1,2 1,2 1. 100190

E-mail: liuchengrui@gmail.com

2. 100190 E-mail: dayiwang@163.com

:

: , ,

Reconfigurability Design for Spacecraft Control System Based on Reliability Constraint

LIU Chengrui1,2, WANG Dayi1,2

1. Beijing Institute of Control Engineering, Beijing 100190, China E-mail: liuchengrui@gmail.com

2. National Laboratory of Space Intelligent Control, Beijing 100190, China E-mail: dayiwang@163.com

Abstract: In order to fundamentally improve the reconfiguration ability of spacecrafts, reconfigurability should be considered in design stage, and the reconfigurability design method must be involved to guide the system design. The objective of this paper is to construct a reconfigurability design method. First, some basic definitions relating to spacecraft reconfigurability are given. Then, on the basis of function tree, a reconfigurability modeling method is established to describe system’s configuration characteristics. Quantitative reconfigurability indexes are further presented and a weak link analysis approach is proposed via the model. In addition, considering reliability constraints, an optimal design method of system configuration is given based on the minimal path set of the reconfigurability model. Finally, the proposed methodology is illustrated and verified in practical analyzing for spacecraft control system. Results show that the method can realize the system configuration design by synthetically considering components, configuration and reconfiguration strategies, and is suitable for the complex system such as spacecrafts.

Key Words: reconfigurability design, function tree, reliability

1

* 61203093

61004073.

[1,2][3]

[4,5,6]

[7 8]

Proceedings of the 33rd Chinese Control ConferenceJuly 28-30, 2014, Nanjing, China

3328

[9,10]LTI [11]

2

2.1

1 system reconfigurability

2 reconfiguration unit RU

3 minimal reconfiguration unit

MRU

4 function tree

1

5 cut set of function tree

6 minimal cut set of

function tree

7 path set of function tree

8 minimal path set of function tree

System function

Higher level Subfunction 1

Higher level Subfunction m

Vertex

Branches

Roots

Lowest level Subfunction 1

Lowest level Subfunction n

MRU 1

MRU 2

MRU k-1

MRU k

1:

2.2

1 2{ , , , }ma a a a 1 2{ , , , }ps s s s

( ) ( ) ( )( ) ( )x t Ax t Bu ty t Cx t

nx mum py pA B C B C

1 2{ , , , }r ma a a a

1 2{ , , , }r ps s s s m m p p

ra a rs s

( ) ( ) ( )( ) ( )

r

r

x t Ax t B u ty t C x t

r arB B r srC C 1{ ( ),ar diag a

2( ), , ( )}ma a i ra a ( ) 1ia( ) 0ia 1,2, ,i m 1{ ( ),sr diag s

2( ), , ( )}ps s i rs s ( ) 1is( ) 0is 1, 2, ,i p

1nr r rrank B AB A B n

ra

3329

1( )nr r rrank C A C A C n

rs ra a

rs s

a s

1 2{MRUs MRU MRU, }NMRU

1{ ,MRUF F

2, , }MF F MRUF

M N

{ ,F}

MRUF

F

Y

Y

Y

(a) (b) (c)k/n

2:

2.3

C

1 2( ) ( ) ( ) ( )i j k nY x x xC C C

1(1,2, , ( ) )i x 2(1,2, , ( ) )j x (1,2, , ( ) )nk x (5)

1 2( ) ( ) ( ) ( )nY x x x (6)

( )ix 1,2, ,i n ix

R

1 2( ) ( ) ( ) ( )nY x x x (7)

1 2( ) ( ) ( ) ( )i j k nY x x xR R R

1(1,2, , ( ) )i x 2(1,2, , ( ) )j x (1,2, , ( ) )nk x (8)

( )ix 1,2, ,i n ix

K/N

5 8

1

10

9

0 1 2

1

1

m

i iim

ii

wr

w 10

i i iw i

m

2

3330

1

M

MT

NIN

11

MI M MNM TN

2

min( ) 1 1,2, ,i iT and iR R 12

T iRi iR iR

3

3.1 MRU

( ) i tiR t e

( )iR t i t i

i T0R

0( )R T R

MRUF

1 1{ , , , }MRU MF F F F

10 20 0, , , MR R R

MRUF

0( )i iR T R 1,2, ,i M

iFT iF

1

( ) 1 1 i

nT

ii

R T e

niF

T iF

1 1

( ) k

nnTi

ik i i k

i k

R T e

n l n liF

T iF

00

0

( )( )!

kn ll T

ik

l TR T ek

0

10 20 0, , , MR R R1n

n l n l( )iR T 0( )i iR T R

1n n ( )iR T

0 0

0 0

( ) 1( )

i

i

R T R n nR T R n n

0n n

3.2

3331

4

0

0

0

r

p

y

19

, ,r p y

, ,

0

1 2 1 1{ , , , , , , , , , }G E Sn n ns G G G E E S S

1 2, , ,Gn

G G G 3Gn

1, ,En

E E

1, ,Sn

S S 1E Sn n

19

x Ax Bu wy Cx v 20

r p yx b b b , ,r p yb b b

r p yu g g g

h h s s sy ,w v, ,r p yg g g

1

21( )

g

r

p

yn

gg gg H H Hg g

21

1 2, , ,gn

g g g gn 3gn H

, , , ,h h s s s

1 , ,s s s

0

0

0 0 1 0 00 1 0 0 1 0

0 0 0 0 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

A

1 0 00 1 00 0 10 0 00 0 00 0 0

B

1 0 0 0 0 00 1 0 0 0 01 0 0 0 0 00 1 0 0 0 00 0 1 0 0 0

C 21

1 1 2 3 1{ , , , , }rs G G G S4 6

r p yx b b b

2 1 2 3{ , , , , , }rs G G G E E ,E E

4 5 yb

x

0

0

0 00 1 0

0 0A

1 0 00 1 00 0 1

B

1 0 00 1 0

C 22

4 3

1 1 1 1{ , , , , , , , , , , , }G E E Sn n n ns G G E E E E S S

3 MRU 1MRU 62.2 10GP Fit

6& 2.0 10GM H Fit 71.6 10S Fit

71.8 10E E Fit 5

0.95 0.95

[12]

0.983 k/nGP1 GPn

3332

&1& , , &GM HnGM H GM H &GM Hn

3 n l1 1 1, , , ( , ) ,

SnS S E E ( ,

EnE )

EnE

GP1GPn

62.2 10 62050

ln(1 0.983) 1.98ln(1 )GPn e

&1& , , &GM HnGM H GM H &GM Hn

3

& 5GM Hn S E E

1Sn

min 1 2 1 5 1{ , , & , , & , }s GP GP GM H GM H S

GP1 GPnGPGM&

H1GM&HnGMH

S1 E 1 E nSnS E n E 1

3:

1. MRU

MRU GP

GM&H

S

E

E

MRU 1iw0.875r

MRU

1Sn2Sn

1Sn 1E En n

min 1 2 1 5 1 1 1{ , , & , , & , , , }s GP GP GM H GM H S E E

1r

5

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[12] , , . . ,,2005.

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