681.3:629.7
. . , . .

. . . . , . , ,
*
.
: , , .
O. N. Zhdanov, V. Kh. Khanov
Siberian State Aerospace University named after academician MF. Reshetnev,
Krasnoyarsk, Russia
TECHNIQUE OF A CHOICE OF THE BLOCK DIAGRAM OF RELIABILITY OF AN ONBOARD COMPLEX OF MANAGEMENT OF THE SMALL
SPACECRAFT
Various block diagrams of reliability of a control system of small spacecraft are considered in this paper. The technique of definition of the optimum scheme is
developed.
Key words: Small spacecraft, control system, reliability.
(), . .
, -
* , 14.B37.21.0451 ї.
. ., . ., 2013
. , (). , , .
. , , , .
' [1], .
(. [2]) , . . (, , , ).
, . () (-) (), , , . , ( ) , , , , .
1. , , , , .
, .
, : .
, .
2. , , , .
.
, , () : = (0.
. -
);
- ;
.
(ї) () , ().
1. 1- . . , , , ї (. 1).
:
- 1 (
. 1. 1-
() A, B, C, D pv p2, p3, p4 , p , , , A, B, C, D, p0 >p, i = 1, 2, 3, 4.

Pf = p2 p3 P 44. (1)
. :
1) ,
2) ,
3) .
.
15
)
\


16
2- . , , (. 2). , .


= , (2 - , ).
1=0 1=1
. (. 3).
:
= 12 34 + (1- ) 12 34 =
= (2
) ,
0 I= 1
(3)
. 2. 2-
. .
: 1 - ,, ( ) + (1 -1) = \ (2 -1). .
4 4
(2)
3- . . . -
. 3. 3-
4- . . (. 4).
,
(1) = , .
1=0

= 1 -
(1)
: 1
1=0 1
((1 - ,) 4 + (1 2 ) ,34 2 +

P(2) = p.
1=0
,
= ((1 + ( = . +(1-] ) =
1 1 1=0 1=0 1=0
= 11 (2 4 ). (4)
1=0 1=0
5- .
^
. (. 5).
.
: , (, , , ) . .
, 2 44. (5)
: , , , . .
, , , , 0(1 - ,) 1 23
, , , , , -
∞; ,(1 - ) 2 4 00.
{, , } ( ), (., , [2, . 136]), :
(6)
+ (1 " 3 ^.^ + 21 'Pi ) +
+ 41 2 .1-1" Pp)212_ )2 +4 +
+21 -.Pi))(1-p^)p^p2p2
+ (2" -)i2 4 423 + + 2^2)(.. - . )P2P2PiP4 + + 2^2 ." )2241 + + 2. ." 33 + + (. ".))2"2)22"34 + 2 "2 . )2 "2 2 )2 4 ). 2 2 +
+ 2 " -)-." )(. " 4 ~^))\ + 2 " 2)(. " )( . "- 4 )24. + + 2 -Pl)(1-P2)(1-P3)(1-P4)P1P2P3P4
, (6)
, ill (2 - ) - (7)
1= v ,=1 J
: , , . , Ao Bo B . .
: , , . . , , , Ao, , .
17
V I )


18

: . .
: , , . . . , , . .
: , , , . .
1 (1 - ,). (8)
1=0 1 ,=0 1
, (5), (7) (8),
= >
,=0
, (2-
,=1
,)-
+
+1 + (1 - )
,=
-4 ,( 2 - ,) .
1 - 0, 4
(1- ) ( 2-).
(10)
(9)
6- . , , . , , . , (. 6).
, 1 - ., ( ) 1 - (1 - ,)2 = . (2 - .).
=1

= , 11 (2 - ,).
1 ,= 1,= 1
2.
, . .
. :
1) ,
2) .
( , ) .
. (1), (2) (10) : , 1, 2, 3, . , , .
. 6. 6-
1. , .
.
[ 0 (2- ) - 0+ 1(1- )] <
= =1 = J
∞(2-.)
=0 = =

<1)
(2 - ) - 1 (1-) < (2 - .),
=1 = =
, , :
(1 - ) (1 (1 - ) ]<
V 1 J
( 2 - )( 2 - 2 ).
=1
(12)
(12) .-
:
1 + (1 - ) < 2 (2 - ),
=1 =1
:
(1 - )< 2 (2 - )-1.
=1 =1
(13)
(13) , .: (2 - . ) > 2 - . ,
= i0
. = 1 - ..
. .
,
2 + 1)(2 + 1)(3 + 1) ( + 1) - 1 = = 21 2 3 + 1 + { }.
(11) , 1.
. .
2. , .
.
(2 - ) > 2 - (14)
= =
(14)
: S1 = (. 1) = (. -1).
,

S1 =
= 7
1∞1 034 1,
< <1
S2 - -
= 7 -1
- , 01234 -1. (15)
1 7 ,

2 - (1 - ) 2 S2 = -
=
-

- 1 01^3/∞ -1,
/ 7
(15) . S1 > 2 + S2. . = 1 - (14) .
(4) (10) 2.
.
. 1, . - , ^ - , - .
1

=
=

1 = 1 =
2 = (2 - )
3 = (2-^0) 7=0
4 , ( 2 - ) 1 = =
5 1 = . (2 - ) I- - . )] -1 = V =1 = J
6 . (2 - ) 1 = =
19
V I )


20

3.
.
(. . 1) .

1. . 1 .
2. , .
, :
, ;
;
.
, , , :
;
;
;
.
. . 2, .
1. 0,5, 0,4. , , ( , ) ( ) .
2. 0,9, 0,85. , , . .
3. 0,999, 0,9999. .
4. ,
, , , , .
, , [3]:
2
( )
.
0,5 0,7 0,8 0,9 0,99 0,999 0,9999
? 0,03125 0,16807 0,32768 0,59049 0,950990 0499 0,995009 990004999 0,999500 0999900005
?> 0,158203 125 0,480024 727 0,679477 248 0,864536 409 0,989604 0593960401 0,998996 004005994 0,999899 9600040006
? 0,046875 0,218491 0,393216 0,649539 0,960499 950399 0,996004 999995004 0,999600 0499999995
?' 0,061523 4375 0,307892 4751 0,547985 8176 0,832301 5599 0,997598 0247911955 0,999975 0998002498 0,999999 75009998
? 0,095703 125 0,386846 719 0,609222 656 0,837137 673 0,989217 9193961787 0,998992 017991994 0,999899 9200179992
?' 0,237304 6875 0,624032 1451 0,815372 6976 0,950990 0499 0,999500 0999900005 0,999995 00001 0,999999 950000001
(), ;
- ( ), : 1) , - ( ) ; 2) , ;
(); , (UART, CAN .) SpaceWire; , ();
(), , .
,
:
1.
, .
2. .
3. . - , .

1. ECSSE-ST-50-12C SpaceWire - Links, nodes, routers and networks. - European Cooperation for Space Standardization (ECSS), 2008. 129 .
2. . ., . ., . . . . : , 1965. 525 .
3. . ., . ., . ., - . . : [ ] , , -12 : . . : , 2012. . 1539-1546.
20.12.2012 .
21