Servo Motor(4)

7/30/2019 Servo Motor(4)

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PMSM (Permanent-Magnet Synchronous Motor)

Control of Servo Motors

Structure of Synchronous motor

Stator : 3-phase ac voltage are applied to 3-phase winding.

The number of turn of stator winding : sinusoidal distribution.Rotor : Rotor winding is excited : Rotor current Slip ring DC voltage source

Flux is generated by the dc current

a Stator

b

Rotor

c

Slip

Ring

DC Power

Supply

3-ACVoltage


2/18

PMSM (Permanent-Magnet Synchronous Motor)


Torque production of synchronous motor

Rotor : Flux N-S is produced by dc-excited rotor winding.

Rotor has to rotate with synchronous angular speed for generating torque

a

b c

NS

N

S

e

e

Rotating MMF axis

Magnetic axi

A rotating field of constant amplitude is produced by three-phase ac current

with synchronous angular speedSynchronous angular speed

,wheref= source frequency, P = # of pole.

ibia ic3-Phase

et

Current

P

fe

4

Voltage, current, MMF, and emf : sinusoidal waveform


3/18

Structure of PMSM


Structure of PMSM

Demerit of synchronous motor

- Slip ring, dc power supply are needed

- Rotor : dc-excited winding Heavy, large size High moment of inertia

aStator

b

Rotor

Permanent-Magnet

c

NSd-axis

Stator : 3-phase ac voltage are applied to 3-phase winding.

The number of turn of stator winding : sinusoidal distribution.

Rotor : Permanent-magnet : sinusoidal distribution of flux density

Features of BLDC motor:

- Rectangular distribution of magnetic flux in the

airgap

- Rectangular current waveform

- Concentrated stator winding

Features of PMSM :

-Sinusoidal or quasi-sinusoidal distribution

of magnetic flux in the airgap

-Sinusoidal or quasi-sinusoidal current waveform

-Quasi-sinusoidal distributed stator winding


4/18

Structure of PMSM


Features of BLDC motor:

- Rectangular distribution of magnetic flux in the airgap

- Rectangular current waveform- Concentrated stator winding

Features of PMSM :

-Sinusoidal or quasi-sinusoidal distribution of magnetic flux in the airgap

-Sinusoidal or quasi-sinusoidal current waveform

-Quasi-sinusoidal distributed stator winding

aStator

b

Rotor

Permanent-Magnet

c

NSd-axis

a

Stator

bc

Permanent-Magnet

NS d-axis

Rotor

BLDC Motor PMSM


5/18

Principle of Vector control


Torque production of DC motor

Quadrature

axis

Directaxis

Field Coil N SN

S

(MMF)

Brush

Phasor diagram for Flux and MMF

MMF ( Ia )

Torque equation

ae IKT Maximum torque

The magnetic field is controlled to be orthogonal

to the magnetic flux by Permanent-magnet like DC motor

Detecting continuously the position of magnetic flux

The magnetic field is controlled to be orthogonal

to the magnetic flux

Principle of vector control for ac machine (PMSM)

NS

N

S

e

e

Rotating MMF axis

Magnetic axis


6/18



2-axis reference frame

- The stator and rotor equations are referred to a common frame of reference

Common frame of reference(1) Stator or stationary reference frame

- non-rotating

(2) Synchronous reference frame

- d, q axis rotates with the synchronous angular velocity

2-axis Arbitrary or freely rotating reference frame

- d, q axis rotates with the angular velocity

c-axis

b-axis q-axis

d-axis

tfds

fqs

fdqs

a-axis


7/18



Complex notion of 3-phase variable

csbsas faafff2 1)3/2()3/4(2)3/2( ,, aeeaeawhere jjj

Vector notation in d-q axis variables

fefaaffejfff jcsbsasj

qsdsdqs

3

2)(

3

2 2

[1]2-axis stationary reference

- d-axis is assigned to a-phase axis.

- non-rotating

a-axis

c-axis

b-axis

ds

qs

C l f S M


8/18



- At =0, variables in stationary reference frame is derived as

d- & q-axis currents in stationary reference frame

ffaaffjfff csbsass

qs

s

ds

s

dqs

3

2)(

3

2 2

)(3

2)(

3

2 )3/2()3/2(2cs

j

bs

j

ascsbsas

s

qs

s

ds ieieiiaaiijii

])2

3

2

1()

2

3

2

1([

3

2])

3

2sin

3

2(cos)

3

2sin

3

2(cos[

3

2csbsascsbsas ijijiijiji

)](23)(

21[

32 csbscsbsas iijiii

As 0 csbsas iii ascsbs iii

)(3

1csbsas

s

qs

s

ds iijijii ass

ds ii )(3

1csbs

s

qs iii

,

,

- Magnitude of d-q axis current = Magnitude of three phase current

- Ac signals with synchronous speed

C t l f S M t


9/18



[2]2-axis synchronous rotating reference

- d-q axis is rotating with synchronous speed

At = e = et, d-&q-axis variables in synchronous rotating reference frame is derived as

)sin)(cos(3

2)(

3

2 2ee

s

qs

s

ds

js

dqs

j

csbsas

je

qs

e

ds

e

dqs jjffeffefaaffejfffeee

a-axis

c-axis

b-axis q

d

te = e

e

e

- d-&q-axis variables in synchronous rotating reference frame has dc value



10/18



Example)

- Three-phase current

)3

4cos(),

3

2cos(),cos( tIitIitIi emcsembsemas

tj

mcs

j

bs

j

asseeIieieii

2

3)3/2()3/2(

- Stator current with complex notation

d- & q-axis current in stationary reference frame

tjmtjmssqssdssdqsee eIeIijiii

23

3

2

3

2

asem

s

ds itIi cos , tIi ems

qs sin

d- & q-axis current in synchronous rotating reference frame

mtjtj

mtj

seqs

eds

edqs IeeIeijiii

eee

23

32

32

m

e

ds Ii 0e

qsi

ibia ic

i

s

ds is

qs

Ieds

Ieqs

3-Phase

at synchronus

et

et

et

Current

referenceframe

Current

referenceframe

Current

at stationary)sin(cos tjtI eem



11/18



d-,q- axises variables in a stationary reference frame Synchronous rotating reference frame

,

)sin)(cos(3

2)(

3

2 2ee

s

qs

s

ds

js

dqs

j

csbsas

je

qs

e

ds

e

dqs jjffeffefaaffejfffeee

)cossin()sincos( esqse

sdse

sqse

sds ffjff

e

s

qse

s

ds

e

ds fff sincos es

qse

s

ds

e

qs fff cossin

d-,q- axises variables in a Synchronous rotating reference frame Stationary reference frame

)sin)(cos( eee

qs

e

ds

je

dqs

s

qs

s

ds

s

dqs jjffefjfffe

e

e

qse

e

ds

s

ds fff sincos ,

e

e

qse

e

ds

s

qs fff cossin

Three-phase variables 2-axis variables stationary reference frame

cs

bs

as

s

qs

s

ds

f

f

f

f

f

2

3

2

30

2

1

2

11

3

2

2-axis variables stationary reference frame Three-phase variables

s

qs

s

ds

cs

bs

as

f

f

f

f

f

2

3

2

12

3

2

1

01



12/18

Voltage equation of PMSM


Equivalent circuit of PMSM

2-axis voltage equations in a synchronous reference frame

RsVa

Vb

Vc

ia

ib

ic

Rs

Rs

Ls

L

L

ea+ -

eb+ -

ec+ -s

s

qssedsssds iLipLRV )(

edsseqsssqs iLipLRV )(

Torque equation of PMSM

qse iKT

Phasor diagram for flux, current, and voltage

- voltage equations in a synchronous reference frame at steady state condition

differential operatorp = 0,Rs term is neglected

qsseds iLV

EiLiLV dsseedsseqs , where emf eE



13/18



Phasor diagram for flux, current, and voltage

d-axis

q-axis

E

e Ls ids

e Ls iqs-

Vs

ids

iqsis

The d-axis current is in phase with fluxd-axis current Flux component,

q-axis current Torque component- Torque of PMSM qse iKT

qsdss jiii

Stator current



14/18


f

Flux is generated by permanent-magnet Flux component of stator current ids = 0

qsqsdss jijiii

Stator current

Voltage equation of PMSM at ids = 0

qsseds iLV

EV eqs

Phasor diagram for flux, current, and voltage at ids = 0

d-axis

q-axis

E

Vsiqs is=



15/18

Characteristics of PMSM

f

Comparsion between the characteristics of PMSM and that of DC motor.

Phasor of flux and armature current

MMF ( Ia )

DC Motor

d-axis

q-axis

E

i qs i s=

PMSM

The flux position is detected. Phase angle of

stator is controlled according to flux position

The MMF is orthogonal to Flux by operation

of both the brush and commutates

Flux is generated by permanent-magnetFlux is generated by field winding current

q-axis stator currentArmature current

PMSMDC Motor



16/18

Frequency control of PMSM


Pfe /4

fEV es 2

f

Vs

Frequency of ac source current is controlled

The synchronous speed of rotating field produced by three-phase ac current is changed

Rotor speed (= synchronous speed) is controlled

-In order to keep the flux constant, the ratio between voltage and frequency is constant

- Neglecting impedance voltage drop in voltage equation

- (Vs/f) control at motor speed < base speed (rated speed)

Flux = constant Speed voltage Torque = constant

Both the frequency and voltage are controlled



17/18


Voltage, flux, torque, power versus speed

Constant Torque Region Constant Power Region

Power

Torque

b

Vs

r

(1) Motor speed < base speed

Flux = constant Speed voltage Torque = constant Power

Constant torque region

(2) At motor speed = base speed voltage = rated voltage(3) Motor speed > base speed

Speed voltage is limited to rated value Flux Torque

Power = constant Constant power region

Flux weaking control



18/18

Flux weaking control of PMSM

Flux weaking control

- Flux should be decreased when the motor speed is controlled over a rated speed.

- d-axis current is applied in opposite direction for demagnetizing the permanent-magnet

d-axis

q-axis

E

e Lsidse Ls iqs-

Vs

ids

iqsis

- Magnitude of stator current22

qsdss iii

* Speed d-axis current stator current Limiting maximum stator current

demagnetizing the permanent-magnet

Date post:	14-Apr-2018
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Servo Motor(4)

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