servo motor(3)

7/30/2019 Servo Motor(3)

1/24

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


2/24

Detection method of rotor flux position


- 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


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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(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


4/24

Three Phase Unipolar-Driven BLDC motor using LED and Photo transistor


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


5/24

Three Phase Bipolar-Driven BLDC motorusing LED and Photo transistor


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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[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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(2) Sector 2




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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(3) Sector 3




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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(4) Sector 4



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


0,, cPbPa iIiIi



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(6) Sector 6


- 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



11/24

Three Phase Bipolar-Driven BLDC motor using LED and Photo transistor


[2] Control method at Reverse rotation

(1) Sector 1


* 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



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(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


Transistor Tr1, Tr5, Tr6 are conducting

a

b (0)c (E)

(E)

N

S

(4) Sector 4



a

b (0) c (0)

(E)

N

S



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(5) Sector 5



(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



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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



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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



16/24


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



17/24


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



18/24


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



19/24


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



20/24


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

)(



21/24

Torque - Speed Characteristics Curve

Torque-Speed characteristics Curve

Te

m

V

V '

V''

V'''

Decrease

V & f

TL



22/24

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 )(



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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



24/24

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

servo motor(3)

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