Колесников А.А. Синергетические методы управления сложными системами: энергетические системы
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∆h =0 h
˜α = const ˜α
p = const p
D = const D
ϑ = const ϑ
p = const p
N(p ,µ )=const N
p = const p
D (p ,p )=const D
∂ρ
∂t
+
ρv =0,
∂ρu
∂t
+
(ρiv)=Q,
∂ρv
∂t
+ ·(P + ρvv)=ρg,
ρ u i v
Q g P
· vv
p = p(ρ, ϑ)
Q = Q(ϑ, θ, v),
p ϑ θ
∂
∂t
(mc
θ)=q − q,
m c
q q
q
α
q = αΠ(θ −ϑ),
Π
D
i p
D
Q
V
x
()
()
d
dt
(ρ
V
+ ρ
V
)=D − D
;
d
dt
(ρ
V
i
+ ρ
V
i
+ G c θ )=Q + D i − D
i
,
ρ
ρ
i
i
V
V
G c θ
D
i
D
Q
i
p
θ
ϑ
Q = α (θ − ϑ
)F ,
α F
Q
θ − ϑ
α →∞ θ = ϑ
ρ
= ρ
(p ) ρ
= ρ
(p ) i
= i
(p ) i
= i
(p ) ϑ
= ϑ
(p )
V
+ V
= V = const
(ρ
−ρ
)
dV
dt
+
V
∂ρ
∂p
+(V −V
)
∂ρ
∂p
dp
dt
= D
− D
;
(ρ
i
−ρ
i
)
dV
dt
+
V
∂ρ
∂p
i
+
∂i
∂p
ρ
+(V −V
)
∂ρ
∂p
i
+
∂i
∂p
ρ
+G
c
∂ϑ
∂p
dp
dt
=
= D
i − D
i
+ Q.
p
V
D Q
p D
i
i
i = i
e
11
(p )
dV
dt
+ e
12
(p ,V
)
dp
dt
= D
− D − D
;
e
21
(p )
dV
dt
+ e
22
(p ,V
)
dp
dt
= D
i − D i
− D
i
+ Q,
D e
ij
e
11
= ρ
− ρ
;
e
21
= ρ
i
− ρ
i
;
e
12
= V
∂ρ
∂p
+(V −V
)
∂ρ
∂p
;
e
22
= V
∂ρ
∂p
i
+
∂i
∂p
ρ
+(V −V
)
∂ρ
∂p
i
+
∂i
∂p
ρ
+G
c
∂ϑ
∂p
.
θ = ϑ
α
G c
dθ
dt
= Q − α
(θ − ϑ
)F .
e
11
(p )
dV
dt
+ e
12
(p ,V
)
dp
dt
= D
− D −D
;
e
21
(p )
dV
dt
+˜e
22
(p ,V
)
dp
dt
= D
i − D i
− D
i
+ α (θ − ϑ
)F ;
G
c
dθ
dt
= Q − α
(θ − ϑ
)F .
˜e
22
= V
∂ρ
∂p
i
+
∂i
∂p
ρ
+(V − V
)
∂ρ
∂p
i
+
∂i
∂p
ρ
∗
dV
/dt = −dV
/dt =0 i
(e
22
− e
12
i
)
dp
dt
= Q − D
(i
− i ) − D
r,
r = i
− i
V
e
22
dV
/dt =0
∗
D =0
D = D
D = D
+ D
dV
dt
= −
e
12
(p ,V
)
e
11
(p )
dp
dt
;
∆
e
(p ,V
)
e
11
(p )
dp
dt
= D
i − D i
− D
i
+ Q,
∆
e
= e
11
e
22
− e
12
e
21
V
p
V
(p )
V
p
f(p ,V
)=0
D
V
∆
e
e
11
dp
dt
= D
i − D i
− D
i
+ Q −
e
21
e
11
(D − D −D
).
e
21
e
11
= i
−
ρ
r
ρ
− ρ
= i
−
ρ
r
ρ
− ρ
∆
e
e
11
dp
dt
= Q +
ρ
r
ρ
− ρ
− (i
− i )
D − (D ρ
+ D
ρ
)
r
ρ
− ρ
.
V
D
(e
22
− e
12
i )
dp
dt
= Q − D
(i
− i ) − D
(i
− i );
∆
e
(p ,V
)
e
11
(p )
dp
dt
= Q − D
(i
− i ) − D
(i
− i ),
e
11
(p
0
)
d(∆V
)
dt
+ e
12
(p
0
,V
0
)
d(∆p
)
dt
=∆D
− ∆D −∆D
;
e
21
(p
0
)
d(∆V
)
dt
+ e
22
(p
0
,V
0
)
d(∆p
)
dt
= D
0
∆i +i
0
∆D −i
0
∆D −i
0
∆D
+∆Q−
−
D
0
∂i
∂p
p =p
0
+ D
0
∂i
∂p
p =p
0
∆p
i
e
11
(p
0
)
d(∆V
)
dt
+ e
12
(p
0
,V
0
)
d(∆p
)
dt
=∆D
− ∆D −∆D
;
e
21
(p
0
)
d(∆V
)
dt
+ e
22
(p
0
,V
0
)
d(∆p
)
dt
=∆Q + i
0
∆D − i
0
∆D −i
0
∆D
−
−
D
0
∂i
∂p
p =p
0
+ D
0
∂i
∂p
p =p
0
∆p
.
∆
e
(p
0
,V
0
)
e
11
(p
0
)
d(∆p
)
dt
=∆Q +
ρ
r
ρ
− ρ
− (i
− i )
0
∆D −
ρ
r
ρ
− ρ
0
∆D −
−
ρ
r
ρ
− ρ
0
∆D
−
D
0
∂i
∂p
p =p
0
+ D
0
∂i
∂p
p =p
0
∆p
,
()
0
A
d(∆p
)
dt
+ β
1
∆p =∆Q + β
2
∆D − β
3
∆D −β
4
∆D
,
A = V
0
ρ
r
ρ
− ρ
+ ρ
∂i
∂p
p =p
0
+(V − V
0
)
ρ
r
ρ
− ρ
+ ρ
∂i
∂p
p =p
0
+ G c
∂ϑ
∂p
p =p
0
;
β
1
= D
0
∂i
∂p
p =p
0
+ D
0
∂i
∂p
p =p
0
;
β
2
=
ρ
r
ρ
− ρ
− (i
− i )
p =p
0
; β
3
=
ρ
r
ρ
− ρ
p =p
0
; β
4
=
ρ
r
ρ
− ρ
p =p
0
.
−β
1
/A
A β
1
∂i
∂p
< 0
p<−
∂i
∂p
∂i
∂p
,
p = D
0
/D
0
∆h =∆
V
− V − (1 − ¯ϕ )V
F