Servo Motor(4)
Transcript of 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
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PMSM (Permanent-Magnet Synchronous Motor)
Control of Servo Motors
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
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Structure of PMSM
Control of Servo Motors
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
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Structure of PMSM
Control of Servo Motors
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
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Principle of Vector control
Control of Servo Motors
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
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Principle of Vector control
Control of Servo Motors
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
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Principle of Vector control
Control of Servo Motors
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
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Principle of Vector control
Control of Servo Motors
- 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
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Principle of Vector control
Control of Servo Motors
[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
Control of Servo Motors
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Principle of Vector control
Control of Servo Motors
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
Control of Servo Motors
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Principle of Vector control
Control of Servo Motors
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
Control of Servo Motors
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Voltage equation of PMSM
Control of Servo Motors
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
Control of Servo Motors
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Voltage equation of PMSM
Control of Servo Motors
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
Control of Servo Motors
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Voltage equation of PMSM
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=
Control of Servo Motors
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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
Control of Servo Motors
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Frequency control of PMSM
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
Control of Servo Motors
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Frequency control of PMSM
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
Control of Servo Motors
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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