Математическое моделирование электромеханических систем. Аналитические методы. Глазырин А.С. - 187 стр.

UptoLike

ВУЗ: 

ТПУ | Томск

Составители: 

Рубрика: 

187
H ДВ.ГС H ДВ.ГС
ДВ ДВ ДВ ДВ
00
sin( )
()
tt
cU R M cU R M
e
f
dd
JL JL
−ατ
⋅− ⋅ ⋅− ⋅
⋅βτ
⋅ττ= ⋅ τ=
⋅⋅β
∫∫
H ДВ.ГС
22
ДВ ДВ
0
sin( ) cos( )
t
cU R M
e
JL
−ατ
⎛⎞
⋅− ⋅
−α ⋅ βτ −β⋅ βτ
=⋅ ⋅=
⎜⎟
⎜⎟
⋅⋅β α+β
⎝⎠
()
H ДВ.ГС
22
ДВ ДВ
sin( ) cos( )
tt
cU R M
te te
JL
−α −α
⋅− ⋅
⎡
⎤
=− ⋅ α⋅ β ⋅ +β⋅ β ⋅ −β =
⎣
⎦
⋅⋅β⋅α+β
()
(
)
()
H ДВ.ГС
H ДВ.ГС
22 22
ДВ ДВ ДВ ДВ
sin( )
t
cU R M t e
cU R M
JL JL
−α
⋅− ⋅ ⋅α⋅β⋅
⋅− ⋅
=− −
⋅⋅α+β ⋅⋅β⋅α+β
(
)
()
H ДВ.ГС
22
ДВ ДВ
cos( )
.
t
cU R M t e
JL
−
α
⋅− ⋅ ⋅ β⋅
−
⋅⋅α+β
Третье слагаемое –
ДВ.Г 2 ДВ.Г 2
2
ДВ
ДВ.Г
ДВ
ДВ ДВ ДВ
()RRFp
L
R
c
Lpp
LJL
⋅ω ⋅ω ⋅
=
⎡⎤
⎛⎞
⋅⋅+ +
⎢⎥
⎜⎟
⎜⎟
⋅
⎢⎥
⎝⎠
⎣⎦
ДВ.Г 2 ДВ.Г 2
ДВ ДВ
() sin( )
.
t
R
ft R e t
LL
−α
⋅ω ⋅ ⋅ω ⋅ ⋅ β
=
⋅β
Четвертое слагаемое найдем по теореме дифференцирования ори-
гинала:
2
22
2
ДВ.Г
ДВ ДВ ДВ
()
()
p
df t
pFp
dt
R
c
pp
LJL
⋅ω
=
⋅ω ⋅ ω ⋅ =
⎛⎞
⋅+ +
⎜⎟
⎜⎟
⋅
⎝⎠
2
2
sin( )
sin( ) cos( ) .
t
tt
de t
ete t
dt
−α
−α −α
⎡⎤
⋅β ω
⎤
=ω ⋅ = ⋅ −α⋅ ⋅ β +β⋅ ⋅ β
⎢⎥
⎦
ββ
⎣⎦
В итоге запишем оригинал скорости:
(
)
()
H ДВ.ГС
2 С
22
ДВ
ДВ ДВ
sin( )
()
t
cU R M
ci M e t
t
J
JL
−α
⋅− ⋅
⋅− ⋅ ⋅ β
ω= + −
⋅β
⋅⋅α+β
(
)
()
(
)
()
H ДВ.ГС H ДВ.ГС
22 22
ДВ ДВ ДВ ДВ
sin( ) cos( )
tt
cU R M t e cU R M t e
JL JL
−α −α
⋅− ⋅ ⋅α⋅β⋅ ⋅− ⋅ ⋅ β⋅
−−+
⋅⋅β⋅α+β ⋅⋅α+β
ДВ.Г 2
2
ДВ
sin( )
sin( ) cos( ) .
t
tt
Re t
ete t
L
−α
−α −α
⋅ω ⋅ ⋅ β
ω
⎡
⎤
++⋅−α⋅⋅β+β⋅⋅β
⎣
⎦
⋅β β

Страницы