227 非正弦永磁同步电机转矩脉动抑制
第30卷第2期
2009年6月
上海海事大学学报
JOURNALOFSHANGHAIMARITIMEUNIVERSITY
V01.30No.2
Jun.2009
ArticleⅢ:1672—9498(2009)02・0065-07
,n
●_・■●●■1l
。1。orq
ue
ripple
compensation
lna
non-sinusoinal
permanentmagnetsynchronousmotor
ZHOUZhibinl,XIE
(1.LogisticsEnSin∞riIlg
Weil,Luc
LORON2
College,ShanghaiMaritime
Univ.,sh锄gIlai200135,China;
2.DepartmentofElectricalEngineering,Polytech’Nantes,Nantes44603,France)
Abstract:Ino耐ertostudytheinfluencedistributioninPMSMwith
a
a
on
thetorquetipplesexertedbythenon-sinusoidalfluxlinkage
permanentmagnetsynchronous
motor(PMSM),acontrolsystemofthenon・sinusoidal
largecoggingtorqueissimulatedinMatlab/Simulink.AnIterativeLearningControl(ILC)compensation
algorithmisappliedtocompensatethespeedandtorquerippleofthePMSM.Twodi珏:巳陀ntschemeswithILCimplementedinspeedloopandintorqueloopshowthatbothILCschemesKeywords:torquetipple
Call
ale
compared.The
simulationre8u【协
beusedto
compensatethetorqueandspeedtipples.
learningcontrol
compensation;non—sinusoidal;PMSM;iterative
CLCnumber:TM303;TM341;TM351
Documentcode:A
非正弦永磁同步电机转矩脉动抑制
周志斌1,谢卫1,Luc
LORON2
(1.上海海事大学物流工程学院,上海200135;2.南特综合理工学院电气工程系,南特44603法国)
摘要:为研究永磁同步电机中非正弦气隙磁链分布及其对转矩脉动的影响,用Matlab/Simulink对磁链非正弦、且存在较大齿槽转矩的永磁同步电机及其控制系统进行仿真。采用迭代学习控制算法抑制永磁同步电机转速和转矩的脉动。对转速环和转矩环下两种不同的迭代学习控制方案进行比较。仿真结果表明,两种不同的迭代学习控制方案均可以抑制转矩和转速的脉动。关键词:转矩脉动抑制;非正弦;永磁同步电机;迭代学习控制
o
IntroaUC咖
Permanentmagnet
哪are…appeal…ing础asc踞andmidba抵tes
synchronousmotors(PMSM)
fo,。三竺i2藏
its
electricalpmplllsionsystems.Withoutexcitationwind・
Receiveddate:2008-10-24;Revisedtittle:2008-12-20Foundationitem:InnovationFundofShanshaiEducation
LeadingAcademicTechnology
Biography:ZHOU
Committee(08ZYl08);InnovationFundofShanghaiEducationCommittee(0972162);
Shanghai
Education
Discipline响ectof
Committee(J50602);MountaineeringProject0fSIlangllaiScience&
Committee(06DZI1202)
is
Zhibin(1983一)。Male,BorninShanghai,Graduatestudent,Beseawhsubject
pcmmnentmagneticsynchronousmachineand
contr01.(E・mail)zlonbin@163.coal
XⅢWei(1965一),Male,BorninIj蚰y1埔nHu’11811,PTofb啪r.Doctor,Research缸bject
is
ElectricalDrive
Sy8t锄,
(E-mail)weixie@嘲.shmtu.eclu.∞
nis60+21‘“。e2t
66
JOURNALOFSHANGHAIMARJTIMEUNIVERSITY
V。01.30
ings
ordampingwindings,thePMSMhas
a
verycorn-
pactstructureandfewlossesintherotor.AdvantagesofthePMSM
ale
highpowerdensity,hishtorque—to-
inertiaratio,andhiShelectricalefficiency.
However,themain
disadvantage
ofPMSMisthe
torqueripples.Thesetorqueripplespulsateperiodical・lywiththerotor
position,which
causes
periodicoscil-
lationsofthemotorspeed,especially
whenthespeed
is
low.Speed
ripplesseverelylimittheperformance
of
servo
systems
in
hish・precision
tracking
applica-
tion8.[t-23
1
Main
torqueripples
andtheir
sourcesTherealetwo
major
types
of
permanent
magnet
(PM)motors:sinusoidaland
trapezoidal.Thedomi—
nant
torque
production
mechanism
in
most
PM
machinesisasfollows.
Anydivergence
from
ideal
conditionsin
a
PM
motordrivergivestheriseoftheundesiredtorqueput-sations.Thetwomaintorquepulsating
components
are
thecoggingtoquegeneratedbytheinteractionofthe
rotor
permanent
magnetand
stator
slots,andthe
torque
ripple
generated
by
theinteraction
ofstatorcurrent
magnetomotiveforces(MMF)and
therotor
magnet
fluxdistribution
intheairgap.【3】Thereis
no
stator
current
excitationinthecoggingtorque
production.
Intrapezoidalpermanent
magnetmotors,thereis
anotheradditional
zoureeoftorqueripplecommonly
knownascommutationtorque.
2Simulationof
a
non.sinusoidal
PMSM
2.1
Equationsfor
a
non.sinusoidal
PMSM
InPM
synchronous
motors,a
sinusoidalflux
densitydistributionaroundtheair
gap
is
difficultto
achieve.Therefore。when
thenon.sinusoidal
flux
link-
ageinteractswiththesinusoidalstatorcurrents,itwillgiverisetotheperiodictorque.[43’11leinducednon-si—nusoidalfluxlinkage
from
the
rotormagnetsin
the
stator
windingcanalsobeexpressedas
a
sumofodd
cosineswherethecoefficientsdecreasempidly.The
induced
fluxlinkagefrom
rotor
permanentmagnetsto
phaseⅡCallbewrittenas
肇乙(0)=9lCOS0+93C08(30)+
仍COS(50)+仍cos(70)+…
(1)
‰(0)and虬(0)can
beobtainedbyshifting
theelectrical
angle
0in
Eq.(1)by一寺1rand寻仃,respectively.And
then,transformingthe%,‰,
%to
the由coordinate
systemusingthe
Blondel-
Park’s
transformation,wecan
get
【芝】=【_:1二:二篇篡誓::::器二.斗
【妒由::fasc。e。s。(,6#+)n+CdL
怕(6口)+n
12mln
(120)’。:…】
+…J
(2)
‘’
Fromthe
equationsabove,weshouldnoticethatthe
non-sinusoidalflux
densitygenerates
fluxlinkage
har-
monics
beth
on
dandq
quantities.Thisisverydiffer-
ent
fromanideallysinuzoidalPMSM,inwhichqo
is
a
constant
and%is
zero.
Thetotal
flux
inthestator
can
be删tten
as
盼眩挑】+【乏】
(3)
where,乙,厶represent
the
stator
inductances
on
由-axisandia,ifalethe由一axisstatorcurrents.
ThevoltageequationsforthePMsynchronousmotorwiththenon・sinusoidalfluxlinkage眦
JⅡd=R.id+LaDid+D%一wLqig一∞‰f4、tu口=R.i口+£口Di叮+D%+o)Ldid+∞虬
where,R.isthestatorresistance,∞istheelectrical
angularspeedoftlle
mtor,D=面d
isthe
dmrential
operator.
Theelectromagnetictorqueequationforsynchro-
nous
machinesis
瓦=.-np(缈ai,一嚷‘)
(5)
where,厅口isthenumberofpole
pairs.combiningEq.
(3)and(5),assumingLa=£口and
usingthemethodoffield-orientedcontrolofPMSM(the
d-axiscurrentis
controlledto
zero),we
get
,
瓦=÷,l,%i,
(6)
From
Eq.(6),we
can
noticethattheelectromagnetic
torquewillalsohavetorquerippleharmonicsatthe6th
andthe12thordersdue
to%which
includesthe6th
and
the12thfluxharmonics.Themechanicaldynamics
are
No.2
ZHOUghibin.甜a/:Torqueripplecompensationin
a
non—sinasoidalpermanentmagnetsynchronousmotor67
f如m=(瓦一正一k—rf.o)/j(7)
LDO=03=n口∞m
where,Jistheinertiaoftherotor,tiselectromagnet-
ic
torque,瓦is
load
torque,k
isthecoggingtorque,
and‰is
thefrictiontorquewhereisnormallymod-
eled
by%。=/ua.,where肛is
known鹪thefriction
coefficient.Thesecondequationshowstherelationshipanaongtheelectricalangle0,therotorelectricalangu—laxspeed
to
and
themechanicalangularspeed∞_.
2.2Parametersofthe
PMSM
ThegiVen
parameters
of
a
PMSM
a弛shownin
Ta
hle1.
Tabk1
Parametersof
the邮M
Parameter
ValueR./ft
0.5匕/mH
7
Lq/mH
7
J/(ks・m)
0.0465
np
4.Number0fslots
48O/Wb
0.13∥(r・rain一1)
3000
It
iS
possibleto
messill肥theflux
harmonics
inducedbyrotorpermanentmagnetbymeasuringtheback
elecu'omotiveforceat
eachstage,and
then
a
frequency
analysis
using
theFastFourierTransform
(F订)can
be
performed.whenrotational
speed
is
high,theeffectsofcoggingtorquec肋beneglected,
and
thebackelectromotive
force(back—EMF)canbe
expressed
as
e.=D望-,眦=一9lrosin(∞t)一
3妒3wsin(30r)一5仍wsin(Scot)+…
(8)
Fig.1give,theFFfranalysisoftheback—EMFin
phase
a
mea8tl陀d
at
the
speed
of3000r/rain(∞=
400百斌t/s).
,-量lg.1耵啊舢叫y幽荫back・EMF
inphase
a
Table2showsthecoefficientsof
flux%which
were
fiquredby
Eq.(8).Thecoefficients
of%and
%canbe
obtainedcombiningEq.(2)andTable
2.
Table2
qcoeflldenlsoftheinduced
flux吧
h/mWb
妒5/mWb妒7/mWb
妒ll/mWb妒13/mWb
l
127.30
1.1l
O.57
0.5l
0.06
Forthecoggingtorque,thereisno
unifiedanaly-
ticalmodel
because
itsgenerationmechanisminvolves
complexfielddistributionsaroundstatorslots.Howev—er,whatcanbeassuredisthatthecoggingtorqueis
a
periodic
function
ofrotor
position
andits
shape
depends
on
thenumberofstatorslotsand
poles.【5】An
approximateexpressionisused船thecogging
torque
modelinthis
machine.
7k=5.6sin(480。)+1.87sin(2
x
480。)+
0.9sin(3x480。)
(9)
2.3
Simulationofthebasiccontrolsystem
Fig.2showstheblockdiagramofthebasiccontrol
systemforthePMSM,whichincludesthreeparts:thespeedcontrolthe
PMSM.For
the删loop
loop,thecurrentcontrolloop
and
andcurrentloop,thePIcontrollers
are
used
and
the
parametersofthem
are
tunedbytheNonSymmetricalOptimumMethod.[61
№.2
Block
diagramof
the嘲ccontrol
systemforthePMSM
11lereferencecurrentgenerationmodule
can
be
deducedfromtherelationship
between
theelectromag-
nefictorqueandtheq-axiscurrent.Inidealcase,we
can
get
1
瓦=音np吼oi,=反oi,
(10)
Therefore,thereferencecurrentgenerationmodulecan
beexpressed∞
.mf
1,r-d
~2瓦1
(11)
where,.|I由isthetorqueconstantand妒由istheaverageDCcomponentoftheflux
linkage%which
isalready
JOURNALOFSHANGHAIMARITIMEUNIVERSITY
V01.30
obtainedinsection
2.2(noticethat吼o2妒1).
ThesimulationsystemisbuiltinMatlab/Simulinkanditssimulationresults
are
shownin
Fig.3,from
whichwe
can
seethat:atthespeedof500r/min,the
speedrippleisnot
obvious;butatthelowspeed
of
5r/rain,thespeedrippleisabout30%oftherefer-
ence
speed.This
comparison
showsthat
the
speedrippleproblem
can
beneglectedathJish
speed,be—
catlse
thespeedrippleswould
be
filteredbytheinertia
ofthemachine;butatlowspeed,thespeed
ripple
problemisverysevelre.
哪.、穹
(a)at500r/min
(b)at5r/min
Fig.3
Speed
waveformsofthePMSM
Fromthesimulationresults,wealsofindthatthe
current
andspeedPIcontrollers
arenot
able
toavoid
the
speedripple
causedby
the
torqueripples
even
whentheya弛well-tuned.
IterativeLearningControlfor
speed
and
torqueripple
compensation
IterativeLearningControlalgorithm
Inthispaper,we删配Iterative
kaming
Control
(ILC)methodto
compensatethespeedandtorquerip-
pies.The
motivationofILCcomesfromtherecosni—
tion.Itsknowledgecanbe
learnedfromexperience.In
words,when
a
controltaskis
performed
repeat-
edly,wecan
gainextrainformationfromnewsources
such
as
previouscontrolsignal
and
tracking
elror
pro-
files,which
can
be
viewed
as
somekindof“experi.
ence”.This
kindof“experience”8erges鹪anew
source
ofknowledge
related
to
the
dynamicprocessmodel,andaccordingly
reduces
the
need
for
the
processmodelknowledge.[7。8】
Thecharacteristicsof
ILC疵
(1)It
not
onlyincorporatestracking
eITor
atthe
moment,butalsoincorporatesprevioustrackingeiTor
andpreviouscontrolsignal.
(2)Itrequiresminimumsystemknowledge。and
specificparametersoftheplantisnotnecessary
(3)It
isveryeffective
on
rejecting
theperiodic
disturbances
orerIors.[9
3
There
are
various
algorithms
for
ILC.Inthis
ease,we
choose
a
P—typelearningalgorithm.Thepro-
posedILC
schemeis
illustrated
in
Fig.4,andthe
followinglearninglawisused
ui+l(t)=(1一a)ui(I)+圣e‘(t)+Fe^l(t)
(12)
where,i=1,2,3…istheiterationnumber,ui(‘)is
thepreviouscontrolsignalgeneratedby
ILC,ej(t)is
theprevious
ell-or
signal,el+l(f)isthepresent
error
signal,痧and厂ale
error
learning
gains,and口is
a
forgettingfactorwhosevalueisintherangeof0
and
1.
Specifically
inFig.4,the
control
signalⅡ(I)
referstothe
compensationsignal
oftheq-axisI℃f.er℃noe
current
删el"ror・
signal,andthe
error
si伊ale(I)refem
tothe
AnotherimportantcharacteristicofILC
isthatit
doesn’tchangetheexistingcontrollers.ILCmodifiesthecontrolinput
or
adds
a
compensation
sigllaltothecontrolinput,which
meansthat
ILC
can
work
very
wellwiththeorisi,lalcontrolsystemtocompensatethe
3
3.1
other
No.2
ZHOUZhibin.da/:Torquetipplecompensationin
a
non—sinusoidal
permanentmagnetsynchronousmotor69
periodicaldisturbances.
waysofimplementingILCschemeintothecontrolsys—ternofPMSM:onethetorqueloop.
Thespeed
error
3.2
ImplementationofILCscheme
Torqueripplescausedbythefluxharmonicsand
isthespeedloopandtheotheris
cogging
torquecausedby
statorslotseffecthave
one
signalisalreadyavailableinthe
commongroundthatthey
call
a弛periodical.ILC
two
algorithm
basiccontrolsystemforthePMSM,soit’sveryeasytoimplementILCschemeintotheILCsystemisshowninFig.5.
beusedtocompensatethe
8sine
differentkindsof
speedloop.Thespeed
torqueripplesatthe
time.Thereistwodifferent
№・5
Itthiscase,the
original
Block
diagramofthecontrolsystemwithILCinspeedloop
to
ILCmoduleisparalleltothe
a
minimizethe
speed
ripple.
care
speed
PIcontrollerandworksasfeedforward
Insomeapplications,wewould
themotortorquethanthe
to
moreabout
controllerwhichisabletoveryquickly.The
compensate
the
speed
ripple
speed,which
meanBwewant
speedPIcontrollerproducesthe
I.∞tef
keepthemotortorquemoresmoothand
torque
want
todi-
mainq-axiscurrentreferencewouldlearntheperiodic
andtheILCcontroller
andthenproduce
rectlyreducethe
ripples.Thenwein
torque
mayuse
in
speed
elTor
anotherscheme诵tllILCloopshown
thecompensationsignalAi口thatcooperateswithtllei器
Fig.6.
№.6
Block
magramofthecontrolsystemwithILCintorqueloop
InFig.6,themotortorqueshouldbeexpressed:pensive.Atorque
ofthe
the
observerwouldincreasethecom-high
咒=t—k,which
presentsthetotaltorquegenera-plexity
controlsystem
andestimatingthe
tedinthemachinetodrivetheloadreferencetorqueshould
torque正.So
theload
frequencytorqueripplecomponentsisnoteasy.
beequal
to
to
torque.
periodic
3.3SimulationresultsofthetwoILCschemes
Inthissection,wecomparethedifferenteffectsof
The
role
ofILC
to
schemeis
compensate
torque
be
eITOFS
better缸lackthereferencetorque.Once
themotortorque
no
equals
thereferencetorque,therewill
twoILC
schemesbysimulation.Duetothe
differentshould
torque
ripplesandthespeedwillbeconstant.
schemein
real
loopsanddifferentkindsofsignal
notent
use
elTOI暑,we
TheproblemoftorqueloopILCapplicationisthat,formakingget
the
a
thesamelearninggains咖andFforthediffer-
torqueloop,ithasto
would
ILCschemes.Ithasbeenprovedthatlarge西and
torque
feedback
sign8l,which
a
be
rinthetorqueloopILCschemewouldnlakethesys-tern
achievedintwoways:oneisbyusingtorquenans-
unstable.…Here.for
ducertomeasurethetorqueandtheotherisbydesig-ning
a
choose咖=54,F=39;andchoose痧=180。F=130.
For
a
forthe删loop
r/rain
andwith
the
torqueloop
ILCweILCwe
torqueobservertoestimatethetorque.Using
a
torquetransducerwouldmakethedrivesystemvery
ex-
givenspeedof15
a
load
70
JOURNALOFSHANGHAIMARITIMEUNIVERSn-Y
referencevalue.Thesetwofactors
V01.30
torqueof2N・m,weactivatetheILCcontrollerafter3
seconds
andgetthe
followingresults
a8
can
becalculated
shownin
fromthesimulationresultsshowninFig.7
and
Fig.8,
Fig.7andFig.8.
and’I铀le
3showsthecalculationresults.
Table3Calculationof
S盯andT盯
耵lF/%
409.56
S砌Ⅳ%
e孳
占
WithoutILcWith8peedloopILCWith
torque
11.30.672
言
loopⅡC
Forthe
(B)with11C
speedloopILC
compensationseheme,
in删loop
largelearninggains国andf‘’spoedripple
Canbe
to
a
chosenandthe
error
Canbereduced
smallbound
immediately(Fig.7(a)).Simulation8(a)shows
目二JresultfromFig.
thatwhenthe
speedrippleiscompensa-
ted,themotortorqueripplewouldreduced,whilemanyproduced
(b)mthILCin
Fig.7
loop
be
correspondinglynoiseswouldbe
is
the
price
high-frequency
inthe
motortorque,which
torque
payingforthereductionof
Forthe
torqueloop
speed
ILC
ripple.
Speedresponsewaveforms
compensationscheme,
thetorqueripplewouldbe
noises(other
intorqueis
harmonics
reduced,andno
quantifies)wouldbeinduced
directly
ripples(Fig.8(b)).Whenthetorqueripple
reduced,thespeedripplewillbecorrespondingly
the
compensated,but
this
schemeis
speedripplecompensationin
a8
not嬲quick
in
spe沧dloopILC
(Fig.7).
(-)mthⅡcin。peedloop
4Conclusions
ItiSclearthatnon-sinuseidalfluxlinkagedistri-
bution
暑
induced
by
rotor
permanent
magnets
would
己
、
h
causetorqueripplesintheelectromagnetictorque,and
duetothepresenceofthestatorslots,acoggingtorquewouldappearinthePMSM.Atlow
speed,the
call
problemdolittletorquetorque
of8peedrippleissevereandPIcontrollersto
‘b)with
Fig.8
ILC
rejectthesespeedripples
ILC
schemesin
caused
by
the
m
tongueloop
Motortorquewave重orms
ripples.The
speedloopand
loopa弛implementedinthebasiccontrol
ToevaluateofthetwoILC
and
system.The
are
comparethecompensationeffects
ufle
simulationresultsshowthatbethschemes
ableto
schemes,we
speedtipplefactor
ale
compensate
Itiseasier
the
speedand
mole
torqueripplessuccessfully;
(SRF)and
fined
by
torquerippleratioof
factor(1W),which
peaI【一to-peal【value
de-
and
attractivetoimplementtheILC
the
thetothe
compensation
schemeinthe
speedloopinpractice.
No.2
ZHOUZhibin,eta/:Torqueripplecompensationin
a
norl-sinusoidalpermanentmagnetsynchronousmotor71
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非正弦永磁同步电机转矩脉动抑制
作者:作者单位:刊名:英文刊名:年,卷(期):被引用次数:
周志斌, 谢卫, Luc LORON, ZHOU Zhibin, XIE Wei, Luc LORON
周志斌,谢卫,ZHOU Zhibin,XIE Wei(上海海事大学物流工程学院,上海,200135), Luc LORON,Luc LORON(南特综合理工学院电气工程系,南特,44603,法国)上海海事大学学报
JOURNAL OF SHANGHAI MARITIME UNIVERSITY2009,30(2)0次
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