МатМод_УК_ЗО

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4.2.3. ,

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6,3	10	12,5	16	20	22	25	28	32		36
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12

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0,8	1,0	1,2		1,4		1,6	1,8		2,0		2,2	2,4		2,8
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13

4.2.4. ( .

:

- 0 $ 1

1 .

-! $

	1
	-
		1
-	-

:

-!

		1
( )
-
		1

14

&+08-!&- *

.

m1

m2

m3

F

C1

C2

C3

. 1. $

C1	C2	C3	F
m1	R1 m2	R2 m3	R3

. 2.

1	2	3
m1	R1 m2	R2 m3	R3

. 3. ,

15

1		2		3
m 1		R 1 m 2	R	m	3	R 3	F
				2
I 11	I12	I13	I14	I15		I16	I 17

. 4. 2 , -

$ , .

1

d( I11 )

1

∫( I11

− I12 )dt = 0,

+

C

1

dt

m

1

−

1

∫( I11 − I12 )dt + ( I12 − I13 ) R1 = 0,

m1

− ( I12 − I13 ) R1

1

d( I13 )

1

∫( I13

− I14 )dt = 0,

+

+

C 2

m2

dt

−

1

∫( I13 − I14 )dt + ( I14 − I15 ) R2 = 0,

m2

− ( I14 − I15 ) R2

1

d( I15 )

1

∫( I15

− I16 )dt = 0,

+

+

C3

m3

dt

−

1

∫( I15 − I16 )dt + ( I16 + F ) R3 = 0.

m3

16

I			1		I			2		I	7		3
	1				4
			m		R	1	m				R	m3		R	3	J
			1				2					2
			I 2	I 3			I 5		I 6			I 8		I 9
	.5. 2 ,												-

$ , .

+ I 1 + I 2 + I 3 − I 4				= 0 ,
+ I 4	+ I 5	+ I 6	− I 7	= 0 ,
+ I 7	+ I 8	+ I 9	− J
				= 0 .

I1 = C1 ∫(U C 1 )dt = C1 ∫(ϕ 3 )dt;

I

= m

d (U m1 )

= m

dϕ 3

;

2

1

dt

1

dt

I

=

U R1

=

ϕ 3

;

3

R1

R1

I 4

= C 2 ∫U C 2 dt = C 2 ∫(ϕ 2 − ϕ 3 ) dt;

I

= m

d (U m 2 )

= m

dϕ 2

;

5

2

dt

2

dt

I

=

U R 2

=

ϕ 2

;

6

R2

R2

I 7

= C 3 ∫U C 3dt = C 3 ∫(ϕ1 − ϕ 2 ) dt;

I

= m

d (U m 3 )

= m

dϕ1

;

8

3

dt

3

dt

I

=

U R1

=

ϕ1

.

9

R3

R3

17

& $ .

2	R3	3	C2	4	L1	5
						L3
I1	R2		C1	C3		L2
	R1
					6	7
	1				R4

E1 E2

8

. 6. 3 $

) 1

-

					(
			E1	E2	C1	C2	R1	R4	L1
9		3	0	0	-1	+1	0	0	0
		R2	-1	0	0	0	+1	0	0
		R3	-1	0	+1	0	+1	0	0
		L2	0	0	-1	+1	0	+1	+1
		L3	0	-1	+1	-1	0	0	-1
		I1	+1	0	0	0	-1	0	0

UC3 − U C1 + U C2 = 0;

UR2 − E1 + U R1 = 0;

UR3 − E1 + U C1 + U R1 = 0;

U L		+ U C		+ U C		+ U R		4	+ U L	= 0;
	2		1			2			1
U L		− E 2		+ U C		− U C	2	− U L		= 0;
	3			1					1
U I	1	+ E1	− U R		= 0.
				1

IE1

IE2

IC1

IC2

IR1

IR4

IL1

+I R2 + I R3

+ I L3 = 0;

+I C3 − I R3

−I C3 − I l2

−I R2 + I R3

−I L2 = 0;

−I L2 + I L3

−I 1 = 0;

+I L2 − I L3 = 0;

+I L3 = 0;

+I 1 = 0;

=0.

& $ .

18

) 2

. 6

	1	2	1	2	3	R1	R2			R4	L1	L2	L3	I1
1	-1	0	0	0	0	-1	0		0	0	0	0	0	0
2	0	0	0	0	0	+1	-1		-1	0	0	0	0	+1
3	0	0	-1	-1	0	0	0		+1	0	0	0	0	0
4	0	0	0	+1	-1	0	0		0	0	-1	0	0	0
5	0	0	0	0	0	0	0		0	0	+1	-1	+1	0
6	0	0	0	0	0	0	0		0	-1	0	+1	0	0
7	0	-1	0	0	0	0	0		0	0	0	0	-1	0

) , .

− I E1 − I R3 = 0;

I R1 − I R2 − I R3 + I 1 = 0;

− I C1 − I C2 + I R3 = 0;

I C2 − I L1 − I C3 = 0; I L1 − I L2 + I L3 = 0;

−I R4 + I L2 = 0;

−I E2 − I L3 = 0.

.

E1 = f (t);

E 2 = f (t);

I 1 = f (t);

U R

ϕ

1

− ϕ

2

E

1

− ϕ

2

I R

=

1

=

=

;

1

R1

R1

R1

I R

=

ϕ 2

;

I R

=

ϕ

2 − ϕ 3

;

I R

=

ϕ 6

;

2

R2

3

R3

4

R4

I C

= C1

d (ϕ 3 )

;

1

dt

d (ϕ 3 − ϕ 4 )

I C

2

= C2

;

dt

I L

=

1

∫ (ϕ 4 − ϕ 5 )dt;

1

L1

I L

=

1

∫ (ϕ 5 − ϕ 6 )dt;

2

L2

I L

=

1

∫ (ϕ 5 − ϕ 7 )dt =

1

∫ (ϕ 5 − E 2 )dt;

3

L3

L3

I C

= C3

d (ϕ 4 )

3

dt

19

&+08-!&- '

# .

& .

kbx p + VF = Q,

−pF = − R,

−pF2 + C2 x = 0,

" .

V = Q − (kbRF2 R / F )(C2 F ) .

F

3 .

	5 $
	5
	4
V
# $,	3
	2
	1
	0
	0	2 0	4 0	6 0
		$ , F

% .

& .

e	dp	+	p	+ VF = Q,
1 dt			N	1

MdV1 − pF1 = −R, dt

m dV2 − pF2 + C2 ∫V2 dt = 0,

dt

5$ V Q $ -

.

										20
										S 2QF m + QF C						2
	V (S ) =										1			1
		S (S 4 Mme + S 3																M + F 2 m]+
										kbx0 mM				+ S 2 [e C			2
						1				2	p					1				1
												0
			kbx																	.
						C			M						+ F 2C					)
		+ S			0		2		+ F kb p				0	M					2
				2		p				2						1
								0
5$ V1 Q $
	.
	V (S ) =									S 2 8 + 320000										.
	S (S 4 0,00001 + S 3 0,005 + S 2 1,208 + S 626,5 + 32000
5 .
	S1 = 0;	S2 = −55,9;							S3 = −488,0;					S4,5	= −21,9 ± j 341,9.
5$ V Q $ -
.
V (t) = 10 − 11,6 e −55,9t + 2,8 e −488t											+ 2,4712 e −21,9t							cos(341,9t + 2,06751).
1
3					.
		&
			15
		V	10
		# $,
				5
				0
				-5	0					0,05				0,1						0,15
											(, t