1 5an =5am =

11 5 / 5 1aa

a

nR

m= = =

1 15ar =15ap =

' 11 15 /15 1aa

a

rR

p= = =

4.3

am 1an ap 1ar 1aR '1aR

A1 4 4 12 12 1 1

A2 4 4 12 12 1 1 A3 5 5 15 15 1 1

1

1

1

2

5

[1] Zhang Y M, Jiang J. Bibliographical review on reconfigurable fault-tolerant control systems. Annual Reviews in Control, 2008, 32: 220-252.

[2] . [J]. , 2004, 25(5): 516-519.

[3] Park E, Tilbury D M, Khargoneka P P. Modular logic controllers for machining systems: formal representation and performance analysis using Petri nets[J]. IEEE Transaction on Robotics and Automation, 1999, 15(6): 1046-1061.

[4] , , , . [J]. , 2007, 18(17): 2050-2055.

[5] , . PB [J]. , 2009, 22(2): 57-59.

[6] , , , . [M]. , : 2009.

[7] Yuehua Cheng, Bin Jiang, Yanping Fu, et al. Robust Observer Based Reliable Control for Satellite Attitude Control Systems with Sensor Faults[J]. International Journal of Innovative Computing, Information & Control, 2011,7(7B):4149-4160.

[8] N E Wu, K Zhou, G Salomon. Control reconfigurability of linear time-invariant systems[J]. Automatica, 2000, 36(11): 1767-1771.

[9] B C Moore. Principal component analysis in linear systems: controllability, observability, and model reduction[J]. IEEE Transaction on automatic control, 1981, 26(1): 17-32.

[10] C W Frei, F J Kraus, M Blanke. Recoverability viewed as a system property[C]// European Control Conference ECC’ 99. Karlsruhe, Germany, 1999.

[11] H Yang, B Jiang, M Staroswiecki. Fault Recoverability analysis of switched systems[J]. International Journal of Systems Science, 2012, 43(3): 535-542.

[12] Afreen Siddiqi. Reconfigurability in Space Systems: Architecting Framework and Case Studies.Massachusetts Institute of Technology ,2006.

2013 25th Chinese Control and Decision Conference (CCDC) 4903