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Automatic control by meiling chen 2
Example : An Armature control DC motor
aR aL
ai
tea
fR
fL
teb
m
mJ LTArmature circuit Field circuit
te f
fi constant
)1()(
)(
ss
K
sE
s
m
m
a
m
Automatic control by meiling chen 3
)1( ss
K
m
m
m
aE
+-
)(sH
)(sGc)(sR
)1(1)(
2.0
2
s
m
m
sH
K
let Design controller
Sensor
Automatic control by meiling chen 4
Case I : Proportional control KsGc )(
Ksss
K
sssK
ssK
sR
sm
10)5)(1(
10
)1(1
)12.0(2
1
)12.0(2
)(
)(
01056 23 KsssCharacteristic function :
ks
Ks
ks
s
106
1030106
51
0
1
2
3
30 k
Automatic control by meiling chen 5
5 1 02
0k0k0kk
k
k
3k
3k
)5)(1(
10)(
ssssGH
Open loop transfer function : 707.0cos
Automatic control by meiling chen 7
)5)(1(
10)(
ssssGH Type I system
sss
as
Ksss
vs
sss
ps
eGHsKsR
esGHKsR
eGHKsR
v
2
0
1
1
0
10
1
lim)(
lim)(
0lim)(
3
2
Automatic control by meiling chen 8
)5)(1(
10)(
ssssGH )(dBGH
GH
1.0 1 10
0900180
090
0180
5
decdB20
decdB60
decdB40
0270
G.M.
P.M.
1g
Automatic control by meiling chen 10
Case II : Proportional Integral control s
KKsG I
Pc )(
)1( ss
K
m
m
maE
+-
)(sH
)(sR
Sensor
PK
sK I
1
1
)5(
10)(
ssss
KsKsGH IpOpen loop transfer function :
a zero
a pole
Automatic control by meiling chen 11
1
1
)5(
10)(
ssss
KsKsGH Ip
Type II system
aksss
as
sss
vs
sss
ps
eGHsKsR
esGHKsR
eGHKsR
12
0
10
10
1
lim)(
0lim)(
0lim)(
3
2
The system order
sse
Automatic control by meiling chen 12
1
1
)5(
10)(
ssss
KsKsGH Ip
)(10)5)(1(
10
)5)(1(
)(101
)5)(1(10
1
2
2
Ip
Ip
KsKsss
s
sss
KsKsss
GH
G
I
P
IPp
Ip
p
I
KK
KKK
s
s
KK
s
Ks
Ks
101030
360100300
106
1030106
1051
2
0
1
2
3
4
Automatic control by meiling chen 13
5 1 02
0pk0pk0kk
k
k
3k
3k
1
1
)5(
10)2()(
2
1
1
)5(
10)(
1
ssss
sKsGH
K
Klet
ssss
KsKsGH
p
P
I
Ip
pk
pk
pk
2g
Automatic control by meiling chen 15
1g
2g
g2 (PI controller) is unstable g1 (P controller) is stable
2g
1g
Automatic control by meiling chen 16
Case III : Proportional derivative control
)1( ss
K
m
m
maE
+-
)(sH
)(sR
Sensor
PK
sKD
sKKsG DPc )(
Sensor
1
1
)5(
10)()(
ssssKKsGH DpOpen loop transfer function :
a zero
Automatic control by meiling chen 17
1
1
)5(
10)()(
ssssKKsGH Dp Type I system
sss
as
Ksss
vs
sss
ps
eGHsKsR
esGHKsR
eGHKsR
v
2
0
1
1
0
10
1
lim)(
lim)(
0lim)(
3
2
Automatic control by meiling chen 18
1
1
)5(
10)15.0()(
5.0
1
1
)5(
10)()(
1
ssssKsGH
K
Klet
ssssKKsGH
p
P
D
Dp
5 1 02
0pk0pk0kk
k
k
3k
3k
pk
pk
pk
3g
Automatic control by meiling chen 21
Case IV : Proportional Integral derivative control
)1( ss
K
m
m
maE
+-
)(sH
)(sR
PK
sKD
sKs
KKsG D
IPc )(
1
1
)5(
10)()(
ssssK
s
KKsGH D
IpOpen loop transfer function :
sK I
Automatic control by meiling chen 22
)1)(5(
10)5.0()(
1,5.0
)1)(5(
10)(
1
1
)5(
10)()(
2
2
ssss
ssKsGH
K
K
K
Klet
ssss
sKK
KK
sK
ssssK
s
KKsGH
p
P
D
P
I
p
D
p
Ip
DI
p
Open loop transfer function :
Type II system
sse
Automatic control by meiling chen 25
Case V : phase lead control
0,)(
)()(
abbs
assGc
b a
0)(tan)(tan,)(
)()( 11
babj
ajjGc
Case VI : phase lag control
0,)(
)()(
babs
assGc
ba
0)(tan)(tan,)(
)()( 11
babj
ajjGc
Automatic control by meiling chen 26
)1( ss
K
m
m
m
aE
+-
)(sH
)(sGc)(sR
)6(
)3()(
s
ssGc
Phase lead:
1
1
)5(
10
)6(
)3()(
ssss
ssGH 5g
)3(
)6()(
s
ssGc
Phase lag:
1
1
)5(
10
)3(
)6()(
ssss
ssGH 5g