automatic control by meiling chen1 lesson 4 modeling automatic control 1. modeling
TRANSCRIPT
Automatic Control by Meiling CHEN 1
Lesson 4
modeling
Automatic control1. modeling
Automatic Control by Meiling CHEN 2
Mechanical system
spring
Translational mechanical components
k
)(tx
)(tf
)()( tkxtf
k
)(t
Rotational mechanical components
)(t
)()( tkt
Automatic control
Automatic Control by Meiling CHEN 3
Mechanical system
Translational mechanical components Rotational mechanical components
M
)(tx
)(tf
)()( txMMatf
J)(t
Viscous friction (linear)
)(tf
)(tx
)()()( txBtBvtf
B B )(t
)()( tBt
)()( tJt
)(t
)(t
Automatic control
Automatic Control by Meiling CHEN 4
Mechanical system
Translational mechanical components Rotational mechanical components
M
)(tv
)(tf J)(t
Coulomb friction (nonlinear)
)(tv
)(tf
)(t
cF
cF
cT
cT
)(t
)(t
Automatic control
Automatic Control by Meiling CHEN 5
static friction (nonlinear)
M
)(tv
)(tf
)(tv
)(tf
sF
sF
Automatic control
Automatic Control by Meiling CHEN 6
Example 1
txdt
xd
dt
xxdxx
dt
xxdxx
dt
txdx
sin35)(
6)(2
0)(
6)(2)(
47
222
212
12
21212
12
1
Automatic control
Automatic Control by Meiling CHEN 7
Example 2
208)(54
06)(523
2122
22
12112
12
dt
d
dt
d
dt
d
dt
d
Automatic control
Automatic Control by Meiling CHEN 8
Gear train11 , rN
22 , rN
111 ,,
222 ,,
1
2
1
2
2
1
2
1
2
1
r
r
N
N
Mechanical system
2
1
2
1
N
N
r
r(1)
2211 rr (2) 2211 (3)
2211 rr (4)
Automatic control
21 SS no energy loss
Nr
21 SS
Automatic Control by Meiling CHEN 9
Example 3
)1(11111 BJ
)2(22222 BJ
12
12
12
12
11
22
N
N
N
N
N
N
Automatic Control by Meiling CHEN 10
Automatic control
Automatic Control by Meiling CHEN 11
Example 4
5
0
21211
1 9cos8))()((5
1))()((4
)(3)(21 tdttitititi
dt
tditiloop
0)(7)(
6))()((4))()((5
12 2
212
0
12 tidt
tdititidttitiloop
t
Automatic control
Automatic Control by Meiling CHEN 12
Automatic control
Automatic Control by Meiling CHEN 13
aR aL
ai
tea
fR
fL
teb
m
mJ LTArmature circuit Field circuit
te f
dt
diLeiRte a
abaaa )(
Lm
mm
m
aim
Tdt
dB
dt
dJ
ikT
2
2
fi constant
mbb ke a
a
m
a
ba
a
aa eLdtL
ki
L
R
dt
di 1
Armature control DC motor
Automatic Control by Meiling CHEN 14
aa RsL 1
)(
1
mm BsJs
skb
ik)(sTm)(sIa
)(sEa
)(sEb
)(sm
)1()(
)(
ss
K
sE
s
m
m
a
m
+-
Automatic Control by Meiling CHEN 15
aR aL
ai
tea
fR
fL
teb
mmJ LT
Armature circuit Field circuit
te fconstant
Lm
mm
mm Tdt
dB
dt
dJT
2
2
fim ikT dt
diLiRte f
ffff )(
field control DC motor
Automatic Control by Meiling CHEN 16
ff RsL 1
)(
1
mm BsJs ik)(sTm)(sI f
)(sE f )(sm
))(()(
)(
ffmm
i
f
m
RsLBsJs
K
sE
s