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Elenergiteknik 1

Control

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Elenergiteknik 2

Position control

position

reference positio

ncontrol

speed referenc

e speedcontro

l

currentreference

current

control

Motor

speed

current

position

+ -

equip

acc/torq/curr

motorvoltage

+ -

+ -

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Elenergiteknik 3

Speed control

11

sTs

sJ 1

speed referenc

e ω* current loop

inertia Speed ω

+ -

Kw

torque referenc

e -+

loadtorque

torque

sw

s

w

ss

w

s

w

L

TJk

TJk

TTs

kTJs

kJs

JTT

dtdTT

dtdJ

4

21

21

1

1

2

2*

Torque referenc

e

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Elenergiteknik 4

DC-motor

m

0a

x

y

ai

fi

A rm atu re w in d in g

C om pen sation w idn in g

C om m u tation po le

F ield w in d in g

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Elenergiteknik 5

Detailed picture of the rotor

ai a

i

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Elenergiteknik 6

Current control of DC-motor

Current referenc

e current control

voltage

Mod

4QC Motor

Current

+ -

torque referenc

e

m1

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Elenergiteknik 7

Current control of DC-motor, cont’d

mraaia

mrs

aaaa

mra

aaaa

aaaa

kkikikku

kT

kikiLku

dtdiLRe

dtdiLiRu

**

* 1

0

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Elenergiteknik 8

Puls width modulation

Carrier wave voltage reference

Output voltage0 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

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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

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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 0.010

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:• va*=u*/2• vb*=-u*/2• Example:

– Udc=300 V– u*=100 V

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Elenergiteknik 11

Permanent magnetized synchrounous motor, PMSM

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Elenergiteknik 12

3-phase PMSM

a+ a+

a- a-b+

b+

b -b -

c+c+

c-c-

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Elenergiteknik 13

Vektor control of a PMSM-motor

isx-regisx

*

isy*

isx-reg

usx*

usy*

e+jΘr 2Φ/3Φ Mod 3fas-

omr

2Φ/3Φ e-jΘr

Motor

+ -

+ -

isa,b,c

usa,b,cusα,β

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Elenergiteknik 14

Convertion of current from stator to rotor coordinates

titii

titii

titijtiti

eieii

sssy

sssx

ssss

tjs

js

xys

rr

sincos

sincos

sincossincos

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Elenergiteknik 15

Current control PMSM

msy

sx

msxss

sysyssyssy

syss

sxsxssxssx

ms

msss

ssssss

Ti

andi

where

iLT

iiLiRu

iLT

iiLiRu

Ti

jiLjT

iiLiRu

**

*

**

**

**

**

**

0

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Elenergiteknik 16

Convertion of stator voltage from

rotor to stator coordinates

tutuu

tutuu

tutujtutu

eueuu

sxsys

sysxs

sxsysysx

tjxys

jxyss

rr

sincos

sincos

sincossincos

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Elenergiteknik 17

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

ssc

ssb

sa

uuu

uuu

uu

23

21

32

23

21

32

32

m

x

y

au

bu

cu

m

x

y

u

usu

su

r

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Elenergiteknik 18

The 3-phase voltage

-400

-300

-200

-100

0

100

200

300

400

0 50 100 150 200 250 300 350 400

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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

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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

uaref & tri

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-500

0

500va

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-500

0

500vo

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-500

0

500ua

varef tri

va

v0

u=va-v0 grundton 50 Hz

2minmax

**

**

**

z

zcc

zbb

zaa

u

uuvuuvuuv

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Elenergiteknik 21

3-phase output voltage as vector

)(21

23

32 3

43

2

cba

jc

jba

uuju

eueuujuuu

)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