7 / 11
A
3
=
B
⊥
2
A
2
B
⊥
T
2
=
a
2
13
+ 1 ;
(25)
B
3
=
B
⊥
2
A
2
B
2
=
−
a
13
a
42
h a
13
h
2
+
a
24
h
2
.
(26)
On the basis of formulae (3) and (13)–(26) it is possible to find the
observer matrix
L
0. In their general form formulae for the matrix
L
0
component look very bulky. Therefore, it was decided not to present these
expressions. To provide the fastest convergence with the usage of the
solution obtained in the paper, it is necessary in (3) to assume own values
equal to zero:
Φ
0
= Φ
1
= Φ
2
= Φ
3
. Then the observer matrix
L
0
in
accordance with (3) will gain the following appearance:
L
T
0
=
l
1
l
2
l
3
l
4
,
(27)
where
l
1
=
−
a
2
13
−
4;
l
2
=
−
a
24
(6
a
2
13
+4
a
4
13
+
a
6
13
+
a
24
a
42
h
2
−
a
42
a
3
13
h
2
+
a
24
a
42
a
2
13
h
2
+
a
24
a
42
a
4
13
h
2
+3)
h
(
a
2
13
+ 1)(
a
13
+
a
24
)
−
−
3
a
2
13
+ 3
a
4
13
+
a
6
13
+ 3
a
24
a
42
h
2
−
a
42
a
3
13
h
2
+ 4
a
24
a
42
a
2
13
h
2
+ 2
a
24
a
42
a
4
13
h
2
+ 1
a
42
h
3
(
a
2
13
+ 1)(
a
13
+
a
24
)
;
l
3
=
a
6
13
−
a
42
a
5
13
h
2
+
a
24
a
42
a
4
13
h
2
+ 3
a
4
13
−
5
a
42
a
3
13
h
2
+ 3
a
2
13
−
3
a
42
a
13
h
2
+ 1
a
13
a
42
h
3
(
a
2
13
+ 1)(
a
13
+
a
24
)
−
−
a
6
13
+
a
24
a
42
a
4
13
h
2
+4
a
4
13
−
a
42
a
3
13
h
2
+
a
24
a
42
a
2
13
h
2
+6
a
2
13
+
a
24
a
42
h
2
+3
h
(
a
2
13
+ 1)(
a
13
+
a
24
)
−
a
31
h
;
l
4
=
−
2
a
6
13
+3
a
24
a
42
a
4
13
h
2
+7
a
4
13
−
2
a
42
a
3
13
h
2
+5
a
24
a
42
a
2
13
h
2
+9
a
2
13
+4
a
24
a
42
h
2
+ 4
h
2
(
a
2
13
+ 1)(
a
13
+
a
24
)
.
(28)
Thus, with the help of the above method it is quite easy to get the
matrix for the pitch channel and it will look as follows:
L
T
ϑ
=
l
ϑ
1
l
ϑ
1
.
(29)
Here
l
ϑ
1
=
−
2
, l
ϑ
2
=
−
1
/h
.
The analysis of the expressions (28), which, in accordance with (27) and
(29), represent the analytical algorithm of the observer synthesis shows that
its realization is based on the fulfillment of such elementary operations as
addition, multiplication and division. This fact allows stating the possibility
of doing the algorithm in real time with the help of the onboard computer.
The results of simulation.
Let’s do mathematical simulation. Let the
main moments of SC inertia kg/m
2
have the following values:
J
x
= 77521
;
ISSN 0236-3933. HERALD of the BMSTU. Series “Instrument Engineering”. 2014. No. 5
9