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Brushless DC (BLDC) Motor
Control of Servo Motors
Structure of DC motor Structure of BLDC motor
Direaxi
Field Coil NS
a
f
aField
AmartureAmarture Coil
Commutator Brush a
Stator
b c
Permanent-Magnet
NS d-axis
Rotor
Both the brush and commutator in the DC motor are removed.
Flux by field winding current Permanent-Magnet
Stator Rotor
The direction of armature current is changed by Brush & Commutator by power semiconductor switch according to the position of flux
Rotor Stator Stator : 3-phase winding
Rotor : Permanent-Magnet : uniform flux
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Detection method of rotor flux position
Control of Servo Motors
- The Hall voltage is proportional to flux
- The polarity of hall voltage Direction of flux
- can not detect precisely the flux
- Simple circuit & low cost
Detection method of rotor flux position
Hall device
MR (magnetoresistor) sensor LED and Photo transistor
(1) Hall device
Hall effect
B
IC
VH
ICd
Output voltage of Hall deviceBBI
d
KV CH
Armature winding, Permanent-Magnet, Hall device at BLDC
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Detection method of rotor flux position
Control of Servo Motors
(2) MR (magnetoresistor) sensor
- Resistance Flux- can detect precisely the flux
(3) LED and Photo transistor
- The precision problem for measuring the flux
- Using LED, Photo transistor and shutter
-One PT is in in on state
- Two PTs are in off state
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Three Phase Unipolar-Driven BLDC motor using LED and Photo transistor
Control of Servo Motors
Tr1 Tr2 Tr3
W1 W2 W3EB
I BI 1 I 2 I 3
Simplified Driver Circuit
* Conduction period for each winding : 120.
(1) PT1 ON state
Tr1 ONstate W1 is exciting (I1) P1 (S pole) Rotor rotates
(2) PT2 ON stateTr2 ONstate W2 is exciting (I2) P2 (S pole) Rotor rotates
(3) PT3 ON state
Tr3 ONstate W3 is exciting (I3) P3 (S pole) Rotor rotates
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Three Phase Bipolar-Driven BLDC motorusing LED and Photo transistor
Control of Servo Motors
Tr1 Tr3 Tr5
Tr4 Tr6 Tr2
a
b
c
a
bc
E
ia
ib
ic
PT4
PT1
PT2PT
PT3PT5
6
Shutter with six PTs
Six switching devices State of six phototransistorsPT1 Tr1, PT2 Tr2, PT3 Tr3, PT4 Tr4, PT5 Tr5, PT6 Tr6
Three switching device are conducting with rotor (flux) position.
Control of drive circuit of BLDC
[1] Forward rotation
[2] Reverse rotation
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Three Phase Bipolar-Driven BLDC motorusing LED and Photo transistor
Control of Servo Motors
[1] Control method at forward rotation
(1) Sector I
- Phototransistors PT1, PT2, PT6 are in ON state Transistor Tr1, Tr2, Tr6 are conducting
NS
PT4
PT1
PT2PT
PT3PT5
6
Driving circuit when Tr1, Tr2, Tr6 are conducting
Tr1 Tr3 Tr5
Tr4 Tr6 Tr2
a
b
c
a
b (0)c (0)
E
(E)
MMF
N
S
NS
Stator current of BLDC motor :
PcbPa IiiIi ,0,
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Three Phase Bipolar-Driven BLDC motorusing LED and Photo transistor
Control of Servo Motors
(2) Sector 2
- Phototransistors PT1, PT5, PT6 are in ON state Transistor Tr1, Tr5, Tr6 are conducting
Driving circuit when Tr1, Tr5, Tr6 are conducting
Stator current of BLDC motor :
N
S
a
b (0)c (E)
(E)
N
S
Tr1 Tr3 Tr5
Tr4 Tr6 Tr2
a
b
c
a
b (0)c (E)
E
(E)
MMF
N
S
0,, cPbPa iIiIi
PT4
PT1
PT2PT
PT3PT5
6
C l f S M
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Three Phase Bipolar-Driven BLDC motorusing LED and Photo transistor
Control of Servo Motors
(3) Sector 3
- Phototransistors PT4, PT5, PT6 are in ON state Transistor Tr4, Tr5, Tr6 are conducting
Driving circuit when Tr4, Tr5, Tr6 are conducting
Stator current of BLDC motor :
N
S
a
b (0)c (E)
(0)
N
S
PT4
PT1
PT2PT
PT3PT5
6
Tr1 Tr3 Tr5
Tr4 Tr6 Tr2
a
bc
a
b (0)c (E)
E
(0)
Flux
N
S
PcPba IiIii ,,0
C t l f S M t
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Three Phase Bipolar-Driven BLDC motorusing LED and Photo transistor
Control of Servo Motors
(4) Sector 4
- Phototransistors PT4, PT5, PT3 are in ON state Transistor Tr4, Tr5, Tr3 are conducting
Stator current of BLDC motor :
N S
a
b (E) c (E)
(0)
N
S
PcbPa IiiIi ,0,
(5) Sector 5
- PT4, PT2, PT3 are in ON state Transistor Tr4, Tr2, Tr3 are conducting
N
S
a
b (E) c (0)
(0)
N
S
Stator current of BLDC motor :
0,, cPbPa iIiIi
Control of Servo Motors
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Three Phase Bipolar-Driven BLDC motorusing LED and Photo transistor
Control of Servo Motors
(6) Sector 6
Stator current of BLDC motor :
- PT1, PT2, PT3 are in ON state Transistor Tr1, Tr2, Tr3 are conducting
N
S
a
b (E) c (0)
(E)
N
S
PcPba IiIii ,,0
Table. Operating condition of switching devices on each sector (Forward rotation)
0001116
0011105
0111004
1110003
1100012
1000111
Tr6Tr5Tr4Tr3Tr2Tr1
Switching
device
Sector
Control of Servo Motors
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Three Phase Bipolar-Driven BLDC motor using LED and Photo transistor
Control of Servo Motors
[2] Control method at Reverse rotation
(1) Sector 1
Driving circuit when Tr4, Tr5, Tr3 are conducting
* Phototransistor is in ON state Matched transistor is not conducting- Phototransistors PT1, PT2, PT6 are in ON state
Transistor Tr1, Tr2, Tr6 are not conducting Transistor Tr4, Tr5, Tr3 are conducting
NS
PT4
PT1
PT2PT
PT3PT5
6
Tr1 Tr3 Tr5
Tr4 Tr6 Tr2
a
b
c
a
b (E)c (E)
E
(0)
Flux
S
N
NS
Control of Servo Motors
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Three Phase Bipolar-Driven BLDC motor using LED and Photo transistor
Control of Servo Motors
(2) Sector 2
- Phototransistors PT1, PT2, PT3 are in ON state
Transistor Tr1, Tr2, Tr3 are not conducting Transistor Tr4, Tr5, Tr6 are conductingN
S
a
b (0)c (E)
(0)
N
S
PT4
PT1
PT2PT
PT3PT5
6
(3) Sector 3
- Phototransistors PT4, PT2, PT3 are in ON state
Transistor Tr1, Tr5, Tr6 are conducting
a
b (0)c (E)
(E)
N
S
(4) Sector 4
- Phototransistors PT4, PT5, PT3 are in ON state
Transistor Tr1, Tr2, Tr6 are conducting
a
b (0) c (0)
(E)
N
S
Control of Servo Motors
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Three Phase Bipolar-Driven BLDC motor using LED and Photo transistor
Control of Servo Motors
(5) Sector 5
- Phototransistors PT4, PT5, PT6 are in ON state
Transistor Tr1, Tr2, Tr3 are conducting
(6) Sector 6
- Phototransistors PT1, PT5, PT6 are in ON stat
Transistor Tr4, Tr2, Tr3 are conductinga
b (E)c (0)
(E)
N
S
a
b (E)c (0)
(0)
N
S
Table. Operating condition of switching devices on each sector (Reverse rotation)
1110006
1100015
1000114
0001113
0011102
0111001
Tr6Tr5Tr4Tr3Tr2Tr1
Switching
device
Sector
Control of Servo Motors
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Torque and emf equations
f
- Two-pole with arc of 180
- Uniform flux
-
The center of N-pole : d-axis ( = 0)-Turn number of a1-A1 coil : N1
Flux linkage at coil a1-A1 with N1
ldrBN 0 11max1 )( (B() = Bg constant)lrBN g 11max1
- 1=1max at =0 1 1=0 at =/2 1 < 0 ar > /2
Flux linkage equation
max11)2/(
1)(
(0 < )
2
1max
1max-
Stator
a1a2
NSd-axi
A 1
A 2
r1
r
l
= 0
=
1
Control of Servo Motors
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Torque and emf equations
f
[V]
emf equation at winding a1-A1 (emf == voltage induced by flux)
d
d
edt
d
d
d
dt
de 111
1
eglrBNe 111 2
- Two pole, Three phase, Two slots(winding) at each phase
- Space interval of each slot =0
0
30)(2)(2)(3
360
slotonepairPhase
Control of Servo Motors
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Torque and emf equations
Flux density, Flux linkage at a1-A1 & a2-A2, emf of both windings, Total emf
- emf : Trapezoidal shape,
The actual flat top : 120 due to fringing filed
Control of Servo Motors
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Torque and emf equations
Three-phase current, emf, torque
- emf : Trapezoidal shape,
The actual flat top : 120 due to fringing filed
- Ideal three phase armature current and emf
- Armature current : Rectangular shape,
Flat top = 120 at half period
- emf : Trapezoidal shape ,Flat top = 120, In phase to current
180o
360o
t
ia
Ip
Ip-
180o
360o
t
eaEp
Ep-
180o
360o
t
ib
180o
360o
teb
180o
360o
t
ic
180o
360o
t
ec
180o
360o
t
Te
Control of Servo Motors
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Torque and emf equations
Torque equation for three phase BLDC motor
Output power
ccbbaaeieieieP
Torque
e
ccbbaa
e
ee
ieieiePT
The armature current is in phase with the emf at the period of flat top of emf (60)each phase
0,, cPbPa iIiIi 0,, cPbPa eEeEe
e
PP
e
PPPP
e
ccbbaa
e
ee
IEIEIEieieiePT
20))((
Period I (30t < 90),
Period I (90t < 150)
PcbPa IiiIi ,0, PcbPa EeeEe ,0,
,
e
PP
e
PPPP
e
ccbbaa
e
ee
IEIEIEieieiePT
2))((0
Control of Servo Motors
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Torque and emf equations
Torque is constant at overall period
Period I (150t < 210)
PcPba IiIii ,,0 PcPba EeEee ,,0
e
PP
e
PPPP
e
ccbbaa
e
ee
IEIEIEieieiePT
2))((0
Magnitude of flat-topped phase emf at one winding :egph lrBNe 12 , Nph : the number of turn
lrArea 1 gBlr 1egph rlBNe
1
2 ,
Combined emf of two phases in series : E = 2e
eegph KrlBNE
14
)4
( phNK
Torque equation
Output power
IrlBNIrlBNeITP egphegphee
1142
22
Control of Servo Motors
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Torque and emf equations
Torque equation
IKIrlBNP
T gphe
e 14
* DC Motor
Kea , ae IKT
Torque/speed characteristicsERIE
dt
dILRIV
R
KV
R
EVI
K
VT
K
R2)(
Alternative formulations for torque and emf
- Alignment torque
ddi
diLdiii
ddLT msrmsrsme )()( 11max1 2
21)2/(1)( rlBN
gm
ssgsgm
se iKirlBNilrBNd
diT 1111
44
)(
Control of Servo Motors
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Torque - Speed Characteristics Curve
Torque-Speed characteristics Curve
Te
m
V
V '
V''
V'''
Decrease
V & f
TL
Control of Servo Motors
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Voltage equation for BLDC Motor
3-Phase voltage equation (Matrix expression)
c
b
a
c
b
a
ccbca
cbbba
caaba
c
b
a
c
b
a
e
e
e
i
i
i
LLL
LLL
LLL
p
i
i
i
R
R
R
V
V
V
00
00
00
LLLL cba , MLLL cbcaab
c
b
a
c
b
a
c
b
a
c
b
a
e
e
e
i
i
i
LMM
MLM
MML
p
i
i
i
R
R
R
V
V
V
00
00
00
0 cba iii
- Assumed
- Using
c
b
a
c
b
a
c
b
a
c
b
a
e
e
e
i
i
i
ML
ML
ML
p
i
i
i
R
R
R
V
V
V
00
00
00
00
00
00
3-Phase voltage equationaaaa epiMLRiV )(
bbbb epiMLRiV )(
cccc epiMLRiV )(
Control of Servo Motors
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Torque and emf equations
Effects of inductance
180o
360o
tia
Ip
Ip-
180o
360o
t
eaEp
Ep-
180o
360o
tib
180o
360o
t
eb
180o
360o
tic
180o
360o
t
ec
180o
360o
t
Te
* Cogging torque
S d l l f BLDC M
Control of Servo Motors
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Speed control loop for BLDC Motor
ai *
i a ib ic
BLDC
ib*
ci*
Hysteresis
Controller
E
*r
r
Resolver
Signal
Processor
Transformer
r
r
r
*I
180o
360o
t
I
I-
180o
360o
t
180o
360o
t
ia*
ib*
ic*
*
*
Three-phase reference current
PI controller
))(( ** rrI
PS
KKI
Hysteresis current controller
t
ia*
HB
ia
ia* ia