E2 Control

Industrial Electrical Engineering and Automation

Elenergiteknik

1

Control

Industrial Electrical Engineering and Automation

Elenergiteknik

2

Position control

position

reference

position

control

speed
reference

speed

control

current

reference

current

control

Motor

speed

current

position

+


-

equip

acc/

torq/

curr

motor

voltage

+


-

+


-

Industrial Electrical Engineering and Automation

Elenergiteknik

3

Speed control

1
1


s
T
s
s
J

1
speed
reference
ω
*

current
loop



inertia



Speed
ω

+


-

K
w

torque
reference


-

+

load

torque

torque

s
w
s
w
s
s
w
s
w
L
T
J
k
T
J
k
T
T
s
k
T
J
s
k
J
s
J
T
T
dt
d
T
T
dt
d
J





























4
2
1
2
1
1
1
2
2
*




Torque
reference

Industrial Electrical Engineering and Automation

Elenergiteknik

4

DC
-
motor

m

0

a

x
y
a
i
f
i
Armature winding
Compensation widning
Commutation pole
Field winding
Industrial Electrical Engineering and Automation

Elenergiteknik

5

Detailed picture of the rotor

a

i

a

i

Industrial Electrical Engineering and Automation

Elenergiteknik

6

Current control of DC
-
motor

Current
reference

current
control

voltage

Mod

4QC

Motor

Current

+


-

torque
reference

m

1
Industrial Electrical Engineering and Automation

Elenergiteknik

7

Current control of DC
-
motor, cont’d





















m
r
a
a
i
a
m
r
s
a
a
a
a
m
r
a
a
a
a
a
a
a
a
a
k
k
i
k
i
k
k
u
k
T
k
i
k
i
L
k
u
dt
di
L
R
e
dt
di
L
i
R
u




























*
*
*
1
0
Industrial Electrical Engineering and Automation

Elenergiteknik

8

Puls width modulation

Carrier wave

voltage

reference

Output voltage

0

0.005

0.01

0.015

0

20

40

60

80

100

0

0.005

0.01

0.015

0

20

40

60

80

100



sa



0



va



+50



-

50



Industrial Electrical Engineering and Automation

Elenergiteknik

9

4Q PWM

•
1 voltage, 2 potentials

•
infinite number of combainations of
va* and vb* for u=va
-
vb.

•
Set va*=u*/2 och vb*=
-
u*/2


i

L, R

+ e
-

id

sa

+ u
-

sb

0

va

vb

+Ud/2

-
Ud/2

Industrial Electrical Engineering and Automation

Elenergiteknik

10

0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
-200
0
200
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
-200
0
200
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
-200
0
200
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0
200
400
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
-5
0
5
varef
vbref
va
vb
ua
ia
Control of a 4
-
kv. DC conv:

•
v
a
*=u*/2

•
v
b
*=
-
u*/2

•
Example:

–
Udc=300 V

–
u*=100 V

Industrial Electrical Engineering and Automation

Elenergiteknik

11

Permanent magnetized synchrounous
motor, PMSM

Industrial Electrical Engineering and Automation

Elenergiteknik

12

3
-
phase PMSM

a+
a+
a-
a-
b+
b+
b-
b-
c+
c+
c-
c-
Industrial Electrical Engineering and Automation

Elenergiteknik

13

Vektor control of a PMSM
-
motor

i
sx
-
reg

i
sx
*

i
sy
*

i
sx
-
reg

u
sx
*

u
sy
*

e
+j
Θ
r




2
Φ
/
3
Φ





Mod





3fas
-

omr





2
Φ
/
3
Φ





e
-
j
Θ
r




Motor

+


-

+


-

i
sa,b,c

u
sa,b,c

u
s
α
,
β

Industrial Electrical Engineering and Automation

Elenergiteknik

14

Convertion of current from


stator to rotor coordinates


















































t
i
t
i
i
t
i
t
i
i
t
i
t
i
j
t
i
t
i
e
i
e
i
i
s
s
sy
s
s
sx
s
s
s
s
t
j
s
j
s
xy
s
r
r




















sin
cos
sin
cos
sin
cos
sin
cos



Industrial Electrical Engineering and Automation

Elenergiteknik

15

Current control PMSM







m
sy
sx
m
sx
s
s
sy
sy
s
sy
s
sy
sy
s
s
sx
sx
s
sx
s
sx
m
s
m
s
s
s
s
s
s
s
s
s
T
i
and
i
where
i
L
T
i
i
L
i
R
u
i
L
T
i
i
L
i
R
u
T
i
j
i
L
j
T
i
i
L
i
R
u









*
*
*
*
*
*
*
*
*
*
*
*
*
0













































Industrial Electrical Engineering and Automation

Elenergiteknik

16

Convertion of stator voltage from


rotor to stator coordinates
















































t
u
t
u
u
t
u
t
u
u
t
u
t
u
j
t
u
t
u
e
u
e
u
u
sx
sy
s
sy
sx
s
sx
sy
sy
sx
t
j
xy
s
j
xy
s
s
r
r













sin
cos
sin
cos
sin
cos
sin
cos



Industrial Electrical Engineering and Automation

Elenergiteknik

17

Conversion from two phases
αβ
-
frame
to three phases abc
-
frame











































s
s
c
s
s
b
s
a
u
u
u
u
u
u
u
u
2
3
2
1
3
2
2
3
2
1
3
2
3
2
m



x

y





a

u

b

u

c

u

m



x

y







u



u

s

u

s

u

r



Industrial Electrical Engineering and Automation

Elenergiteknik

18

The 3
-
phase voltage

-400
-300
-200
-100
0
100
200
300
400
0
50
100
150
200
250
300
350
400
Industrial Electrical Engineering and Automation

Elenergiteknik

19

Symmetrized motor voltage

-800
-600
-400
-200
0
200
400
600
800
0
0,002
0,004
0,006
0,008
0,01
0,012
0,014
0,016
0,018
0,02
Industrial Electrical Engineering and Automation

Elenergiteknik

20

Control of 3
-
phase converter

•
Symmetration of
references

0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
-500
0
500
ua
r
ef & tri
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
-500
0
500
va
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
-500
0
500
vo
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
-500
0
500
ua
varef
tri
va
v0
u=va-v0
grundton 50 Hz
2
min
max
*
*
*
*
*
*








z
z
c
c
z
b
b
z
a
a
u
u
u
v
u
u
v
u
u
v
Industrial Electrical Engineering and Automation

Elenergiteknik

21

3
-
phase output voltage as vector

)
(
2
1
2
3
3
2
3
4
3
2
c
b
a
j
c
j
b
a
u
u
j
u
e
u
e
u
u
ju
u
u























)
100
(
u


)
110
(
u


)
010
(
u


)
011
(
u


)
001
(
u


)
101
(
u


)
000
(
u


)
111
(
u



id

sa

0

va

+Ud/2

-
Ud/2

sb

vb

sc

vc

+
uab

-

+ ubc

-

-

uca
+

+


ua


-

+


ub


-

+


uc


-

vo