Diplwmatikh Gia Kinhthres

&

: ,

,

MAKO ERBIN

: . ...

, 2011

.

&

: ,

,

: . ...

xx 2011.

() () () ................................... ................................... ................................... . . ... ... ...

, 2011

() ...................................

...

Copyright . , 2011.

. All rights reserved.

, , , . , , , . .

.

, , . , .

, . . .

, , , . :

.

Abstract The control of electric motion is necessary in modern times for saving energy,

increasing production while reducing costs and generally improves the quality of life. In the evolution of control systems of electric motion and especially the wide spread in all phases of production, processing and distribution of industrial products led to the rapid development of power electronics and further development of digital technology.

The need for high quality torque control, speed and position of the electric motion led to the development of servomotors systems that achieve controlled dynamic response and good stability in order to reject disturbances. This kind of control requires proper of the action and interaction of all components to achieve the desired result. This corresponds to very good knowledge of control techniques and even more comprehensive understanding of the operation of electrical machines and torque production methods.

The purpose of this diploma thesis is to analyze the several construction types of engines that are mostly used in servomotor systems and to study the technique of vector control, which leads to their precise, reliable and effective control. Keywords:

.

1 ....................................................... - 1 -

1.1 - ......................................- 1 -

1.2 .......................................................................................................- 6 -

1.2.1 - - 6 -

1.2.2 ( PM dc-commutator motors)- 7 -

1.2.3 () .................................................................- 7 -

1.2.4 ...............................................................- 9 -

1.2.5 ..................................................................- 10 -

1.3 ............................................................- 11 -

1.3.1 ......................................- 11 -

1.3.2 ..........................- 14 -

1.4 .. - 21 -

1.4.1 ...............................- 21 -

1.4.2 / ...........................- 24 -

1.4.3 ..................................................- 26 -

1.5 .....................................................................................................- 26 -

2 .......................................... - 29 -

2.1 ...................................................................................................................- 29 -

2.2 .......................- 30 -

2.3 ........................................................................................................- 31 -

2.3.1 ..............- 32 -

2.3.2 - 37 -

2.3.3 .- 41 -

2.3.4 ..................................................................................- 46 -

2.3.5 ....- 51 -

2.4 ( commutator DC-PM machines) .........................................................................................................................- 59 -

2.5 .......................................................- 61 -

2.5.1 (SynRM) .............................................................- 61 -

2.5.2 (SRM).....................- 65 -

2.6 ...............................................................- 68 -

2.6.1 (squarewave PM trapezoidal PM brushless dc machine) ..........................................................- 68 -

2.6.2 (sinewave PM brushless ac machine) - 69 -

3 ........................................................... - 70 -

3.1 ...................................................................................................................- 70 -

3.2 ........................................................................- 71 -

3.3 ................................................................................................................- 75 -

3.4 ...............................................................................................................- 83 -

3.5 ........................................................................................- 86 -

3.6 .............................................................................................- 89 -

3.7 () - 92 -

3.8 ........................................................- 96 -

3.9 .........- 97 -

3.10 .........................................- 99 -

3.11 ............- 102 -

3.11.1 ..........................................................- 102 -

3.11.2 ...............................................- 102 -

3.11.3 ................- 110 -

ii

iii

4 & ............................................... - 111 -

4.1 ...............................................................................- 111 -

4.2 ....................................................................................................- 115 -

5 .............................................................................................................. - 117 -

1

1.1 -

.

:

1) (..

),

2) (..

, , ,

)

3) (..

)

(drives) .

,

.

- 1 -

, .

:

1) ( ),

( )

2) ( ,

, ,

)

3) (

,

. ,

,

,

. ,

(

)

(servo system) .

.

. ,

.

. ,

.

,

.

:

1) -

.

- 2 -

. ,

(permanent

magnet dc-communicator motors)

universal (

),

.

2) .

.

3) .

(permanent magnet synchronous motors)

(reluctance motors).

(- -

)

.

4) .

.

(stepper motors), (hysteresis motors)

.

1.1

1 2 brushless

.

,

( )

( ).

brushless . ,

-

.

brushless,

.

- 3 -

1.1 brushless

,

.

(PM)

2 :

1) (SPM, surface PM

motors).

(

- 4 -

brushless dc motors). ,

. ,

,

.

2) (IPM, interior PM

motors).

.

:

(SRM, switched

reluctance motors). brushless,

.

.

,

.

. ,

.

(stepper motors)

, (linear motors),

(axial flux motors), (hysteresis motors) .

brushless

.

, ,

. ,

.

- 5 -

1.2

1.2

.

- brushless

,

.

1.2

.

1.2.1 -

,

, .

( choppers)

,

.

,

- 6 -

. ,

,

,

ad-ac .

,

brushless

- ,

.

.

1.2.2 ( PM dc-commutator

motors)

,

.

.

, , ,

.

. ,

.

1.2.3 ()

:

.

brushless,

( ).

( V/f)

- 7 -

(inverter).

, ,

. ,

(power converter) ,

.

, ()

(

).

,

.

,

(vector control , field-oriented control).

.

.

.

,

, brushless

,

.

brushless ,

. ,

V/f .

.

- 8 -

1.2.4

. , ,

( ) .

( ) . ,

( )

.

( ),

.

,

.

(brushless PM ac synchronous motors sineware PM brushless motors),

. ,

(square-wavw PM brushless motors)

,

, brushless dc

.

(surface type) (interior

type).

.

,

.

,

.

, ,

.

- 9 -

.

. ,

( )

.

1.2.5

. ()

.

,

. ,

.

,

.

:

(synchronous

reluctance motors) ,

, (switched reluctance

motors), .

. ,

,

. ,

,

( 20.000 ).

. ,

.

- 10 -

1.3

1.3

.

1.3

(command signals) (reference

signals) (feedback signals)

(power converter) .

,

.

.

1.3.1

1.4

.

.

.

- 11 -

1.4

: () ()

1.4. (-

)

0

(rectifier),

.

1.5 (ac-dc )

1.5

.

, .

,

, .

.

,

,

( 1.6.) ac-dc (

1.6.).

, 1.6.

. 1.6.

.

- 13 -

1.6 Ac-dc

: ()

()

1.3.2

1.7

(, ).

( ) . ,

( ),

.

1.7

.

- 14 -

.

:

(1) - (rectifier-inverter)

(2)

1.3.2.1 -

( 1.8)

1.8 -

:

() (voltage source)

() (current source),

. ,

:

() ,

() ,

() ,

- 15 -

,

,

- ,

. 1.9

-

.

.

1.9

1.10 PWM

.

,

- 16 -

.

(Pulse Width Modulation, PWD).

,

. ,

, MOSFRTs IGBTs.

PWM

Vc ( 5 10 kHz)

Vr

( 1.10).

Vr Vc ,

.

.

Vr ,

, Vr

.

1.11

1.11. ,

. ,

Idc ,

,

1.12..

, .

- 17 -

, .

1.12 () ()

,

(hysteresis band current control inverter).

PWM ,

(

1.9). 1.13 PWM

,

. , PWM

.

- 18 -

1.13 PWM

1.3.2.2

dc ( 1.14).

-

( )

. ,

.

1.14

,

(step-down cycloconverter),

(step-up

- 19 -

cycloconverter).

,

.

.

,

1.15..

1.15 () , ()-()

, ()

.

- 20 -

1.15.-

. 1.15.

fout = fin / n, n

.

1.15.

1.15.,

. 1.15.

fin . ,

fout = 3 fin .

1.4

,

.

.

: ,

, ,

, , ,

,

( ).

: ,

.

1.4.1

()

().

- 21 -

,

, , . ,

, ( Joule

)

.

.

1.4.1.1

,

,

)1.1(PP

Plossin

outm +=

,

)2.1(PPP

Pconvlossin

outm ++=

Pout ( ), Ploss

Pconv .

.

(r = b)

(r = max)

,

.

b .

( ). ,

,

(

).

1.4.1.2 [kW/Nm]

. ,

- 22 -

,

.

. ,

. ,

.

1.4.1.3 ( ) [Nm/m3 Nm/Kg]

(torque density)

(power density)

. ,

.

,

, , ,

.

1.4.1.4 [kW/kVA]

(power factor, PF)

in

in

SPPF = (1.3)

Pin Sin ,

(rms) Vs

Is.

.

,

cos3

==SS

in

IVPPF (1.4)

- 23 -

,

-

. ,

.

Fourier .

1.4.2 /

1.4.2.1 [rad/sec2]

Tpeak J

/

/

JT

a peak=max (1.5)

, , -

/.

b,

Tpeak (

),

peak

bbaccel T

Jpa

pt ==max

(1.6)

p . taccel

.

,

,

.

1.4.2.2

tpeak

, Tpeak.

1-5 msec.

,

,

- 24 -

.

.

1.4.2.3

. pulse/Tnom

, .

, pulse/Tnom .

1.4.2.4

(max/b)

b

( ).

( )

( ).

.

,

. max/b 2 3

3 4 .

,

.

1.4.2.5 ,

,

( ). ,

,

,

.

- 25 -

1.4.2.6

.

.

.

1.4.2.7

,

.

.

1.4.3

. :

a) (, , ,

, .)

b)

c)

( )

1.5

servus .

. ,

.

, Le-Servomoteur Farcot

1868

. 1898

- 26 -

H. Calendar

1908 E. Sperry .

, , ,

,

, . ,

.

( ,

, ).

(vector control)

,

. ,

( )

.

,

. ,

.

,

( 20.000 rpm),

. ,

.

,

. ,

.

V/f, .

. , ,

, .

,

- 27 -

brushless

.

- 28 -

2

2.1

,

.

, ,

, , ,

.

.

brushless

brushless ( ) - (

).

.

,

- 29 -

, ,

.

2.2

,

. brushless ()

(PM synchronous machines)

. (PM dc-commutator

machines) ,

.

(

, )

, .

(commutation).

,

- ,

.

( ,

). ,

,

.

.

brushless dc.

. ,

-

. brushless

brushless dc brushless ac

- 30 -

.

brushless , brushless dc

, brushless ac

.

, ,

, .

. ,

. , ,

.

:

a) ,

b)

,

( ,

,

).

( 80-

100 kW). (

1 MW),

.

2.3

.

- 31 -

. ,

,

. ,

,

.

2.1

.

2.1 .

2.3.1

2.3.1.1 (interior-rotor PMSM)

,

.

.

.

.

- 32 -

/

.

. ,

,

.

(

,

),

.

2.2

: () ()

2.3 8- : ()

()

- 33 -

2.2

.

,

. 2.3 8-

.

cogging.

(

) .

,

.

,

( )

(

). , ,

cogging.

. ,

, cogging

- . , cogging

.

cogging

.

(torque

ripple). ,

.

cogging . 1-2%

. cogging

. ,

.

- 34 -

2.4..

.

2.4. .

2.4 cogging : ()

, () , ()

, ()

cogging ,

( 2.4.).

- 35 -

2.4.,

- ( s). cogging

.

,

.

2.3.1.2 (exterior-rotor PMSM)

,

.

. ,

.

.

2.5 : () , ()

2.5

.

, ,

.

- 36 -

2.6 : ()

, ()

.

() .. ( 2.6.),

( 2.6.). ,

.

(

).

2.3.2

2.3.2.1 (distributed stator

winding PMSM)

(2.3.1).

.

2.3.2.2 (concentrated stator

winding PMSM)

,

.

- 37 -

, ( 2.7.)

( 2.7.)

2.7 : ()

, ()

2.8

2.8

.

(stepper motors).

( 2.9). ,

- 38 -

.

. ,

.

2.9 : () , ()

.

.

( 2.10) .

,

. ,

,

.

.

( 2.11.)

( 2.11).

.

- 39 -

2.10 : () , ()

- 40 -

2.11 : ()

, ()

2.3.3

2.3.3.1 (radial flux PMSM)

,

.

- 41 -

D ( 2.12.).

2.3.3.2 (axial flux PMSM disk type PMSM)

,

( 2.12.).

Do Di .

2.12 : () , ()

2.13 : ()

, ()

- 42 -

O .

,

( ).

, .

( )

(

). 2.13

.

,

.

,

.

,

.

( 2.14)

.

( 2.14.)

( 2.14.)

2.14 : () , ()

, ()

.

- 43 -

, .

,

.

(

)

. ,

cogging, ,

. ,

.

2.15 ()

, () ( )

- 44 -

,

.

.

, , (

).

(

2.15.).

.

(wheel motors). 2.15.

.

,

.

( , differential

operation)

.

-

( coreless ironless axial

flux PMSM) cogging.

,

.

,

, brushless 2.16.

.

- 45 -

2.16 brushless

2.3.4

2.3.4.1 (linear PMSM)

, ()

.

( 2.17.) ,

( 2.17.).

2.17

: () , () .

- 46 -

, (

), ( ).

,

( ).

2.17.1 2.17. ,

2.18. 2.18.

(

).

2.18 :

() , ()

2.19 : ()

, ()

- 47 -

2.19

(

2.17.) 2.20.

2.17.. ,

. ,

,

.

2.20 : () , ()

- 48 -

, ,

( 2.10.).

, , ,

, , ,

.

,

(electromagnetic levitation system).

2.21. -

,

.

.

, 500km/h,

, ,

, . ,

,

.

2.21

- 49 -

2.3.4.2 (slotless PMSM)

.

( 2.22).

2.22

2.23

: () , () , ()

- 50 -

. ,

.

( 2.22) ( 2.23).

(torus-slotless PMSM) .

2.3.4.3 (coreless ironless PMSM)

cogging .

. , , .

,

2.16,

.

2.3.5

.

,

.

,

ggmm ABAB = (2.1) m

g (flux

concentration factor)

g

m

AAC = (2.2)

(Bg = CBm).

- 51 -

m

g

g

m

AA

llPC = (2.3)

(2.2)

==

Cll

AA

llPC

g

m

m

g

g

m 1 (2.4)

,

.

,

rr

m BPCPCB

rec+= (2.5)

Br .

(2.1)-(2.5)

r

rg

m

g

m

g BCl

ll

l

Brec

+=

)1)((

(2.6)

, ,

C, lm

g

. ,

(2.6)

,

C PC,

,

.

,

. , , Lmd

Lmq d q .

(saliency ratio)

md

mqqd L

L= (2.7)

- 52 -

.

qd=1 ( Lsq= Lsd, Lsq= Lmq+ Lsi

Lsd= Lmd + Lsi Lsi ),

qd >1 ( Lmq > Lmd )

. qd=1,

qd > 1,

. , qd

.

qd .

2.3.5.1

2.24 6-

: () , () -

, () , ()

.

- 53 -

2.24.

.

(-) .

.

-

(

), .

,

.

. C

Bg Br (

2.6) m ( 2.1). ,

.

. ,

,

.

.

.

.

,

( ),

sqsd LL = (2.8)

, qd=1. ,

.

, (ring magnets)

. 2.25

- 54 -

. ,

2.11. & 2.11..

2.25 4-

2.3.5.2 - (surface-inset mount PMSM)

( 2.24.). ,

.

. ,

, .

( ) ,

. d-

. q-

900/p ( 900) d-

( 2.24.).

,

q-

d-

sdsq LL > (2.9)

- 55 -

-

. ,

,

2.9,

Lsd Lsq qd

.

,

.

, ,

,

.

2.3.5.3 , (interior

mount radially magnetized PMSM)

2.24.

4.26 .

.

(

) . ,

.

4.26 8-

,

- 56 -

.

,

, C ,

(2.6).

2.3.5.4

(interior mount circumferentially magnetized PMSM)

2.24.

.

,

.

2.24.. C,

.

( 2.24. & 2.24.)

. ,

2.24., qd

. ,

. 2.27 6-

.

,

.

,

- .

2.24. 2.24. ,

,

2.28.

/p

- 57 -

2.24. /2p

2.24..

2.27 6-

: () ()

2.28 ,

,

,

. ,

.

- 58 -

2.4

( commutator DC-PM machines)

, .

-

brushless .

2.29

.

4.29 4- : ()

()

.

2.30 ( )

- 59 -

2.30 & 2.31

,

. , 2.31

, .

.

2.31 ( )

2.32 -

.

- 60 -

2.32

. - .

2.5

:

.

:

a) ( )

b)

.

, .

,

,

.

.

, ,

.

2.5.1 (SynRM)

( ).

Lsd & Lsq d q

.

.

.

d q.

( , )

Lmd/Lmq.

- 61 -

d Lmd > Lmq Lmd/Lmq > 1. ,

.

:

2.5.1.1 (SynRM with

segmented poles)

(segmented solid iron poles) -

( 2.33.).

.

.

2.33 4- : ()

, () ()

()

- 62 -

Lmd/Lmq

. ,

, .

.

(

). Lmd/Lmq

.

2.5.1.2 (SynRM with flux barriers)

.

q- ( ),

( 2.33.). ,

q-

d-.

Lmd/Lmq

. ,

.

. , q-

. ,

. ,

,

(,

).

- 63 -

2.5.1.3

(SynMR with distributed anisotropy rotor and

conventional laminators)

( 2.33.)

2.33., q-

.

,

(

).

, Lmq

Imq , ,

Lmd/Lmq .

Lmq

. Lmd/Lmq

,

. ,

. ,

.

2.5.1.4 (ALA, SynRM with

axially laminated anisotropic rotor)

d- ( 2.33.).

.

- ( )

.

Lmd/Lmq .

,

.

- 64 -

, q-,

( )

.

,

.

2.5.2 (SRM)

.

. m ,

Ns Nr. ,

m-, s/r . 2.34.

2.35

4- 8/6.

. ,

4-, 5- .

, ,

. ,

.

.

,

.

.

cogging (

2.3.1). 4.36 2- 4/6

(bifurcated stator teeth).

4- 2.34..

2.36

,

.

- 65 -

2.34 : () 2- 4/2 () 3-

6/4 () 3- 3/2 () 4- 8/6

2.35 4-, 8/6: ()

()

- 66 -

2.36 2- 4/6

2.37 :

() 2- 4/2 () 3- 6/2

, (

, 1- 2-). ,

- 67 -

.

(stepped gap), 4.37..

, ,

4.37..

2.6

.

.

( )

,

.

:

(brushless dc)

(brushless ac).

.

,

. ,

,

.

2.6.1 (squarewave

PM trapezoidal PM brushless dc machine)

, , 2.38. -

( )

.

,

.

- .

brushless dc.

( Lsd = Lsq )

.

- 68 -

2.38 : ()

()

2.6.2 (sinewave PM brushless ac machine)

, ,

( 2.38.) - .

.

brushless ac .

d q

,

.

.

- 69 -

3

3.1

.

.

,

. (Space-

Phasor Theory). ,

,

. ,

(generalized machine theory).

.

- 70 -

,

.

3.2

)cos()( += tXtx p (3.1)

}Re{)( )( += tjpeXtx (3.2) ejt Euler

tjte tj sincos = (3.3)

)( + tjpeX

)( += tjpeXX (3.4) , x(t)

. X=pX (t + ), .

,

(time phazor

time vector). , ,

, 3.1.

(time circular vector).

,

. ,

,

. ,

.

- 71 -

3.1

3.2 () ()

,

)cos()( += tUtu p (3.5)

)cos()( += tIti p (3.6)

- 72 -

)( += tjpeUU (3.7)

)( += tjpeII (3.8) ,

jpeU=U (3.9)

jpeI=I (3.10)

, ,

-. ,

,

.

.

t ( 3.2).

,

.

( , , )

. ,

.

,

(space vectors).

,

.

,

, . ,

,

- 73 -

. ,

)cos()( += tXtx pj

peX=X (3.11)

mm jp

j etetx )]cos([)( +==X (3.12) m

( 3.3).

3.3 x(t)=Xpcos(t+) ()

() t. ,

.

,

(.. )

(.. X ).

(3.11) (3.12)

,

m. ,

,

.

pX

+t )cos(X p,

.

(

) .

- 74 -

m=0,

00 )][cos()( jpj etXetx +==X (3.13)

,

)( mtjpeX

++=X (3.14) t, X m=t+.

(3.4) (3.14) ,

. ,

. m (3.14)

, ,

(t= ),

.

3.3

.

,

.

.

, . ,

,

,

. ,

.

.

- 75 -

,

( )

.

- sA (

) . ,

( ,

).

( ), 3.4

3.4 s

Ampere ( 3.5.)

=S C

dlHdsJ (3.15)

- 76 -

,

+

3.5 s (

-) () C

()

.

.

(3.18)

)2/cos(),( 11 += ss Ftf (3.20)

- 78 -

}Re{}Re{),( 12/

11 jsjjjss eeeetf FF == (3.21)

aja

jss etijejF

)(211 ==F (3.22)

-,

.

.

. ,

ej ,

(3.21).

3.6

- 79 -

=/2 -

( 3.6),

(3.22)

jojss etieF )(

2011 ==F (3.23)

ej0 . ,

sF 1

-.

-,

0)( jaa eti=i (3.24)

aas iF = 2

1 (3.25)

-,

.

3.17

...])(5cos[51)](3cos[

31))[cos((2),( +++= utiNtJ aaaaa (3.26)

)cos()(2),( = aaaa tiNtJ (3.27) 3.27

]Re[)(2Re),( 11

j

ajj

aaa eeetiNtJ a J=

= (3.28)

ajaaa etiN

= )(21J (3.29)

-,

. ,

= /2,

SSj

Sj

aaa jjFeFetiN 112/

12/

1 )(2 FJ ==== (3.30)

- 80 -

,

,

)sin()(2),(),( 0101 == aaag

sg

s tiNltf

ltB (3.31)

=/2

cos)(2),( 01 tiNlt aags = (3.32)

lg ( ,

) 0 (0=410-7 Vs/Am).

1s(,t) f1s(,t),

,

ajaa

gs

gs etiNl

jl

)(2 0101 == FB (3.33)

=/2

)(2)(2 0001 tNletiN

l aagj

aag

s iB

== (3.34)

-

== 2/ 2/ 111 )(2),()( tlrBdtlrBt sss (3.35) , r

( 3.4)

l

)(2 01 tiNlB aa

gs

= (3.36)

.

jaa

gs etiNl

lDj )(2 01 = (3.37)

=/2

aag

s NllD i

01

2= (3.38)

D (D=2r).

- 81 -

jaag

sas etiNllDjN )(2 2011 == (3.39)

=/2

aaaa

gs LNl

lD ii == 201 2 (3.40)

a

ga Nl

lDL 202 = (3.41)

-. L

3.41

. ,

,

),(),( 01 tfltB s

gs = (3.42)

,

)()(4

)(2

)],([)( *20202/

2/tiLtiN

llDtiN

llrdtlrBt aaaa

gaa

gss ==== (3.43)

20*

4 aga Nl

lDL = (3.44)

-,

. (3.41) (3.44)

aaa LLL 233.18

2* == (3.45)

, ,

1/1.233=0.811 81.1%

.

-

. ,

.

.

- 82 -

3.4

.

,

, .

3.7, sA

isA(t) sA.

0- sAisA(t).

. 3.19

sA

)(21 tiNKF sAsAdAs = (3.46)

2/2/sin

=

dAK (3.47)

(winding distribution factor).

(=>0) 1lim = dAKA .

,

(Pitch factor) KpA

)(21 tiNKKF sAsApAdAs = (3.48)

)2/sin( SppAK = (3.49) Sp .

- 83 -

3.7 sA

( )

pAdAwA KKK = (3.50) sA

sAwAsAeq KKN = (3.51) , (5.19)

)(21 tiNF sAsAeqs = (3.52)

nsbas 1111 ... FFFF +++= (3.53)

- 84 -

jsAsAeq

jss etiNjejF a )(

211 ==F (3.54)

=/2, -

,

sAsAeqj

ss NejF iF 20

11 == (3.55)

ajsAsAeqnsbas etiN

)(2... 1111 =+++= JJJJ (3.56)

=/2

sAsAeqs Nj iJ 2

1 = (3.57)

nsba 111 ,...,, JJJ

0)( jsAsA eti=i sA . , =/2

sAsAeqg

sg

nsbas NlliFBBBB

01

01111

2... ==+++= (3.58)

sAsAsAsAeqg

sg

nsbas LNllD

liiF ===+++= 20101111 2...

(3.59)

2020 )(22 wAsAg

sAeqg

sA KNllDN

llDL

== (3.60)

sA ( ).

, (2p=2).

, sA

2

0

2

0 22

=

=

g

wAsA

g

sAeq

gsA l

KNl

lDp

Nl

lDL (3.61)

p .

- 85 -

3.5

3.8

,

p/3

2

. 3.8 (2p=2) .

3.8 ,

, .

(s=NsA=NsB=NsC

Kws=KwA=KwB=KwC). , sA

(=/2).

- 86 -

sA, sB, sC

[ ])()(2

)cos( sese tjtjssessA ee

ItIi ++ +=+= (3.62)

[ ])3/2()3/2(2

)3/2cos( ++ +=+= sese tjtjssessA eeItIi (3.63)

[ ])3/4()3/4(2

)3/4cos( ++ +=+= sese tjtjssessA eeItIi (3.64)

0)( jsAsA eti=i (3.65) 3/2)( jsBsB eti=i (3.66) 3/4)( jsCsC eti=i (3.67)

sssCsBsA iiii 2

3=++ (3.68)

s

(stationary reference frame),

.

(stator reference frame).

(3.65)-(3.67) (3.68)

[ ])()()(32 2 tititli sCsBsA

ss ++=i (3.69)

1, a 2a

sA, sB, sC , 1=ej0, 3/2jea = 3/4jea = . , (3.62)-(3.64) (3.59)

)( sejs

ss eI

+=i (3.70) (3.70)

e

. ,

.

- 87 -

,

.

, ,

sA

)()()( tiMtiMtiL sCACsBABsAsAsA ++= (3.71) LsA sA MAB MAC

sA sB sC, .

, (LsA= Ls= LsC= Lss)

(MAB= MBA= MBC= MCB= MCA= MAC= Ms). ,

(iA(t)+isB(t)+isC(t)=0),

)()()( tiMLLt sAssmslsA += (3.72) )()()( tiMLLt sBssmslsB += (3.73) )()()( tiMLLt sCssmslsC += (3.74)

Lsl Lsm , (Lss=Lsl+Lsm).

,

2/)3/2cos( smsms LLM == (3.75) , (3.72)-(3.74)

)()()2/3()( tiLtiLLt sAssAsmslsA =+= (3.76) )()()2/3()( tiLtiLLt sBssBsmslsB =+= (3.77) )()()2/3()( tiLtiLLt sCssCsmslsC =+= (3.78)

ssmsls MLLL += (3.79)

mslsmsls LLLLL +=+= 2/3 (3.80) Ls Lm

g

seqsmm l

lDp

NLL 0

22

23

23

== (3.81)

seq=wsNs .

- 88 -

[ ])()()(132 2 tatat sCsBsA

ss ++= (3.82)

(3.76)-(3.78) (3.82)

(2.69)

sss

ss L i= (3.83)

,

[ ])()()(132 2 tuatuatu sCsBsA

ss ++=u (3.84)

3.6

3.9

- 89 -

(3.69) ,

,

,

[ ])()()(132 2 tiatiti rCrBrA

rr ++i (3.85)

irA(t), irB(t) irC(t) rA, rB,

rC ( 3.9). (3.85)

r (

). ,

. ,

,

.

[ ])()()(132 2 tatt rCrBrA

rr ++= (3.86)

rrr

rr L i= (3.87)

Lr (Lr=Llr+3/2Lrm,

3.4).

,

2/)3/2cos( rmrmr LLM == (3.88)

g

seqreqrssr l

lDpNN

MM 022== (3.89)

Nreq=KwrNr .

(3.81) (3.89)

aLL

NN

MM mmseq

reqrssr 3

232 =

== (3.90)

- 90 -

=seq/Nreq .

r ( ),

)]()3/4cos()()3/2cos()([cos)( tititiMtiL rCrrBrrArsrsAssA +++++= (3.91) )]()3/2cos()(cos)()3/4[cos()( tititiMtiL rCrrBrrArsrsBssB +++++= (3.92) )](cos)()3/4cos()()3/2[cos()( tititiMtiL rCrrBrrArsrsCssC +++++= (3.93)

rjrrsr

sss

ss eML

ii23+= (3.94)

, ir = ir /

(3.94)

rjrrm

sss

ss eLL

ii += (3.95) rri ,

, rje

rjrr

sr e

ii = (3.96) ,

. (3.95) tjj rr ee =s

rmsss

ss LL ii += (3.97)

.

(3.95),

rjssm

rrr

rr eLL

+= ii (3.98)

( )rjssrs e = ii rsm

rrr

rr LL ii += (3.99)

rr =mrl LL +

. aii rr /= mrlr LLaL =+= 2

- 91 -

[ ] srssjrrssmCmBmAsm retiatiati iiiii +=+=++= )()()(132 2 (3.100) imA(t), imB(t), imC(t) .

[ ] smmsrssmmCmBmAsm LLtatat iii =+=++= )()()()(132 2 (3.101)

3.7 ()

,

,

. ,

.

e (e-r)

.

(e=r),

e=r

.

. ,

)()( tjiti ssssa

ss +=i (3.102)

. (3.69)

(3.102)

)(),( titi ssssa

)(31)(

31)(

32)( titititi sCsBsA

ssa = (3.103)

)]()([3

1)( tititi sCsBss = (3.104)

- 92 -

,

)()()( tititi sossasA += (3.105)

)()(23)(

21)( 0 titititi s

ss

ssasB ++= (3.106)

)()(23)(

21)( 0 titititi s

ss

ssasC += (3.107)

is0(t) .

)]()()([31

0 tititii sCsBsAs ++= (3.108)

,

, (t) (t) .

.

ssai

ssi

=

sC

sB

sA

ss

ssa

iii

ii

3/4sin3/2sin03/4cos3/2cos1

32

(3.109)

+

=

0

0

0

3/4sin3/2sin

0

3/4cos4/2cos

1

s

s

s

ss

ssa

sC

sB

sA

iii

ii

iii

(3.110)

)()( tijti rrr

rar

r +=i (3.111) rjrr

sr e

ii = rri . ,

, sr C

=

rr

rra

rr

rrs

r

sra

ii

ii

cossinsincos

(3.112)

- 93 -

rra

srsra iCi = (3.113)

r

+= t rrr d0 )0()( (3.114) ,

rs C

=

sr

sra

rr

rrr

r

rra

ii

ii

cossinsincos

(3.115)

sra

rsrra iCi = (3.116)

3.10

s-s

r-r .

.

3.10

- 94 -

, x

y xCy

=

)cos()sin()sin()cos(

xyxy

xyxyyx C

(3.117)

xa

yxya C ff = (3.118)

x y . ,

rCs x=r s=00.

f

x

=

sC

sB

sA

xxx

xxxx

s

xsa

fff

ff

)3/4sin()3/2sin(sin)3/4cos()3/2cos(cos

32

(3.119)

, (

)

+

=

0

0

0

)3/4sin()3/4cos()3/2sin()3/2cos(

sincos

s

s

s

xs

xsa

xx

xx

xx

sC

sB

sA

fff

ff

fff

(3.120)

+= t xxx d0 )0()( (3.121)

(general or arbitrary reference frame), 3.11.

,

.

- 95 -

3.11 --C

x-x

3.8

)()()()()()()( titutitutitutp CCBBAA ++= (3.122) , , , ,

. .

( (3.109)) (

(3.119))

)(tuA )(tuB )(tuC )(tiA )(tiB )(tiC

)()(3)(23)( 00 tituiuiutp

xxxa

xa ++= (3.123)

- 96 -

- 97 -

)()(3]Re[23)()(3]Re[

23)( 00

*00

* titutitutp xxxx +=+= iuiu (3.124)

xxax juu =*u xxax jii =*i

, . , )(0 tu

.

.

)(0 ti

*

23 xxS iu= (3.125)

)Re(SP = )Im(SQ = . ,

[ ] 1cos322Re23)Re( UIIeUeSP iu jj === (3.126)

[ ] 1sin322Im23)Im( UIIeUeSP iu jj === (3.127) iu =1 .

3.9

rm

m

rme

Pdt

dWT ==1

(3.128)

Wm

flossem dWdWdWdW = (3.129) We , Wloss Wf

.

(, ),

(3.124)

]Re[23 ** s

rs

rs

sss

e

dtdW iuiu += (3.130)

,

.

+= rsrsssloss RRdtdW 22

23 ii (3.131)

+=dt

ddt

ddt

dW srsr

sss

sf **Re

23 ii (3.132)

ss ss .

dtd sss /=e dtd srsr / =e dtd rrrr / =e , . (3.130)-(3.132) (3.129)

+

=

dtdR

dtdR

dtdW srs

rrs

rs

rs

r

sss

ssss

ss

ss

m'

*'2'*''*2* Re')Re(23Re)Re(

23 iiiuiiiu

(3.133)

,

dtdR

ss

sss

ss

+= iu (3.134) (3.133) . ,

=

dtdR

dtdW srs

rrs

rs

rs

rm

'*'2'*'' Re')Re(

23 iiiu (3.135)

(3.134)

,

- 98 -

dtdR

rr

rr

rr

r

''' ' += iu (3.136)

(3.136) ejr

rrr jr

rr

jrr

jrr edt

dRee '

'' ' += iu (3.137)

( rjrrs

r e'' uu = rjrrsr e '' ii = )

srr

jr

rrr

jr

jr

rjr

rs

r jedt

dejedt

ddted

dtd

rrrr

+=+== )( (3.138)

(3.137)

srr

sr

rs

rs

r jdtdR '

''' ' += iu (3.139)

(3.135) (3.139)

)Im(23)Re(

23 ** s

rs

rrs

rs

rrm

m jdtdWP ii === (3.140)

*

23 s

rs

rr

me

PT i== (3.141)

*** )( rrr

rjr

rjr

rs

rs

rrr ee iii == , (3.141)

rr

rr

r

me

PT i== 23

(3.142)

(3.141) (3.142),

.

,

. ,

.

3.10

(3.99) rri (3.142),

- 99 -

sr

rr

r

me L

LT i= 23

(3.143)

(3.99) (3.143)

( ) srssmsrssmsrre LLLT iiiii =+= 2323 (3.144) (3.97) ssi (3.144)

ss

smeT i= 2

3 (3.145)

(3.143),(3.145),(3.146)

. ,

,

x.

(3.143)

xs

xr

r

mjrs

jrr

r

mrs

rr

r

me L

LeeLL

LLT xx iii ===

23)()(

23

23

(3.147)

p ,

x

rxs

xr

r

mxs

xr

r

me L

LpLLpT sin

23

23 ii == (3.148)

r . x-

( 3.12)

xs

xr

r

me iL

LpT = 23

(3.149)

rxs

xsi sini= x-

, xr .

- 100 -

3.12

,

(x-)

(3.145) (3.146),

xs

xse ipT 2

3= (3.150)

xxs

xsi sini= x-

, xs (x-) xs

xme ipT 2

3= (3.151)

mxs

xsi sini= x-

xm (x-).

- 101 -

3.11

.

. ,

,

.

.

3.11.1

, F (

, field or excitation current) (field or excitation flux) F

I ( , torque producing current)

aFaFe IIcIcT 1== (3.152) F F

.

aFaFe ccT III == 1 (3.153) ( )

.

( ). ,

.

3.11.2

( ).

- 102 -

.

.

.

,

. ,

,

. ,

. ,

.

:

()

)( xrxsm

xssl

xrm

xss

xs LLLL iiiii ++=+=

xmm

xssl

xs LL ii +=

()

)( xrxsm

xrrl

xsm

xrr

xr LLLL iiiii ++=+=

xmm

xrrl

xr LL ii +=

()

xmm

xm L i=

(3.149), (3.150), (3.151)

() / stator-flux oriented control

xs

xsss

xs

xsse iccT == sini (3.154)

() / rotor-flux oriented control

- 103 -

xs

xrsr

xs

xrre iccT == sini (3.155)

() / magnetizing flux oriented control

xs

xmem

xs

xmee iccT == sini (3.156)

xs , xr , xm , xsi

s, r m

, ,

.

.

, .

( )

xsi

xsi ( )

.

xsai

, (field

oriented control). ,

(

, ).

(vector control).

, .

.

( )

.

.

xsai

xsi

, -

- .

. (3.154)

- 104 -

ss

ssse icT = (3.157)

(3.152), ss F, i

cs=c.

.

ssi

(, )

. ,

,

.

.

.

3.11.2.1

,

.

e

.

(synchronously rotating reference frame)

. ,

(e

r).

=eT eserc ir (3.158)

- 105 -

eee rrr += eseses iii += ,

[ ]eses ii ererre c = (3.159) ,

esi . , ee

rr = 0r =e . (3.158)

ere ser ic = (3.160)

ere ser ic = (3.161)

3.12 ( x

e )

:

a) (direct rotor-flux oriented

control flux-feedback control),

(Hall-effect sensors,

),

b) (indirect rotor-flux oriented

control flux-feed forward control),

, ,

. ,

,

(

).

,

- 106 -

. ,

,

,

.

3.11.2.2

,

, .

r. ,

e r .

,

(r = e )

.

( (3.146)

x=r)

rrm see cT i= (3.162)

rmrm

rm += rrr sss iii += ,

[ ]rrmrrm ssre iicT = (3.163) (3.162)

,

( Fd ), 3.13.

- 107 -

3.13

rsi

3.13.

,

, ,

rs

rFd

rm

rm i)Re( mdL+== (3.164)

rs

rm

rm i)(Im mqL== (3.164)

.

,

, ,

3.13. , (3.164).

rFd

rsimdL

rFd

rsi

rsi

- 108 -

(3.164) (3.165) (3.162),

[ ]rrrrFd )( ssasqsdsee iiLLicT += (3.166) Lsd = Ls1 + Lmd Lsq = Ls1 + Lmq. ,

.

rrFd se ic

rr)( ssasqsde iiLLc

. Lsd < Lsq,

( , )

.

rsai

Lsd =

Lsq (3.166)

rrFd see icT = (3.167)

.

, =0 ,

(e/is)max ,

.

rsai

rsai

rsi

3.11.2.3

( ). (Lsd

Lsq ). ,

, Lsd Lsq .

.

0 rFd =

(3.166)

0 rFd =

r)( srsasqsdee iiLLcT = (3.168)

Lsd > Lsq , ( >0 )

.

rsai

- 109 -

3.11.3

,

.

.

(

dxdLiFe

2

21= ) .

.

.

,

( )

. ,

,

,

.

- 110 -

4 &

4.1

,

,

, ,

- .

.

Watt (.. ,

, ) kWatt (.. , ,

). 4.1

.

- 111 -

4.1 : () , ()

, () , () -

.

- 112 -

1970

mechatronics (

).

.

.

.

,

( 4.2.).

.

. ,

,

.

( 4.2.),

. (mechatronics controller)

(

) .

,

. , ,

.

,

,

.

1986 Bosch GmgH

.

CAN (Controller Area Network) 1993

ISO 11898.

. 1992 -

- 113 -

CiA (CAN in Automation)

CAN

.

4.2 : ()

, () (mechatronics system)

- 114 -

CAN

( ). CAN

.

.

CAN

.

CAN

(CAN Application Layer CAL).

CANopen DeviceNet. CANopen

, ,

., DeviceNet .

4.2

,

.

, .

, ,

.

.

( ).

,

- brushless

.

- 115 -

.

, ,

, ,

. ,

(brushless dc machines)

(brushless ac machines).

, .

.

,

.

.

.

( ,

)

.

.

, . ,

(CAN, CiA, CAL )

.

- 116 -

- 117 -

5

. . , 2008

Stephen Chapman. , 2000

Firoozian, Raziollah. Servo Motors and Industrial Control Theory, 2009

. . , 2000

. . , 2005

R. Krishnan. Electric Motor Drives, Modeling, Analysis And Control, 2003

B. K. Bose. Power Electronicsand Variable Frequency Drives, Technology

And Applications

http://el.wikipedia.org/wiki/_

http://en.wikipedia.org/wiki/Servomechanism

http://en.wikipedia.org/wiki/Stepper_motor

http://www.seattlerobotics.org/guide/servos.html

http://imarinakis.webs.com/electric_engines.htm

http://zone.ni.com/devzone/cda/ph/p/id/234

http://www.metadosi-ischios.gr/article.php?ID=83

http://www.metadosi-ischios.gr/article.php?ID=100

1 1.1 - 1.2 1.2.1 -1.2.2 ( PM dc-commutator motors)1.2.3 () 1.2.4 1.2.5

1.3 1.3.1 1.3.2 1.3.2.1 -1.3.2.2

1.4 1.4.1 1.4.1.1 1.4.1.2 [kW/Nm]1.4.1.3 ( ) [Nm/m3 Nm/Kg]1.4.1.4 [kW/kVA]

1.4.2 / 1.4.2.1 [rad/sec2]1.4.2.2 1.4.2.3 1.4.2.4 (max/b)1.4.2.5 , 1.4.2.6 1.4.2.7

1.4.3

1.5

2 2.1 2.2 2.3 2.3.1 2.3.1.1 (interior-rotor PMSM)2.3.1.2 (exterior-rotor PMSM)

2.3.2 2.3.2.1 (distributed stator winding PMSM)2.3.2.2 (concentrated stator winding PMSM)

2.3.3 2.3.3.1 (radial flux PMSM)2.3.3.2 (axial flux PMSM disk type PMSM)

2.3.4 2.3.4.1 (linear PMSM)2.3.4.2 (slotless PMSM) 2.3.4.3 (coreless ironless PMSM)

2.3.5 2.3.5.1 2.3.5.2 - (surface-inset mount PMSM)2.3.5.3 , (interior mount radially magnetized PMSM)2.3.5.4 (interior mount circumferentially magnetized PMSM)

2.4 ( commutator DC-PM machines)2.5 2.5.1 (SynRM)2.5.1.1 (SynRM with segmented poles)2.5.1.2 (SynRM with flux barriers)2.5.1.3 (SynMR with distributed anisotropy rotor and conventional laminators)2.5.1.4 (ALA, SynRM with axially laminated anisotropic rotor)

2.5.2 (SRM)

2.6 2.6.1 (squarewave PM trapezoidal PM brushless dc machine)2.6.2 (sinewave PM brushless ac machine)

3 3.1 3.2 3.3 .3.4 3.5 3.6 3.7 () 3.8 3.9 3.10 3.11 3.11.1 3.11.2 3.11.2.1 3.11.2.2 3.11.2.3

3.11.3

4 & 4.1 4.2

5