Jeroen De Backer borstelloze gelijkstroommachines Een aan-uit-stroomregeling zonder ...

131 Pages·2012·4.02 MB·English

Een aan-uit-stroomregeling zonder positiesensoren voor
borstelloze gelijkstroommachines
Jeroen De Backer
Promotoren: dr. ir. Frederik De Belie, prof. dr. ir. Jan Melkebeek
Begeleider: dr. ir. Frederik De Belie
Masterproef ingediend tot het behalen van de academische graad van
Master in de ingenieurswetenschappen: werktuigkunde-elektrotechniek
Vakgroep Elektrische energie, Systemen en Automatisering
Voorzitter: prof. dr. ir. Jan Melkebeek
Faculteit Ingenieurswetenschappen en Architectuur
Academiejaar 2011-2012

Een aan-uit-stroomregeling zonder positiesensoren voor
borstelloze gelijkstroommachines
Jeroen De Backer
Promotoren: dr. ir. Frederik De Belie, prof. dr. ir. Jan Melkebeek
Begeleider: dr. ir. Frederik De Belie
Masterproef ingediend tot het behalen van de academische graad van
Master in de ingenieurswetenschappen: werktuigkunde-elektrotechniek
Vakgroep Elektrische energie, Systemen en Automatisering
Voorzitter: prof. dr. ir. Jan Melkebeek
Faculteit Ingenieurswetenschappen en Architectuur
Academiejaar 2011-2012
Voorwoord
Voorubevindtzichmijnthesisverslagovereensensorlozesturingvaneenborstellozegelijk-
stroommotor. Aangezieninhoogperformante,compacteaandrijvingensteedsmeerdittype
vanmotorwordtgebruikt,werdhierdevoorbijejarenreedsveelonderzoekopverricht.
KlassiekgebruiktmenvoordesturingvaneenBLDCmotorhallsensoren. Hoewelhallsen-
soren zeer goedkoopen betrouwbaar zijn zorgen ze voor complicaties bij de bouw van de
motorenverminderenzedebetrouwbaarheid. Eensensorlozebepalingvanderotorpositie
dringtzichdusop.
DesensorlozesturingiseendoorontwikkelingvandereedsopeenBLACmotortoegepaste
VASCO-sturing. Dezesturingwerdontworpendoormijnpromotorenbegeleiderdr.ir.F.De
Belie. Ikwenshemdanooktebedankenvoorhetterbeschikkingstellenvanzijnalgoritme
ensimulatiemodellen. Zonderzijn bijdragewas dezethesisniet mogelijkgeweest. Hijkon
mesteedsmotiverenenzorgdevoordenodigeondersteuning.
Ookwil ik mijn promotorProf. dr.ir. J. Melkebeekbedankenvoor hetmogelijk maken van
deze thesis. Ik wil hem ookbedanken voor de substantie¨lebijdrage tot mijn opleiding. De
kennisdiehijmijbijbrachttijdensdevakkenoverelektrischemachineswarenessentieelom
bepaaldeproblementijdensmijnthesistedoorgrondenenoptelossen.
Mijn medestudenten Pieter Jan Goedertier en Jan Van de Vyver wil ik bedanken voor de
goedesfeerin hetlabo enhunsteuntijdensmijn thesis. Demedewerkersophetlabo Tony,
StefaanenFransiscowilikbedankenvoordehulpbijhetrealiserenvanmijnopstelling.
Tevenswilikmijnfamilieenvriendenbedankenvoorhunsteuntijdensmijnthesis.
JeroenDeBacker,augustus2012
i
Toelating tot bruikleen
De auteur geeft de toelating deze scriptie voor consultatie beschikbaar te stellen en delen
vandescriptietekopie¨renvoorpersoonlijkgebruik.
Elk ander gebruik valt onder de beperkingen van het auteursrecht, in het bijzonder met
betrekking tot de verplichting de bron uitdrukkelijk te vermelden bij het aanhalen van re-
sultatenuitdezescriptie.
JeroenDeBacker,augustus2012
ii
Een aan-uit-stroomregeling
zonder positiesensoren voor
borstelloze gelijkstroommachines
door
JeroenDE BACKER
Masterproefingediendtothetbehalenvandeacademischegraadvan
MASTER IN DE INGENIEURSWETENSCHAPPEN: WERKTUIGKUNDE-ELEKTROTECHNIEK
Academiejaar2011–2012
Promotor: Prof.Dr.Ir.Jan MELKEBEEK
Promotor-Begeleider: Dr.Ir.FrederikDE BELIE
FaculteitIngenieurswetenschappen
UniversiteitGent
VakgroepElektrischeenergie,systemenenautomatisering
Voorzitter: Prof.Dr.Ir.Jan MELKEBEEK
Samenvatting
Vanuit de industrie bestaat al langer de vraag naar sensorloze sturingen voor BLDC mo-
toren. Het vermijden van sensoren rechtsreeksop de motor vergroot de betrouwbaarheid,
dit samengaand met een reductie van de productiekost. Alhoewel reeds vele sensorloze
sturingenbestaan,isdewerkingbijstilstandenlagesnelheidnogsteedseenprobleem.
DaaromzullenweeennieuwstuurschemavoorstellenomkoppelsturingopeenBLDCmo-
tor te kunnen uitvoeren. Hiervoor hebben we een stroomregeling en een schatter voor de
positie nodig. We zullen een voorspellende regelaar opstellen voor de stroomcontrole, en
eenparameterlozepositieschattergebruikmakendvanhetuitspringendpoolkaraktervande
motor. Opmerkelijk is dat we hierbij slechts zullen gebruik maken van e´e´n stroomsensor.
Naast simulaties zullen we deze ookimplementeren op eenmicrocontroller omhun werk-
ingnategaan.
Trefwoorden
BLDCmotor,borstellozegelijkstroommotor,PMSM,sensorlozesturing,stroomsturing,MBPC
iii
1
Low-Speed Salient-Pole BLDC-Machine Control
by Using a Single Sensor
1
Frederik De Belie , Jeroen De Backer, Araz Darba and Jan Melkebeek
Dept. Electrical Energy, Systems & Automation, Ghent University, Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium
1
corresponding author, tel: [phone], fax: [phone], e-mail : [email protected].
sensor vs,v d
Abstract—This paper discusses an enhancement for salient-
i
pole brushless dc-drives using a single current sensor in the dc- s,v
bus.Theimprovementismadebyreplacingthehallsensorswith q
e
a rotor-position estimator, increasing the reliability of the drive θr is,u
V
and reducing its cost. As a result, the BLDC-drive is controlled dc vs,u vs,v vs,w vs,u
by using a single sensor only, requiring a minimum amount of
electronics to process the measurements. The additional advan-
sensor
tageofapositionestimatorinBLDC-drivesisthehighresolution
i
in the rotor position information. This allows to use advanced vs,w s,w
model-based controllers (e.g. programmed current control) and
to extend the range of operation (e.g. higher speed by field i⋆ currentcontrol
weakening).
i
I. INTRODUCTION PWM add currentprogrammedcontrol
Recent advancements in electrical drives have reduced the n
o
nsseeunnmssoibnregsrtooorfassseeinnnssgoolrerlseo,sneseitmihneertthhbeoyddscre-[ld3inu].kciS[n2eg]lfto-hsreeeniastmhineogrubonyrtuossefinncsguorrsrleeelsnfs-t carrier commutati off/on θer estimatoωerr δicxy uv
control refers to methods avoiding rotor-position sensor(s) testsignal δvc w
positionestimator
by using a rotor-position estimator. This paper discusses an
enhancement for salient-pole BLDC-drives by using a single Fig. 1: Overall scheme of the sensorless current controller.
current sensor in the dc-bus and by replacing the hall sensors
with a rotor-position estimator. A contribution of this paper
is the estimation of the rotor position from measurements
programmed controller and requires values for stator resistor,
obtainedfromasinglecurrentsensor,placedinthedc-bus.The
rotorposition,inductanceandback-emf.Besides currentsam-
additional advantage of a position estimator in BLDC-drives
ples taken for current control, additional current samples are
is the higherresolutionin the rotorposition informationcom-
taken to measure the current ripple used in the rotor position
pared to the hall-sensor output. This allows to use advanced
estimator. A measurable current ripple is obtained by adding
model-basedcontrollers(e.g.currentprogrammedcontrol)and
signals to the current controller output. The estimator can
to extend the range of operation (e.g. higher speed by field
modify the PWM carrier in order to reconstruct the phase
weakening).Thedisadvantageoftodaysrotor-positionestima-
currents from samples taken by the single current sensor.
torscomparedtopositionsensorsisthedecreasedaccuracyin
A differentrotor-position estimator is used at low and high
the rotor position and hence commutation instances, resulting
rotor speed. At higher speed (above 10% of nominal speed),
in a larger torque ripple. However, the back-emf in salient-
it is advised to use the back-emf. An overview of back-emf
pole BLDC-machines differs from the trapezoidal waveform.
based sensorless methods for BLDC-drives can be found in
As a result, a small deviation in the commutation moments
[5]. As these estimation methods are well-known, this paper
can be allowed as it has a small influence on the torque
will deal with the low-speed estimation only. The estimator
generationandpoweroutput.Therequirementofanestimator
at low speed obtains the rotor position from measurements
is a morepowerfulcontrollerasthe technologydemandshifts
of the current ripple caused by the phase voltages switching
from hardware (sensors) to software (estimator).
between the positive and negative side of the dc-bus voltage.
II. SENSORLESS CURRENT CONTROL For salient-pole machines this current ripple depends on the
An overview of the sensorless salient-pole BLDC-drive is rotor position, the largest ripple amplitude for voltage vector
given by the scheme shown in Fig. 1. A three-phase voltage- variations along the axis of smallest inductance which is the
sourceinverterisusedasswitchingconverterto supplypower d-axis or axis of the permanent magnets. In order to estimate
to the salient-pole brushless dc-machine. The controller has the rotorpositionwith sufficientaccuracythe currentrippleis
two parts, a conventional current controller and the position increasedbyintroducingdeviationsinthecontrolleroutput.In
estimator. The BLDC-drive is equipped with a single sensor [3],anenhancementisdiscussedforwhichthecurrentsamples
in the dc-bus only, measuring the dc-current. The current of normal control aren’t affected by the controller output
controller is a digital predictive current controller or current deviations. This method is referred to as seamless integration
2
period n period n+1 V e e e
24 a b c
i(n+1)
i(n)
degrees
0
i(n-1) 50 100 150 200 250 300 350 qel
-Vdc/2
d(n)Ts
Ts Vdc/2
Fig. 4: Three-phase back-emf at nominal speed
Fig. 2: Current programmed control: current and voltage
mH
i0 Tias i1 .a5veragei .5 ia iapredicted -.5 ip 9905
v 1.5
85
idc idc idc
80
qr
0
.25Ts .75Ts .25Ts .75Ts .25Ts .75Ts 2p/3 4p/3 2p
(a) duringsteadystate (b) duringtransient, (c) duringtransient, Fig. 5: Current programmed control: inductance as a function of
averagecurrentover predicted currentat rotor position
PWM-period endPWM-period
Fig. 3: dc-current idc and phase current ia, samples at 25% and
75% of PWM-period is closed (duty ratio equals one), while the upper transistor
of another inverter leg switches in order to chop the dc-bus
voltage to the desired phase voltage. In this paper, in order to
of the sensorless method in the current control loop. reconstruct the three-phase currents from the dc-bus current,
Particular attention is given to the current commutation. this conventional switching scheme is replaced by a centered
Duringandafterthisperiodthecurrentripplecanbedistorted PWM scheme and by complementary switching of the lower
due to a strong variation in the controller output. As the and upper transistor as is done in AC-drives. The duty ratio δ
estimator is used to detect the commutation moments, an of the phase with positive currentequals the controller output
estimation error affects on its turn the commutation current. (0.5≤δ ≤1), while the duty ratio of the phase with negative
The problem is illustrated in Fig. 14(a), the 60 degrees com- current is given by the complementaryvalue δ⋆ =1−δ. The
mutation threshold is crossed several times by the estimated resulting dc-currentand phase currentare shown in Fig. 3 for
rotor position, resulting in a distorted current commutation a single PWM period T . Samples are taken of the dc-current
s
shown in Fig. 14(b). To solve this, during commutation, test at 25% and 75% of the PWM period from which the average
signal injection will be removed. A commutation method phase current in that PWM period can be computed, used to
will be discussed to reduce the current ripple distortion after compute the current ripple in the sensorless algorithm:
commutation, resulting in a better position estimation.
i (n+1)=.5i (n)+.5i (n) (1)
v 0 1
A. Current Programmed Controller
For the purpose of predictive currentcontrol, the value of the
Insix step BLDC-drivesthe converteris steered in orderto
current at the end of a PWM-period is predicted by
have a current flowing in two phases only. After each rotor
displacement of sixty degrees a phase commutation of the i (n+1)=1.5i (n)−.5i (n) (2)
p 0 1
current occurs. The amplitude of the current is controlled in
ordertogeneratethedesiredtorque.In[4],apredictivedigital The current at the end of the PWM-period can be written as
current programmed controller for a single-phase switching the current at the end of previous PWM-period added with a
converter is discussed. The current controller is applied here variation.Thisvariationiscausedbythevolt-secondvariation
to BLDC-drives by taking into account the most important with respect to the steady-state voltage vr =Rir+em where
harmonics in the back-emf, Fig. 4 as well as the magnetic R is the total stator resistor and em is the induced voltage of
saliency in the machine on the current. As the latter two thetwophasesthroughwhichthesteady-statecurrentir flows.
depend on the rotor speed and position, a sensor is often Asduringtheperiod(2δ−1)T thevoltageV isappliedand
s dc
applied, replaced here by position estimators. As the current during the remaining PWM-period (2−2δ)Ts the voltage is
commutates between the phases, the phase inductance values zero over the two-phases, it follows that
hastobeknownover120degreesonly,resultinginaperiodic
functionoftherotorpositionasshowninFig.5.Theback-emf i(n+1)=i(n)+∆i(n) (3)
isobtainedfromtheestimatedspeedandopen-circuitinduced
where the current varation of PWM-period n is given by
voltage at nominal speed, stored in a look-up table.
To control the amplitude of a current flowing through two V −v v
phases only, often the lower transistor of one inverter leg ∆i= dc 0(2δ(n)−1)Ts− 0(2−2δ)Ts. (4)
L L
3
δic δvc τq,τd the synchronous time constants of q- and d-axis, can
be approximated by
d-axisNS γδ′ γqδ-axis δicI -2γδ−∆γδ−π/2 δicq = Lτqδvqc and δicd = Lτdδvdc, (7)
S θr δvc independentof the stator resistor R as wellas rotorspeedΩ.
s
N u δicII Toestimatetherotorpositionθr,anauxiliaryangleisused:
(a) Suppliedvoltage (b) Setofcurrentresponsesfortestsignalsδvc theangleγδ ofthevoltagevectorδvc(δvqc,δvdc)withrespectto
deviation δvc and ofequal modulusanddifferent angleγδ. theq-axis,Fig.6(a).Asthesetvalueofthevoltagetestvector
currentresponseδic in
iscomputedbythecurrentcontroller,itsdirectionisknownin
theqd-reference frame
fixedtotherotor. the stationary αβ-reference frame and given by γδ′. From this
and by estimating the auxiliary angle γ , an estimation of the
δ
Fig. 6: Average space vectors used in sensorless control rotor angle θ is obtained as θe = γ′ −γe where xe denotes
r r δ δ
the estimation of x.
The set of current responses for test vectors of equal
From this, the duty ratio δ(n) can be obtained which resulted
modulus and for γ = 0...2π is shown in Fig. 6. This
in PWM-periodn inthe currentvariation∆i(n)=i(n+1)− δ
set of responses is positioned on a circle and is often used
i(n)
in sensorless methods to estimate the rotor angle θ . A
L V −v r
δ(n)= ∆i(n)+ dc 0. (5) parameterlessestimationmethodisused.Forthispurpose,the
2TsVdc 2Vdc current response on a second test vector is measured. From
the first test period, a current response δic (δic ,δic ) is
Using this equation for the duty ratio δ(n +1) of the next xy,I x,I y,I
measured. The modulus of the second test vector deviation
PWM-period, a system of two equations is obtained from
δvc is choosen equal to the modulus of the first test vector
which the current i(n) van be eliminated. Then, controlling II
deviation δvc: ∆vc = ∆vc = ∆vc. However, the vector
thecurrentsothati(n+1)equalsthedesiredvalueic,requires deviation δvcI hasIIa directiIon of γ + ∆γ . The auxiliary
a duty ratio in PWM-period n+1 that equals II δ δ
angle γ has been previously computed as a function of the
δ
δ(n+1)= L (i −i(n−1))+1−δ(n)+ v0 . (6) current responses and is given as
c
2TsVdc vdc 1 δic −δic 2∆γ +π
γb = arctan y,I y,II − δ . (8)
δ 2 δic −δic 4
x,II x,I
B. Estimation of the PMSM rotor position
The sensorless methoddiscussed here can be used in many
Inasalient-polePMSMthephaseinductancesvarystrongly
ways.ApossibleimplementationisgiveninFig.7showingthe
with the rotor position. As a result, the response of the phase
duty ratios, resulting phase voltages and phase currents. The
currents on a voltage deviation from the controller output
dashed lines correspond to half a PWM-period. Each three
dependsontherotorposition.Basedonthisvoltagedeviation,
PWM-periods, test signals are avoided for a single PWM-
in [1], a low-speed position estimator is implemented on a
period during which the average current is measured. From
voltage-sourceinverter(VSI)suppliedPMSM.Inpractice,the
this average current value the predictive controller computes
voltagedeviationsaregeneratedbymodifyingthewidthofthe
the steady-state duty ratio for the next three PWM-periods.
pulsedphasevoltages.Bymeasuringthecurrentripplecaused
Duringthetwo PWM periodsthatfollowsthePWM in which
by the average voltage deviation, an estimation of the rotor
the average current is measured, test signals are added to the
position is made for the purpose of vector control.
steady-statedutyratio.Forthesix-stepBLDC-drive,onephase
In the following, space vectors are used that correspond to
has an average zero value as can be seen in this figure. The
the average value over a time period τ. For sufficiently small
current ripple due to the injection of test signals is clearly
times, the linear small-signal machinemodelis valid by good
visable.Anadvantageofthesensorlessmethoddiscussedhere,
approximation. Hence, the current difference over a time τ
is the negligible influence of the test signals on the average
and caused by a pulsed test signal can be computed by the
current. The current values before and after a test period in
test signal average value over τ. The waveform of the test
whichtestsignalsareinjectedarethesamewhichbenefitsthe
signal has no influence on the current difference and in this
controller as well as the estimator performances.
paperapulsetrainisusedgeneratedbya switchingconverter.
In case the test signals are generated by using a VSI with
PWM, it is convenientto choose the PWM-period or half the C. Using a single sensor
PWM-periodasperiodτ. Inthatcase, theaveragecomponent Test signals are applied in order to introduce a measurable
of the test signal is controlledby the duty ratio that steers the ripple from which the position can be estimated. In Fig. 8(a),
PWM. the phase current, dc-current and sampled dc-current at 25%
In [1], average space voltage vectors, with components vc, and75%ofeachPWM-periodareshown.Fromthis,itfollows
q
vc in the synchronous qd-reference frame, are used in order that the dc-current amplitude corresponds to the amplitude
d
to represent the test signals. The voltage deviations δvc, δvc of a single phase only. To measure the three-phase current
q d
fromthesteady-statevoltagev ,v aredenotedbyδvc and ripple from samples taken by a sensor in the dc-bus only, a
q,0 d,0 q
δvc respectively. It is then shown that the resulting current modifiedPWM-schemecanbeused.BymodifyingthePWM-
d
variations δic, δic after a time τ << min(τ ,τ ), with modulation of one phase from centered to tailing edge, it
q d q d
4
25 ia Dib Dib 25 ia
2.2 torque (Nm)
15 idc 15 idc
5 5 Dic
0 ic 0 ic
-5 -5
2.1
-15 -15 Dia T
s
(A) -25 ib -25 ib
0.5 t (s) t (s)
iA 0.0139 0.014 0.0141 0.0139 0.014 0.0141
0.4
(a) fixedsamplingmomentsat25% (b) modifiedsamplingmoments
0.3 and75%ofPWM-period duringtestPWMperiods
0.2
0.1 Fig. 8: Sampling of dc-current
iC
0
-0.1 1 TA+ 1 TA+ 1 TA+
-0.2 0 0 0
1 TB+ 1 TB+ 1 TB+
-0.3
iB 0 0 0
-0.4 1 TC+ 1 TC+ 1 TC+
-0.5 0 0 0
1 TA- 1 TA- 1 TA-
vA(V)
25 0 0 0
1 TB- 1 TB- 1 TB-
0 0 0 0
1 TC- 1 TC- 1 TC-
-25
0 0 0
vB(V)
25
0 0.1 0.2 0.3 t (ms) 0.3 0.4 0.5 0.6 t (ms) 0.6 0.7 0.8 0.9 t (ms)
0 (a) devations along (b) devations along (c) devations along
u-phase v-phase w-phase
-25
vC(V) Fig. 9: Stearing signals to generate voltage vector deviations,
25
centered PWM
0
1 TA+ 1 TA+ 1 TA+
-25
0 0 0
1 TB+ 1 TB+ 1 TB+
0.5
da 0 0 0
1 TC+ 1 TC+ 1 TC+
0
0 0 0
-0.5 1 TA- 1 TA- 1 TA-
0 0 0
0.5 db 1 TB- 1 TB- 1 TB-
0 0 0
0 1 TC- 1 TC- 1 TC-
0 0 0
-0.5
0 0.1 0.2 0.3 t (ms) 0.3 0.4 0.5 0.6 t (ms) 0.6 0.7 0.8 0.9 t (ms)
0.5 dc (a) devations along (b) devations along (c) devations along
u-phase v-phase w-phase
0
-0.5 Fig. 10: Stearing signals to generate voltage vector deviations,
tailing edge PWM
t (ms)
0 1
stearingsignalsforthesixtransistorsinthecaseofacentered
Fig. 7: Waveforms of duty ratios, voltages and currents. PWM-methodandamodifiedPWM-method.Grayareasshow
the differences between both strategies.
followsthatthedc-currentcanbeusedtomeasuretwophases. D. Commutation
Thisisshownin Fig. 8(b).Samplingthedc-currentat theend Previoussectionsdiscussedthesensorlesspredictivecurrent
of the PWM-period results in a sample for the c-phase and controller for which the current is controlled to a given
a-phase. As the sum of phase currentsis equal to zero, the b- value i . This section deals with the period during which the
c
phasecurrentcanbecomputed.Adisadvantageofthismethod currentcommutatesfrom one phase to another. As mentioned
is the delay between samples taken for each phase. However, before, test-signal injection is avoided during commutation.
signal-injection methods are mostly used at low speed for In most BLDC-drives, the commutation is done by using
which the rotor position variation over several PWM-periods a duty ratio equal to one as the maximum voltage results
can be neglected, introducing a small estimation error. in a fast commutation. However, such strategy affects the
Many PWM-modifications can be developed in order to currents, resulting in an important torque transient. A smooth
measurethe phasecurrentsfromasingle currentsensorin the transition is obtainedhere by computingthe duty ratio during
dc-bus. One possible case is given in Figs. 9-10 showing the commutation. In that way the time gradient of the current