Колесников А.А. Синергетические методы управления сложными системами: механические и электромеханические системы
Подождите немного. Документ загружается.
r
(1)
s
= r
(2)
s
= r
(3)
s
=16, 39 r
(1)
r
= r
(2)
r
= r
(3)
r
=15, 08 L
(1)
m
= L
(2)
m
= L
(3)
m
=0, 624
L
(1)
s
= L
(2)
s
= L
(3)
s
=0, 663 K
(2)
= K
(3)
= 100
λ
(j)
1
= λ
(j)
2
= 500 β
(j)
11
=1 β
(j)
12
=2 β
(j)
21
=3 β
(j)
22
=4 ψ
(j)
r0
=0, 7 λ
(j)
3
= 600 ∀j = 1, 3
Y
0
=0, 5 Z
0
=0, 1 λ
(N)
1
= λ
(N)
2
= λ
(N)
3
= 4000
¯
λ
(N)
1
=
¯
λ
(N)
2
=
¯
λ
(N)
3
= 8000
X
0
=0, 3
˙z
1
(t)=a
1
;
˙z
2
(t)=a
2
;
˙z
3
(t)=a
3
,
z
1
z
2
z
3
a
1
a
2
a
3
(X, Y, Z)
Σ
N
=
)
X = z
1
Y = z
2
Z = z
3
*
.
ψ
(N)
1
= −x
5
sin x
1
− z
1
;
ψ
(N)
2
= x
5
sin x
1
− z
2
;
ψ
(N)
3
= x
3
− z
3
.
ϕ
(1)
2
=
1
x
5
ψ
(1)
r0
γ
(1)
-
J
1
+m
3
(l
3
+x
5
)
2
z
1
λ
(N)
1
+a
1
¯
λ
(N)
1
cos x
1
+
z
2
λ
(N)
2
+ a
2
¯
λ
(N)
2
sin x
1
+
+
2x
2
+
¯
λ
(N)
1
x
5
x
6
+
¯
λ
(N)
1
−
¯
λ
(N)
2
x
6
−
λ
(N)
1
− λ
(N)
2
x
5
cos x
1
sin x
1
−
− x
5
x
2
¯
λ
(N)
1
−
¯
λ
(N)
2
sin
2
x
1
− x
2
x
5
x
6
m
2
(l
3
+ x
5
)+α
(1)
.
;
ϕ
(2)
2
=
J
2
γ
(2)
ψ
(2)
r0
+
g(m
2
+m
3
)−α
(2)
x
4
J
2
−
¯
λ
(N)
3
(a
3
−x
4
)−λ
(N)
3
(z
3
−x
3
)
,
;
ϕ
(3)
2
=
J
3
γ
(3)
ψ
(3)
r0
-
x
5
λ
(N)
1
−λ
(N)
2
+x
6
¯
λ
(N)
1
−
¯
λ
(N)
2
sin
2
x
1
−x
2
2
x
5
+λ
(N)
2
x
5
−
−
z
2
λ
(N)
2
+a
2
¯
λ
(N)
2
cos x
1
+
z
1
λ
(N)
1
+a
1
¯
λ
(N)
1
sin x
1
+
m
3
x
2
2
(x
6
+l
3
)−α
(3)
x
6
J
3
+
+ x
2
x
5
¯
λ
(N)
1
−
¯
λ
(N)
2
cos x
1
sin x
1
+
¯
λ
(N)
2
x
6
.
.
A
0
(0, 0001; 0, 01; 0, 01) A
1
(1, 5; 1, 81; 1, 21) A
2
(1, 5; 1, 81; 0, 61)
A
3
(0, 6; 1, 51; 0, 61)
• A
0
A
1
a
1
=0, 5 a
2
=0, 6 a
3
=0, 4
• A
1
A
2
a
1
=0 a
2
=0 a
3
= −0, 2
• A
2
A
3
a
1
= −0, 3 a
2
= −0, 1 a
3
=0
G
11
¨q
1
(t)+G
12
˙q
1
(t)+G
13
¨q
2
(t)+G
122
˙q
2
2
(t)=M
d1
;
G
21
¨q
2
(t)+G
22
˙q
2
(t)+G
23
¨q
1
(t)+G
211
˙q
2
1
(t)=M
d2
,
q
1
q
2
M
d1
M
d2
˙x
1
(t)=x
2
=˙q
1
(t) ˙x
3
(t)=x
4
=˙q
2
(t)
˙x
1
(t)=x
2
;
˙x
2
(t)=
M
d1
G
21
− G
12
G
21
x
2
+ G
13
G
22
x
4
+ G
13
G
211
x
2
2
− G
13
M
d2
+ G
21
G
122
x
2
4
G
11
G
21
− G
23
G
13
;
˙x
3
(t)=x
4
;
˙x
4
(t)=
M
d2
G
11
− G
22
G
11
x
4
+ G
23
G
12
x
2
+ G
23
G
122
x
2
4
− G
23
M
d1
+ G
11
G
211
x
2
2
G
11
G
21
− G
23
G
13
,
G
11
= R
2
(M +2m(1 + cos(x
3
− x
1
))) + J
1
G
12
= k
D1
G
13
= R
2
m cos(x
1
− x
3
) G
122
=
R
2
m sin(x
1
−x
3
) G
21
= R
2
m + J
2
G
22
= k
D2
G
23
= R
2
m cos(x
1
−x
3
) G
211
= R
2
m sin(x
1
−x
3
)
k
D1
k
D2
m m
∆m G
13
= G
23
G
122
= G
211
˙x
1
(t)=x
2
;
˙x
2
(t)=
M
d1
G
21
− G
12
G
21
x
2
+ G
13
G
22
x
4
+ G
13
G
211
x
2
2
− G
13
M
d2
+ G
21
G
122
x
2
4
G
11
G
21
− G
2
13
+ ν
5
∆m
2
+ ν
6
∆m
+
+
ν
1
∆m
2
+ ν
2
∆m
G
11
G
21
− G
2
13
+ ν
5
∆m
2
+ ν
6
∆m
;
˙x
3
(t)=x
4
;
˙x
4
(t)=
M
d2
G
11
− G
22
G
11
x
4
+ G
23
G
12
x
2
+ G
23
G
122
x
2
4
− G
23
M
d1
+ G
11
G
211
x
2
2
G
11
G
21
− G
2
13
+ ν
5
∆m
2
+ ν
6
∆m
+
+
ν
3
∆m
2
+ ν
4
∆m
G
11
G
21
− G
2
13
+ ν
5
∆m
2
+ ν
6
∆m
,
ν
1
= R
4
cos(x
3
−x
1
)(x
2
4
−x
2
2
cos(x
3
−x
1
)) ν
2
= R
2
(sin(x
3
−x
1
)x
2
4
(J
2
+2R
2
m)) −R
2
cos(x
3
−
x
1
)(M
d2
+2R
2
x
2
2
m sin(x
3
−x
1
)+k
D2
x
4
)+R
2
(M
d1
−k
D1
x
2
) ν
3
= R
4
sin(x
3
−x
1
)((2x
2
2
−x
2
4
)cos(x
3
−
x
1
)+2x
2
2
) ν
4
= R
2
(2M
d2
+x
2
2
M sin(x
3
−x
1
)+2k
D2
x
4
+sin(x
3
−x
1
)x
2
4
(J
2
+2R
2
m)+2R
2
m cos(x
3
−
x
1
)sin(x
3
−x
1
)(2x
2
2
−x
2
4
)+(k
D1
x
2
−k
D2
x
4
−M
d1
+2M
D2
)) cos(x
3
−x
1
) ν
5
= R
4
(2 cos(x
3
−x
1
)+
2−cos
2
(x
3
−x
1
)) ν
6
= R
2
(2 cos(x
3
−x
1
)(2R
2
m(2−cos
2
(x
3
−x
1
))+2J
2
)+R
2
(M +4m)+2J
2
+J
1
)
ν
5
∆m
2
+ ν
6
∆m
˙x
1
(t)=x
2
;
˙x
2
(t)=
M
d1
G
21
− G
12
G
21
x
2
+ G
13
G
22
x
4
+ G
13
G
211
x
2
2
− G
13
M
d2
+ G
21
G
122
x
2
4
+ z
1
G
11
G
21
− G
2
13
;
˙x
3
(t)=x
4
;
˙x
4
(t)=
M
d2
G
11
− G
22
G
11
x
4
+ G
23
G
12
x
2
+ G
23
G
122
x
2
4
− G
23
M
d1
+ G
11
G
211
x
2
2
+ z
2
G
11
G
21
− G
2
13
;
˙z
1
(t)=η
1
(x
1
− x
1k
);
˙z
2
(t)=η
2
(x
3
− x
3k
),
z
1
z
2
η
1
η
2
x
1k
x
3k
M
d1
(x
1
,x
2
,x
3
,x
4
,z
1
,z
2
) M
d2
(x
1
,x
2
,x
3
,x
4
,z
1
,z
2
)
ψ
1
= γ
1
[α
1
(x
1
− x
1k
)+x
2
+ λ
1
z
1
]+µ
1
[α
2
(x
3
− x
3k
)+x
4
+ λ
2
z
2
];
ψ
2
= γ
2
[α
1
(x
1
− x
1k
)+x
2
+ λ
1
z
1
]+µ
2
[α
2
(x
3
− x
3k
)+x
4
+ λ
2
z
2
] ,
γ
i
,α
i
,λ
i
,µ
i
,i=1, 2
T
1
˙
ψ
1
(t)+ψ
1
=0;
T
2
˙
ψ
2
(t)+ψ
2
=0;
T
1
,T
2
> 0
M
d1
M
d2
µ
1
=0,γ
2
=0,µ
2
=1,γ
1
=1
M
d1
=(x
3
− x
3k
)η
2
G
13
λ
2
+(x
1
− x
1k
)η
1
G
11
λ
1
+ G
13
x
4
α
2
+ G
11
x
2
α
1
−
− G
122
x
2
4
− G
12
x
2
−
G
13
z
2
+ G
11
z
1
G
2
13
− G
11
G
21
+
T
1
G
13
ψ
2
+ T
2
G
11
ψ
1
T
1
T
2
;
M
d2
= −(x
3
− x
3k
)η
2
G
21
λ
2
− (x
1
− x
1k
)η
1
G
13
λ
1
− G
21
x
4
α
2
− G
13
x
2
α
1
+
+ G
122
x
2
2
+ G
22
x
4
−
G
13
z
1
+ G
11
z
2
G
2
13
− G
11
G
21
+
T
1
G
21
ψ
2
+ T
2
G
13
ψ
1
T
1
T
2
.
ψ
1
=0∪ ψ
2
=0
˙x
1ψ
(t)=−α
1
(x
1
− x
1k
) − λ
1
z
1
;
˙x
3ψ
(t)=−α
2
(x
3
− x
3k
) − λ
2
z
2
;
˙z
1
(t)=η
1
(x
1
− x
1k
);
˙z
2
(t)=η
2
(x
3
− x
3k
),
x
1
x
3
¨x
1ψ
(t)+α
1
˙x
1ψ
+ λ
1
η
1
(x
1ψ
− x
1k
)=0;
¨x
3ψ
(t)+α
2
˙x
3ψ
+ λ
2
η
2
(x
3ψ
− x
3k
)=0.
α
i
,λ
i
,µ
i
,i=1, 2
x
1
x
3
x
1
= x
1k
x
3
= x
3k
α
1
,α
2
> 0 λ
1
η
1
,λ
2
η
2
> 0
ξ
1
,ξ
2
α
1
=2ξ
1
√
λ
1
η
1
α
2
=2ξ
2
√
λ
2
η
2
λ
1
= λ
2
=5,η
1
= η
2
=10,α
1
= α
2
=5,γ
1
=1,γ
2
=3,µ
1
=2,µ
2
=4,x
1k
=0, 5,x
3k
=1,
T
1
= T
2
=0, 5,k
D1
= k
D2
=1,M =1,m=5,J
1
=3,J
2
=1.
m
µ
1
=0,γ
2
=0,µ
2
=1,γ
1
=1
ψ
1
= α
1
(x
1
− x
1k
)+x
2
+ λ
1
z
1
;
ψ
2
= α
2
(x
3
− x
3k
)+x
4
+ λ
2
z
2
.
m
0
J
0
{x, y} α
F
1
F
2
M
f
j
pr
f
j
tr
β
j
j