Колесников А.А. Синергетические методы управления сложными системами: энергетические системы
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s(t)
U (t) U
1
(t) U
2
(t)
U
syn
= a −
b +
1
T
1
ψ
1
c
= a −
b
c
−
1
T
1
c
U
2
0
−
'
AE
2
q
+2B(δ)E
q
+ D
(
+ λ
1
z
.
z(t)=z(0) + η
U
2
0
− U
2
(t)
dt = z(0) + η
U
0
+ U (t)
∆U (t)dt.
∆U
U
2
= µ
PT
M(t)=M
0
T
1
=1 η = λ
1
=1
∆ω =0
∆U =0
k
0U
ε
U
=0
P
0
T
ω = ω
0
s =0
dδ
dt
= s;
ds
dt
= b
1
(P
0
T
− E
2
q
y
11
sin(α
11
) − E
q
U
c
y
12
sin(δ − α
12
)+w);
dw
dt
= ξs,
w M(t)=M
0
ξ
s =0
ψ
2
= ξs + λ
2
w,
T
2
˙
ψ
2
(t)+ψ
2
=0.
ψ
2
=0 T
2
> 0
ψ
2
= ξs + λ
2
w =0.
ψ
2
=0
dδ
dt
= s;
dw
dt
= −λ
2
w.
λ
2
> 0
s =0
δ = const
P
0
T
= P
0
T
(δ, s, E
q
,w)=E
2
q
y
11
sin(α
11
)+E
q
U
c
y
12
sin(δ −α
12
)−
− w
λ
2
ξb
1
T
2
− 1
− s
λ
2
b
1
+
1
b
1
T
2
.
U
1
= U
U
2
= µ
PT
M(t)=M
0
T
2
=5 ξ = λ
2
=1
t = 300 ...400 ε
U
=5, 33%
s(t)
U (t) U
1
(t) U
2
(t)
s(t)
U (t) U
1
(t) U
2
(t)
s(t) U (t)
s(t) U (t)
∆ω =0
∆U =0
x
c
r
c
x
c
r
c
t =50
x
c
r
c
x
c
r
c
t =50
M(t)=a
F
+ b
F
sin(Ωt).
dw
1
dt
= w
2
+ w
3
;
dw
2
dt
= −Ω
2
w
1
;
dw
3
dt
= ξs,
w
i
,i= 1, 3 Ω
w
1
(t)=
ˆ
M(t)
dδ
dt
= s;
ds
dt
= b
1
(P
0
T
− E
2
q
y
11
sin(α
11
) − E
q
U
c
y
12
sin(δ − α
12
)+w
1
);
dw
1
dt
= w
2
+ w
3
;
dw
2
dt
= −Ω
2
w
1
;
dw
3
dt
= ξs.
P
0
T
P
0
T
ψ
3
= ξs + β
1
w
1
+ β
2
w
2
+ β
3
w
3
,
T
3
˙
ψ
3
(t)+ψ
3
=0.
ψ
3
=0 T
3
> 0
ψ
3
= ξs + β
1
w
1
+ β
2
w
2
+ β
3
w
3
=0.
ψ
3
=0
dδ
dt
= s;
dw
1
dt
= w
2
+ w
3
;
dw
2
dt
= −Ω
2
w
1
;
dw
3
dt
= −β
1
w
1
− β
2
w
2
− β
3
w
3
.
β
1
,β
2
,β
3
A(p)=det(pE − A) = det
p −1 −1
Ω
2
p 0
β
1
β
2
p + β
3
= p
3
+ p
2
β
3
+ p
'
β
1
+Ω
2
(
+
'
β
3
− β
2
(
Ω
2
.
p
1
,p
2
,p
3
A (p)=(p − p
1
)(p − p
2
)(p − p
3
)=p
3
+ p
2
'
−p
1
− p
2
− p
3
(
+ p
'
p
1
p
2
+ p
3
(p
1
+ p
2
)
(
− p
1
p
2
p
3
.
A(p) A (p)
β
1
,β
2
,β
3
β
1
= p
1
p
2
+ p
3
(p
1
+ p
2
) − Ω
2
;
β
2
= −p
1
− p
2
− p
3
+
p
1
p
2
p
3
Ω
2
;
β
3
= −p
1
− p
2
− p
3
.
p
1
,p
2
,p
3
< 0
β
1
,β
2
,β
3
p
1
,p
2
,p
3
< 0
p
1
= p
2
= p
3
s =0 δ = const
P
0
T
= P
0
T
(δ, s, E
q
,w
1
,w
2
,w
3
)=E
2
q
y
11
sin(α
11
)+E
q
U
c
y
12
sin(δ − α
12
)−
− w
1
1 −
β
2
Ω
2
ξb
1
−
β
1
ξb
1
(w
2
+ w
3
) −
1
ξb
1
T
3
ξs + β
1
w
1
+ β
2
w
2
+ β
3
w
3
.
M(t)=
⎧
⎨
⎩
0, 0 <t<10c;
a
F
+ b
F
sin(Ωt), 10 <t<80c,
a
F
= −0, 1 b
F
=0, 05 Ω=2πf f =
E
q
(0)U
c
y
12
Tj
≈ 0, 24
T
1
= T
3
=1 T
2
=5 η = ξ =1 λ
1
= λ
2
=1 p
i
= −0, 01,i= 1, 3
∆U =0, 0003 U
∞
= U =1, 05
∆s =10
−5
s =0
ε
U
< 1%
P
T
(t) δ(t) s(t)
U (t) U
1
(t) U
2
(t)
s(t) U (t)
∆U =0, 0001 U
∞
=1, 012
∆s =4· 10
−3
s =0
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