pf-014893 - iecon'06 - petrella.ppt [modalità compatibilità]
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Speed and Position Estimation for PM Speed and Position Estimation for PM nc
en
ce
CE
CE Speed and Position Estimation for PM Speed and Position Estimation for PM
PF-014893
Speed and Position Estimation for PM Speed and Position Estimation for PM Synchronous MotorSynchronous Motor usingusing
S lfS lf C t d B kC t d B k EMF ObEMF Ob Co
nfe
ren
Co
nfe
ren
is, F
RA
NC
is, F
RA
NC Speed and Position Estimation for PM Speed and Position Estimation for PM
Synchronous MotorSynchronous Motor usingusingS lfS lf C t d B kC t d B k EMF ObEMF ObSelfSelf--Compensated BackCompensated Back--EMF ObserversEMF Observers
ec
tro
nic
s e
ctr
on
ics
2006
20
06 ––
Par
iP
ari
Marco TURSINI Marco TURSINI Roberto PETRELLARoberto PETRELLA Alessia SCAFATI Alessia SCAFATI
SelfSelf--Compensated BackCompensated Back--EMF ObserversEMF Observers
ust
ria
l Ele
ust
ria
l Ele
ber
6b
er 6
--10,
210
, 2 Marco TURSINI, Marco TURSINI, Roberto PETRELLARoberto PETRELLA, Alessia SCAFATI, Alessia SCAFATI
University of L’AquilaUniversity of L’Aquila
EE
E In
du
EE
E In
du
Nov
emb
Nov
emb University of L AquilaUniversity of L Aquila
Dept. of Electrical and Information Engineering (DEIE)Dept. of Electrical and Information Engineering (DEIE)
University of UdineUniversity of Udine
32
32
nd
nd
II
SS16SS16 1 1 Ad d t l d b ti f AC d i
University of UdineUniversity of UdineDept. of Electrical, Managmt and Mechanical Eng. (DIEGM)Dept. of Electrical, Managmt and Mechanical Eng. (DIEGM)
Thursday, November 9Thursday, November 9thth, 2006, 8:00 AM, 2006, 8:00 AM
SS16SS16--1 1 Advanced control and observation of AC drives
PF-014893
Aim of the paperAim of the paperAim of the paperAim of the paper
- provide full analytical description of previously-proposed speed andposition observers for PM synchronous motors, based on back-EMFestimation
- calculate the (steady-state) rotor position estimation errorss
- propose a real-time compensation strategy for rotor position estimationerror in a transducer-less PMSM drive
- validate analytical results by means of simulation analysis and comparey y y pthem with experiments
PF-014893
TransducerTransducer--less drive schemeless drive scheme*αv
*qv
*qi
*rω
SVRiqRvel dq*dv
*βv PWM
Rid αβ
0=*di
dv βv
dq αβqi αiib
iaˆ
ˆ
Luenberger/Sliding Mode
αv
v
αi
iαβ 3βidi
ibic
ˆ
rsinθθ
αˆiv βˆivrθ *
gObserverβv βi
Observerrω
* * i i PMSM
rcosθ
KalmanFilter
)(θ 1rsin
)(θ 1rcos
αv βv αi βi PMSMFilter)(ω 1r
⎟⎠⎞⎜
⎝⎛ += 22
βαβ ˆˆˆθ iiir vvvarccos
PF-014893
Permanent Magnet Synchronous MotorPermanent Magnet Synchronous Motor
ωr dβs
iβ
Hypothesis:Hypothesis:
-- symmetricalsymmetrical--sinusoidal machinesinusoidal machine
θr
qβ vβ
yy
-- non salient rotornon salient rotor
-- represented by tworepresented by two--phase phase
αsαN
equivalent statorequivalent stator--fixed fixed αβαβwindingswindings
vαiαS
[ ] [ ] [ ]vBvBiAi i −+=&
Dynamical model:Dynamical model:
[ ] [ ] [ ]vBvBiAi i+
Tiii ],[ βα=T
[ ] [ ]IAssLR−=
Tvvv ],[ βα=
Tiii vvv ],[ βα= s
[ ] [ ]IBsL1−=
PF-014893
BackBack--EMF and PMSM Extended ModelEMF and PMSM Extended Model
The backThe back--EMF components contain the information on the rotor position:EMF components contain the information on the rotor position:
rreri
rreri
kvkv
θωθθωθ
β
α
cos)(sin)(
=−=
In order to arrange backIn order to arrange back--EMF observer, backEMF observer, back--EMF components are added EMF components are added to the state through a couple of fictitious dynamic equations:to the state through a couple of fictitious dynamic equations:to the state through a couple of fictitious dynamic equations:to the state through a couple of fictitious dynamic equations:
[ ] [ ] [ ]0
−+= iv
vBvBiAi&
&
0=iv
Tii ][ Tii vviix ],,,[ βαβα= Extended stateExtended state
PF-014893
State and disturbance observersState and disturbance observers
[ ] [ ] [ ] zvBvBiAi i +−+=& ˆˆˆ
[ ]zLvi =&
[ ] )( iiK ˆ [ ] )( iiK
Luenberger observer (LO)Luenberger observer (LO) Sliding mode observer (SMO)Sliding mode observer (SMO)
[ ] )(1 iiKz −⋅= [ ] )( iisgnKz −⋅= 1
)(][][][ ~ˆ~ˆ iiKvBxAx)& −++= )(][][][ ˆ~ˆ~ˆ iisgnKvBxAx −++=&)(][][][ )(][][][ g
[ ] [ ] [ ][ ]TIklIkK Gain matrixGain matrix[ ] [ ] [ ][ ]TIklIkK =
k,k, ll Gain coefficientsGain coefficients
PF-014893
Why and how to develop a compensation law ?Why and how to develop a compensation law ?Rotor position estimation error (difference between estimated and actual Rotor position estimation error (difference between estimated and actual position) dynamics: position) dynamics:
[ ] [ ][ ] [ ]iie
ieii
eklveekeBeAe
−−=
−+=&&
&If known, they it can be onIf known, they it can be on--line compensated !line compensated !
Solution of the problem is difficult in the timeSolution of the problem is difficult in the time--domain.domain.
Let us consider the equivalent sLet us consider the equivalent s--domain transfer functions:domain transfer functions:
( ) [ ] ( ) [ ] ( ) ( )sEksEBsEAesEs +
Af l l iAf l l i
( ) [ ] ( ) [ ] ( ) ( )( ) ( ) ( )sEklsVesEs
sEksEBsEAesEs
iiee
ieiii
−−=−
−+=−&
0
0
After some calculations:After some calculations:
( ) ( )( ) ( )sVssss
LsE i
si
&
21
1−−
= ( ) ( )( ) ( )sVssss
hssE ie&
21
2−−
+−=( )( )ssss 21 ( )( )ssss 21
sLlm −=jhhs Δ±−=Δ±−=21, ( ) ( ) mkLRkLRkh ssss −+=Δ+= 241
21 ;
PF-014893
BackBack--EMF estimation errorEMF estimation errorThe asymptotic stability is a sufficient condition for the existence of the The asymptotic stability is a sufficient condition for the existence of the sinusoidal steadysinusoidal steady--state response to sinusoidal excitation: state response to sinusoidal excitation:
( ) ( )⎥⎥⎦
⎤
⎢⎢⎣
⎡
+
+=
= )φω(ω)φω(ω
ω ωωv
vr Frre
Frreve tsink
tcoskjFte 2
2
⎦⎣ v
( )⎪⎧ += )φω(α Frve tcosAte ( )( )⎪⎩
⎪⎨⎧
+=
+
)φω()φω(
β
α
v
v
Frve
Frve
tsinAtetcosAte
( )( )+Δ+Δ−−
−−Δ+Δ+=
= ωωω
ωω)(ω ωω )])(([
)()(222
222222
2
32
hh
hhhjF
rrr
rrv r ( ) 2ωω rervv kjFA =
Actual rotor speedActual rotor speed
⎟⎟⎠
⎞⎜⎜⎝
⎛
Δ+−−Δ
== )(
)ω(ωφωω 2
22
23
hhharctang rr
Frv
rω
PF-014893
Calculation of the rotor position estimation errorCalculation of the rotor position estimation error
αβαβ components of the estimated backcomponents of the estimated back--EMF:EMF:
)t(cosAtsink)t(evv ii φωωω ++−=+=
)t(sinAtcosk)t(evv
)t(cosAtsink)t(evv
v
v
Frvrreeii
Frvrreeii
φωωω
φωωω
βββ
ααα
++=+=
++−=+=
⎟⎞
⎜⎛ Fv φcosAˆ
Rotor position estimation errors:Rotor position estimation errors:
⎟⎟⎠
⎞⎜⎜⎝
⎛
+−=−
v
v
Fvre
Fvrr φsinAk
φcosAarctg
ωθθ Luenberger observerLuenberger observer
( )lLarctg srrr ωθθ =−
F i t f t t th ( t dF i t f t t th ( t d t t ) t iti t t ) t iti
Sliding mode observerSliding mode observer
For a given set of motor parameters, the (steadyFor a given set of motor parameters, the (steady--state) rotor position state) rotor position estimation error depends on rotor speed, but it is independent on feeding estimation error depends on rotor speed, but it is independent on feeding current (i.e. load torque)current (i.e. load torque)
PF-014893
Simulation resultsSimulation resultsSteadySteady state estimation errorsstate estimation errorsLuenberger SM O
Comments:Comments:
LO t iti ti ti LO t iti ti ti
SteadySteady--state estimation errorsstate estimation errorsg800 1600 16000 ∞ k←
-7.41 -6.22 -5.19 -5.08 1000 rpm
-16.97 -13.22 -10.37 -10.08 2000 rpm -- LO rotor position estimation LO rotor position estimation
errors tend to SMO ones for high errors tend to SMO ones for high values of gain values of gain kk
-32.63 -21.99 -15.52 -14.93 3000 rpm
Position error )( θθ rr − [degrees]
-- for the same value of gain for the same value of gain ll, , SMO has smaller estimation SMO has smaller estimation error with respected to LOerror with respected to LO-5
0
degr
ees]
-5.078
-- estimation error reaches nonestimation error reaches non--negligible values at high speednegligible values at high speed
-- compensation is possible by compensation is possible by
-10
mat
ion
erro
r [d
-14.928 -10.079-6.22
LO p p yp p yconsidering the analytical error considering the analytical error as a first attemptas a first attempt
-- actual implementation could actual implementation could -20
-15
Posi
tion
estim l = −28.28; k = 1600 -13.22
SMO
LO
LO
l = −28.28
l = −56.56; k = 1600-- actual implementation could actual implementation could
lead to different results due to lead to different results due to unun--modelled effectsmodelled effects0 500 1000 1500 2000 2500 3000 -25
Rotor speed [RPM]
P
-21.99 SMO l = −56.56
PF-014893
Simulation resultsSimulation resultsTransient estimation errorsTransient estimation errors0
1 Lu e n be rge r O bse rve r
Conditions:Conditions:
Transient estimation errorsTransient estimation errors
-3 -2 -1 0
on e
rror [
degr
ees]
0 .5e-3
P os ition es tim a tion e rro r C om pen sa ted pos itio n es tim a tio n e rro r
Conditions:Conditions:
-- offoff--line operation of the line operation of the observerobserver-6
-5 -4
Posi
tion
estim
atio
l 28 28lo ad in sertion
-- nono--load speed transient from 0 load speed transient from 0 to 1000 RPMto 1000 RPM
-- 1.2 Nm (60% rated) load torque 1.2 Nm (60% rated) load torque
0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .4 0 .4 5 0 .5 -8 -7
T im e [s ]
l = −28 .28 k = 1 600
-6 .2 2 lo ad in sertion
1 S lid in g M o de O b serve r1.2 Nm (60% rated) load torque 1.2 Nm (60% rated) load torque insertion at 0.35sinsertion at 0.35s
-- position estimation error is position estimation error is compensated by means of compensated by means of -2
-1 0
ror [
degr
ees]
-5 .5e -3
P iti ti ti compensated by means of compensated by means of analytical valuesanalytical values
-5 -4 -3
ition
est
imat
ion
err P o s itio n e s tim a tio n e rro r
C o m p e n sa te d p o s itio n e s tim a tio n e rro r
0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .4 0 .4 5 0 .5 -7 -6
T im e [s ]
Pos
i
lo ad in sertion-5 .08
l = −2 8 .2 8
PF-014893
Experimental resultsExperimental resultsThe drive systemThe drive systemThe drive systemThe drive system
Braking test bench
IEEIEE 488 t ll d h t i b k488 t ll d h t i b k
PMSM under test
IEEIEE--488 controlled hysteresis brake488 controlled hysteresis brake(Magtrol HD(Magtrol HD--710710--8NA8NA--0040)0040)
PMSM under test
rated power /current 630 W - 2.5 A rms (*) rated speed/torque 3000 rpm (*) - 2.0 Nm (*) pole pairs 4 no load back EMF @ rated speed 82 72 Vrms (*)no-load back-EMF @ rated speed 82.72 Vrms (*)stator resistance 1.9 Ω stator inductance 6 mH rotor inertia 22⋅10-5 kgm2 inverter DC voltage 300 V
Control & power electronics
1616--bit fixedbit fixed--point DSP microcontrollerpoint DSP microcontrollerIGBT intelligent power moduleIGBT intelligent power module
150 150 μμs control and modulation cycless control and modulation cycles
PF-014893
Experimental resultsExperimental resultsSMO operationSMO operationrω
uncompensated uncompensated
500 RPM500 RPM SMO operationSMO operation
)( rmonrˆ θθ , −
Conditions:Conditions:
-- nono--loadload99°°
500 RPM500 RPM
-- 500 to 2000 RPM500 to 2000 RPM
-- 500 RPM slow varying ramp 500 RPM slow varying ramp incrementsincrements
theoretical compensationtheoretical compensation
99°°
incrementsincrements
Comments:Comments:
-- noise is related to residual noise is related to residual noise is related to residual noise is related to residual “chattering” on the back“chattering” on the back--EMF EMF estimatesestimates
theoretical compensation is not theoretical compensation is not empirical compensationempirical compensation -- theoretical compensation is not theoretical compensation is not the exact one, but provides good the exact one, but provides good resultsresults
i i l ti i i i l ti i
p pp p
-- empirical compensation is empirical compensation is obtained by varying the slope of obtained by varying the slope of the compensating anglethe compensating angle
PF-014893
Experimental resultsExperimental resultsLO operationLO operationrω
uncompensated uncompensated
500 RPM500 RPM LO operationLO operation
)( rmonrˆ θθ , −
Conditions:Conditions:
-- nono--loadload99°°
500 RPM500 RPM
-- 500 to 2000 RPM500 to 2000 RPM
-- 500 RPM slow varying ramp 500 RPM slow varying ramp incrementsincrements
99°°
incrementsincrements
-- same gains as SMOsame gains as SMO
Comments:Comments:Comments:Comments:
-- position error has different slopeposition error has different slope
-- noise is lowernoise is lowerempirical compensationempirical compensationp pp p
PF-014893
Experimental resultsExperimental resultsSMO torque/speed analysisSMO torque/speed analysisSMO torque/speed analysisSMO torque/speed analysis
Comments:Comments:
-- load torque affects position load torque affects position estimation error (differently estimation error (differently from theoretical results)from theoretical results)))
-- the effect of the load torque the effect of the load torque is quite small (less than 2 is quite small (less than 2 degrees in every condition) degrees in every condition) degrees in every condition) degrees in every condition)
-- overover--compensation is compensation is obtained if theoretical laws obtained if theoretical laws are adopted (dotted lines)are adopted (dotted lines)are adopted (dotted lines)are adopted (dotted lines)
-- compensation with compensation with theoretical values leads to a theoretical values leads to a maximum error of 5 degreesmaximum error of 5 degreesmaximum error of 5 degreesmaximum error of 5 degrees
PF-014893
ConclusionsConclusions
TheThe possibilitypossibility toto compensatecompensate thethe intrinsicintrinsic rotorrotor positionposition estimationestimation errorerror inin aatransducertransducer--lessless controlcontrol schemescheme forfor PMPM synchronoussynchronous motorsmotors basedbased onon backback--emfemf observersobservers hashas beenbeen analysedanalysed::
-- itit isis possiblepossible toto evaluateevaluate aa theoreticaltheoretical compensationcompensation lawlaw forfor thethe steadysteady--statestate operation,operation, bothboth withwith LuenbergerLuenberger andand SlidingSliding ModeMode observersobservers
emfemf observersobservers hashas beenbeen analysedanalysed::
pp gg gg
-- suchsuch lawslaws yieldyield satisfactorysatisfactory compensationcompensation alsoalso duringduring fastfast transientstransients
-- itit hashas beenbeen provenproven thatthat thethe presencepresence ofof aa KalmanKalman filterfilter inin cascadecascade toto thethebackback--EMFEMF observerobserver doesdoes notnot introduceintroduce additionaladditional positionposition errorerror atat steadysteady--state,state, andand negligiblenegligible oneone duringduring transientstransients ifif slowslow rampramp--varyingvarying speedspeedstate,state, andand negligiblenegligible oneone duringduring transientstransients ifif slowslow rampramp varyingvarying speedspeedreferencereference isis usedused
-- thethe unun--modelledmodelled effectseffects inin thethe actualactual drive,drive, motormotor andand realreal--timetime systemsystemthethe unun modelledmodelled effectseffects inin thethe actualactual drive,drive, motormotor andand realreal timetime systemsystemintroduceintroduce somesome discrepanciesdiscrepancies fromfrom theorytheory:: exactexact compensationcompensation requiresrequiresaa properproper adjustmentadjustment byby experimentalexperimental teststests