Sensorless Speed and Flux Control Scheme for an Induction Motor With an Adaptive Backstepping Observer

7/21/2019 Sensorless Speed and Flux Control Scheme for an Induction Motor With an Adaptive Backstepping Observer

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2010 7th Inteational Multi-Conference on Systems, Signals and Devices

Sensorless Speed and Flux Conrol Sceme for an Inducon Moor w anAdapve Backseppng Observer

Ramz Tabels, Adel Khede, Med Fauz MmunFauz M'sahl

Monastir Engineering Schoolbn Eljazzar city, 509 , Monastir Tunisia

E-Mails:[email protected][email protected]@enim.u.tn [email protected]

STRCTis paper deas wit te stesis of a adaptiveoiear backsteppig-observer for sesoress speed adux backsteppig cotro of Iductio otor () drivewit oie rotor resistace adaptatio e acksteppigcotro purpose is ased o staiit aasis estabisedfrom Lapuov teor is approac takes sstemoiearities ito accout i te cotro sstem desigstage Cotroed rotor ux ad speed are give from aadaptive acksteppig observer e effectiveess of tisstrateg as ee success veried troug computersimuatios i terms of te efeece trackig aiit adthe robustess agaist parameters vaiatio

x Ict t Bcktppg ctLypv tty cktppgv ct.

NTRODUCTION

Iductio motor () compared to oter eectric

macies, are used i a wide rage of idustriaappicatio, due to its exceet reiaiit, greatobustess ad ess maiteace However, te cotro ofte iductio motor is compex ecause te damicsmode of te macie is oiear, mutivariae, igcouped ad ma state variaes are ot easimeasurae ad te are depedet o te macieparameters variatios [14]e covetioa iear cotro of M ca't keep tesstem trasiet staiit i te situatio were operatiocoditio ad parameters cage wit temperature admagetic saturatio [] It was sow i te iterature tatte oiear mutivariae damic mode of te ca

be exact iearized usig oiear precompesatioso tat iear cotro teor ca be used wie preservigte oiear ature of sstems However, tis teciquerequires te exact mode of te sstem ad caces usefuoiearitiesOe of te most sigicat deveoppemet i tis areaas bee te ed oieted cotro proposed Bascke[4] However, tis strateg is ver sesitive to parametersvariatio. We te macie paameters cage wittemperature ad magetic saturatio, te performace ofte sstem wi be deteriorated. o improve ed oietedcotro, ma modied oiear state feedback scemesave bee poposed suc as, sidig mode cotro, iput

output iearizatio cotro, passivit ased cotro,atess-coto, direct torque cotro, oiearpredictive cotro ad backsteppig cotro.e advaces i oiea cotro teor ave caused a

9784447546/0/$6,00 mO 0 EEE

otae impact o te cotro of iductio motor []Backsteppig tecique as a powerfu too is appied tooiear cotro to preserve te usefu oiearities[1]. is tecique is more suitabe for te situatiowee te sstem mode as ukow parameters.I te ast two decades, te acksteppig tecique asbee wide studied ad deveoped for te cotro ad

state estimatio proems sice te studies ofKaeakopouos, Kokotovic ad orse [8] is cotrotecique aows a good stead state ad good damicbeaviour i te presece of sstem parameters variatioad disturaces [3], [4-5] Severa acksteppigcotro metods ave ee preseted to iductio motordrives. I [5] te oiea adaptive backsteppigcotro is desiged to compesate te ukow sstemparameters ad disturaces. I [3] a ew adaptivebacksteppig cotroer tat acieves goa asmptoticrotor speed trackig for te fu-order, oiea mode ofa iductio motor despite te ucertait i rotorresistace ad time-vaig oad toque coditios. I

[4] a robust adaptive backsteppig cotroer foreciec optimizatio of M wit ucertaities isdesiged. e ack steppig cotro is appied toiductio motor drive wit good traectories trackigpeformace for [], [6-7] However, te performaceaccurac is affected b oad toque ad te macieparameters ucertaities. o overcome tis poem, arotor resistace estimatio tecique is give i tis paperto compesate te ukow variatios, te maorcotriutio of tis paper cosists o te roto resistaceestimatio ased o te adaptive backsteppig oserverSome researces ave proposed various drives witoie rotor resistace or rotor time-costat adaptatio

[], [3] ad [5-7] to produce etter cotro performance,suc as a sidig mode osever, a mode refereceadaptive sstem ad Lueerger oserverI tis pape, a ew adaptive backsteppig oserver isdeveoped for te simutaeous estimatio of te rotorux compoets ad of te rotor resistace for a uder te assumptio tat o te stator currets ad temotor speed are avaiae for measuemet. ecotroer of is desiged ased o acksteppigtecique. additio, a adaptive aw ased o teLapuov staiit teor estimates te rotor resistace.e comiatio of tese two metods represets bot acotriutio of tis work ad a good possibiit to

acieve cassica cotro obectives for sstems avigumodeed or parasitic damics ad parametricucertaities.is paper is orgaized as foows: Sectio provides a



2010 7th Inteational Multi-Conference on Systems, Signals and Deies

detaed rotor ed oreted damc mode. e wetroduced te stess of te oear Backsteppgcotro. I secto 4, te Backsteppg ux observerprovded wt a adaptato of te rotor resstacevaratos s treated. e stabt stud based oLapuov teor s preseted secto 5. Smuatoresuts are ustrated ad dscussed secto 6.

. ROTOR ELD ORENTED M DYNAMC MODEL

e equvaet tow-pase mode of te smmetrca ,uder assumptos of ear magetc cruts ad baaedoperatg codtos, s preseted a referece rotatgframe (d-q) [11-1], as

d dt Is d= - r ls d +W

lsq

+ a d + o· q + u s d

(1)

were te state varabes are te stator currets ( is d' isq) ,te rotor uxes ( d' q) ad te eectrca rotor speed w .e stator votages ( u sd u sq) ad sp freque

w,

/

(

w,

/ =W

,- ) are cosdered as te cotro varabes.

te costats are deed as

M2 M2 R "=R,+

2

R

= - ,L

L

,

L

1= J , r= R", a= .

e eectromagetc torque expressed terms of testate varabes s gve b:

()

B cosderg te rotor vector ux ad to drect axs,te ducto motor equatos te scroous rotatgreferece frame are wrtte te foowg form:

{. W = ; . ( r d = 1 2; . is d = h j

U

,

d

;dt dt dt .

. isq = h + USq; . O s= w + w s /· dt dtThe sleep anglar speed is gen by:

isqw,

/ = Ma 4) d

The nctons dened in the aboe q. are gien by:

n p 1j - r I - wj- e dsq J J

= Ma isd -a d

ad

n �M = e

5)

e cotro obectve s to make te output varabes

(eectrca rotor speed w ad te rotor ux d) track a

desred traector; ts trackg ca be aceved troug abacksteppg agortm b dg a drect reato betwee

output ad ts cotro put (stator votages ( u sd' u sq)).ereaer, oe wses to ggt te robustess of teobservato ad te cotro agortm at varous speedscearos accordg to oad torque ad te rotor resstacevaratos.

. PEED AND LUX BACKSTEPPN CONTROLLER

e Backsteppg cotro mecasms for te rotoraguar speed reguato ad te ux geerato ca bebetter apped to repace te tradtoa oear feedbackpus proportoa-tegra PI cotro of te ed oretedcotro tecque to esure better performaces. e bascdea of te Backsteppg desg s te use of te so-caed

"vrtua cotro to sstematca decompose a compexoear cotro desg probem to smper ad smaeroes. Backsteppg desg s dvded to varous desgsteps. I eac step we esseta dea wt a easer, sgeput-sge-output desg probem, ad eac step provdesa referece for te ext desg step. e overa stabtad performace are aceved b a Lapuov teor for tewoe sstem [], [ 1-1]. e stess of ts cotro cabe aceved tree successve steps. Step 1

I te rst step, t s ecessar tat te sstem ca foowa gve traector. It correspods to make te desg of acotroer to esure a good trackg ad reguato. we

dee=( w c , c ), were ad c >0 are speed adu refeee traetoes. e speed trakg eror em ad

te ux magtude trackg error er are deed b:{m= W e- w 6r= e- d

Usg q. () ad te dervatve of q. (6), oe obta:�m �e (7)r - e 12

However, te trackg performaces w be satsfactor fwe coose te rst Lapuov caddate fucto

I assocated to te ux ad speed errors:2 2m +¢V j=

8

Usg q. (7, te dervatve of q. (9 ) s wrtte as foows



2010 h nen -neence n ses, ns n Deces

9

erefore, te derivative of te Eq. (8) ecomes egativedeite suc as: k 2 k 2

V j=- jO- 2 ¢Wit

kjad

k2are positive parameters.

1

o satisf te coditios metioed aove, it is ecessar tosatisf te foowig equaities O= c - =- kjO

1 ¢= c - d=- k2 ¢

Eq.(1) permits to geerate tese referece currets assuredte Lypuov staiit coditio. ese currets are give:

{(iSdC= ( c + d + k2 ¢ M

1 k I sq c - W c + + W + O k d J J

i S 2

I tis step, we tr to make is d ad isq ecomes as

desired i te previous step. Let us dee oter errorsetwee te currets ad teir refereces =( is d>C - isd

4q ( isqc - isq

akig te derivative of Eq. (4), we otai:

{� (S dC -S d 151q -( lsqc - lsq

Wie sustitutig Eq. (3) i te derivative of Eq. (14), weotai:{ =( sdc - sd=( sdC } - u sd

6eiq=( lS q)c - Isq=( lS q)c -1 4- f US q

Settig Eq. 3 i Eq. (4), we otai:

{ e=

M l

( c + a r r d + kz e¢) - is da

1

eiq=-

( w c + 7 + w + kj eO- lsq kc d J J S 3

ince he rea ips coans o he achine ( u sd' u sq

hae aeare inEq. 16),

e can go o he na sep. No, e ene a ne yano ncion bse on he errors o he spee, he a he staor crrens

8

he eriaie o Eq.18 is gie by:

Vz= O O+e��+ + 19 o lq lq

By

seing Eq. 5 iE.

8, oe obain:

Vz=- kj!- k2 : - kA - k +/ k +( S qc -1 4- u sq+'q ( k4 +( sdC } - u sd

3

0I

order to make te derivative of te compete Lypuovfuctio Eq. e egative deite, te quatitiesetwee pareteses i Eq. (), are cose equa to zero.

{ k 3 eid

: (

�S q)c

= h

f U S q

: 0

1 k ( lsd>C } u s d -qe stator votages cotros are give :

U

d

= ( k 4ei + ( d)C -})I f

Uq

=( k3 : +(

)c

-h)1

Were k3ad k4are positive parameters seected to esure

tat te damics curret coverge is faster ta tose ofte u ad speed.

4. DAPTVE B CKSTEPPING OBSERVER

I tis sectio we wi propose a ew agoritm asedo Backsteppig oserver uder te assumptio tat ote stator currets ad votages are avaiae formeasuremet. e Backsteppig u oserver (BFO) isased o te error of te stator currets geerated from teirmeasured ad estimated vaues wic must e covergedtowards zero [], [5] ad [-1].We cosider te stator currets as te sstem outputs,

YI=I' yz=z 3

e BFO ca e costructed as;

j= - Y Xj + ka rx 3 + kmX 4 + f

u

s

a

+ V i 2 = - # 2- kW rX 3+ ka rx4 +

f

u

p + v p

3= M x - x3- X4

4= M x2+X3- x4were,

4

X I X z X 3 x 4 r= [ is a ( p r a r p J' 5

A

R a=a + a

= +, R = R + M 6 L L

s

ad

R R Mfar

=

_A

=

_A

+

= r+ raL aL

aL

7

were X is te estimatio of X for iE {,,3,4} . ad

v are te cotro iput to e desiged acksteppig

metod. So, a parameters of ductio motor w ecosidered as costat except rotor resistace. e rotorresistace R is cosidered as ucertai parameter wit R as its omia vaue.We dee state error equatio as foows:

=y

= j- j[ = 1 ] Y - z z

ad

8

9

were ad te stator curret ad te rotor u

oserver errors, respective.



2010 7th Inteational Multi-Conerence on Systems, Signals and Devices

Usig Eqs.(3), (4), () ad (), te damicaequatios for te predictio errors are 5. AD PTIVE LAW O ROTOR AND STATOR RESIST NCES AND

( A A ) STABLTY ANALYSS ex =- rex + k (a ex + 0 ex ) + Lm X4+ La ( MXj-X 3) -v , , o desig te oserver ad parameter updatig aws, oe

, =- r e, + k ((- me +a e)-Lmx 3+ La ( M2-X 4)) -v p can dene the following Lyapunov candidate.

= (- +a +mx3+a ( M2-x4were /0 = 0 6

(30)I order to sove te trackig proem, ad to overcome tedicuties tat arise due to te uavaiaiit of oe of testate variaes for measuremet [111], a oieartrackig cotroer is proposed usig te oserver asedack steppig agoritm.i Step 1e rst step i te acksteppig oserver, is to desig astae cotroer for te itegra of te predictio errors

ev, usig ' as virtua cotro variaes wit

staiizig fuctios Y ,Y ), were Y ad Y are p preferece traectories for virtua variaes. coordiate trasformatio is itroduced for te sstem,te we coose te itegra of te currets predictio errors

, as foows p = (31)

ad we dee te trackig errors ad Z of te trackig

predictio currets errors y ' ,

Z = -Y (3) ZP = -Yp

Kowig tat te oservers damics is ased o teexpoetia covergece, we ca impose te variatios ofte referece traectories for virtua variaes as foowsY -

(33)Y

:

Cp � i S 2I tis step, settig te Eq.(33) i Eq.(3), we ca d te

expressio of te trackig errors ad

Z : ] + (34) - + pUsig Eqs.() ad (3), we ca compute te derivative ofEq.(35)

1 ( m ; Ve + +Z +Z + + + + Xu x 1 r

(37)Were r ad { are positive desig costat of adaptive

gai. e derivative of aog te damics of Eqs.(3),

(34) ad (37), ca e expressed as:

k k + R ( - k Z + - k 3

L L L

1 + --+ + +3 L r t

1 m n k( - + { t(38)

So tat te u n ov fuctio is deed positive ad itsderivative deite egative it is ecessar tat:

k k x 3 e M r( z ax 3 - kJz ax j + z x 4 - kJz X 2 _ 1

L L L 1 R

+ Jxje

4 + Jx 2 e +_

r

)=0

1 L r t n

1 m n k( - + = { t

(3)

wic eads to write te mecaism of adaptatio of terotor resistace ad rotor speed are foows:

_

r= ( r ( kJZ X 2 + ' - Jx j e + -- Jx 2 et

L

L (40) k k- + k - L L

6. MULATON RESULTS

(41)

lza -rex] + (aex; + mex) + LmX 4 + LaMj -Xl - Va + �ex] We preset i tis sectio te simuatio resuts of te

zp = -rex, + k ((-m ex + a ex) -Lm X 1 + La (M2 - 4 - v f + �ex, proposed control strategy applied to the two horse power

(35)ad seectig foowig cotro iputs

k(a + +mx4 + + +

v k(- m +a -mx3 + +Z + (36)

were ad are positive desig costats tat

determie te cosed oop damics.

4

squirre cage 1M e caracteristics of te 1M are

summarised i tael e parameters k kz' k3ad k4of

te acksteppig cotro are cose as foows:

kj=60, kz =0, k3 =1 000, k4 =1000. e deveoped

cotro aw supposes tat o te stator currets ad te




stato votages ae avaiae. The blck iaga of the sow te impovemet of te pefomaces of te poposed

contol syste is given b igre 1. coto ougt te oie oto esistace aaptatio.

We ave mae some sceaios of fuctioig i ode to ese esuts sow tat te acksteppig coto wit te

caacteise a impove te pefomaces of te coto poposed oseve ca tack te efeece coto accuate

stuctue. ad quick at ig ad ow spees. Fo te poposed

coto agoitm wit oie oto esistace aapte, we

a

L

A B"kst

Figue1: Bock diagam of te esiged ive sstem.

1) st sceaio cosists to test te tackig spee of te

macie cosideig te omia coitios witout

paametes vaiatios. e efeece spee taecto is

cose as tapezoia fom. e macie sigas esposes

ae iustate gue.

3) secod sceaio cosists to test te sesitivit of te

sstem pefomaces to cage o te oto esistace wit

aaptatio a oa toque at ig/ow spee. We itouce,

at te time t=.5s, a oa toque equa to 4 N.m a

espective at t=1s ad t=3s we ave itouced a

icease of oto esistace equa to 5% a 1%,

espectiv. e coespodig esuts ae iustated

gues 3 to 6.

It is cea fom g.(a) tat te popose appoac ased

1M ive sstem ca foow te efeece spee witout a

ovesoot ad stead-state eo. Fig.(c) pesets te

efeece, ea ad oseve magitue oto ux. e oto

ux efeece is kept at its ated vaue of .9 W. ese

esuts pove tat te speed tackig is quite good ad tat

te oto e is awas we-oieted. B g.3 ad g.4,

we peset a woe of te compaative ecodigs wic

5

ave ecoed a good espose fo te oto speed. ese

esuts pove tat te speed tackig is quite goo a tat

te oto e is awas we-oieted.

T b d f t · : n uc On o or eparame

es

Nominal power 1.5 Kw

Nominal Voltage 230/400 V

Nominal current 3.2/5.5 A

Stator resistance 5.717 nRotor resistance 4.282 nStator inductance 064 H

Rotor inductance 064 H

Mutual inductance 0417 H

Number of pole pairs 2

Moment of ineria 0.0049 Kg.m

Viscous friction coefficient 0.0029 N.m.srad

7. ONCLUSON

I tis pape, we ave eveope a sesoess cotoaoud te Backsteppig stuctue fo iuctio moto dive

usig ot Backteppig stateg a Lapuov staiit

teo. e poposed stuctue cosists i te Backteppig

oto spee ad oto ux oseve associate to oie

aaptive oto esistace estimatio. is coto caies out

asmptotica te output vaiaes pocess towads a

efeece mode estaised statig fom te esie

pefomaces fo te cose oop sstem. e stu of te

used oseve coms its oustess i tems of te

paametic vaiatos a extea istuaces. e

isetio of a adaptive mecaism of oto esistace

cosoidates of avatage te oustess caactes of te

sstem. e otaied esuts sow tat te Backsteppig

oiea coto wit a Backteppig oseve is oust

wit espect to paametic istuaces.



2010 7th Iteatioal Multi-Coferece o Systems, Sigals ad Devices

z u

,

Refeene Osee

°

L

�

�

�

�

�

�

,<Tomes

35

r

3i 25

i 2 .

-

' 15

i"t

°

o(b)

·

1

0

0

��

d)Tms

igure 2. Sensitivity of the system performances to change in the reference speed; (a) reference, real and estimated rotor speed; (b) real and observed magnitudestator current; (c) reference, real and observed magnitude rotor ux (d) electromagnetic and load torque.

--------

I

0

,

�

T J

o �c

<

1

�

¥

�

�

I

J

/e :

:

-

�

•

! il

�

o

o

� ; j

igure 3. Sensitivity of the system performances to change on the rotor resistance with on-line adaptation and load torque at high speed; (a) Load torque; (b)Actual and reference speed; (c) Reference signal of Rr; (d) Estimated and reference speed; (e) Motor and load torque; ( Rotor speed error; (g) Observer

magnitude stator current; (h) Observer magnitude rotor ux; (i) Observer current error; ) Observer ux error.

6




h �__-_____

__:

_=_�

j

_

5a-

.

_____ 6 •4 r----.0

i;r -

o

� 5

I E

•

g

I:

I

:

- o 1 3 5i

�.----------------------·

-2

�

-200

(b).---------------------- 502 50 49.8U-

d

'00 1 2 3 5�

J

5h

1

j

Figure 4. Sensitivity of the system performances to change on the rotor resistance with on-line adaptation and load torque at low speed; (a) Load torque; (b)Actual and reference speed; (c) Reference signal of Rr; (d) Estimated and reference speed; (e) Motor and load torque; ( Rotor speed error; (g) Observer

magnitude stator current; (h) Observer magnitude rotor ux; (i) Observer current error; ) Observer ux error.

EFERENCES

[I] A. Farrokh Payam and B. Mirzaeian Dehkordi, Nonlinear slidingmode controller for sensorless speed control of DC servo motor usingadaptive backstepping observer, 2006 nternational Conference onPower Electronics, Drives and Energy Systems, PEDES '06, 2006.

[2] Huang, K.L. Chen, H.T. Lee and L. Fu, "Nonlinear adaptivebackstepping motion control of linear induction motor," in Proc. theAmerican control conference anchorage,pp. 3099-3104,May 2002.

[3] E. Arbin and M. Gregory, Adaptive Backstepping Control of aSpeed-Sensorless nduction Motor Under Time-Varying LoadTorque and Rotor Resistance Uncertainty. Proceedings of the 38thSoutheaste Symposium on System Theory, TennesseeTechnological University Cookeville, TN, USA, pp 512-518, March5-7,2006.

[4] F. Blaschke, The principle of eld orientation applied to the new rnsctor closd lop ysm fr rotig l mchi imnRev.,34, pp. 217-220,1972.

[5] H. Nademi, F. Tahami and M. Rezaei, Fault Tolerant PMS MotorDrive Based on Adaptive Backsepping Observer with UnknownStator Resistance, 2008 3rd EEE Conference on ndustrialElectronics and Applications, CEA 2008, p 1785-1790,2008.

[6] M.N. Uddin and W. N. Sang, Development and mplementation of aNonlinear-Controller-Based M Drive ncorporating ron Loss WithParameter Uncertainties, EEE Trans. on ndustrial Electronics,Vo.56,No.4, pp. 1263 1272,2009.

[7] H.T. Lee, L. Fu, and F.L. Lian, "Sensorless adaptive backsteppingspeed control of induction motor," n Proc EEE Conference onDecision Control, USA, pp. 1252-1257, December 2002.

7

[8] . Kanellakopoulos, P. V. Kokotovic and A. S. Morse, SystematicDesign of Adaptive Controllers for Feedback Linearizable Systems,EEE Trans. Automat. Contr., vol. 36, pp. 1241-1253,1991.

[9] J. Soltani, A. Farrokh Payam and M.A. Abbasian, A SpeedSensorless Sliding-Mode Controller for Doubly-Fed nductionMachine Drives with Adaptive Backstepping Observer, Proceedingsof the EEE nteational Conference on ndustrial Technology CT,p 2725-2730, 2006.

[10] M. Jalalifarl, A. Farokhpayam, S. Sadeghi, S. M. Saghaeiannejad,Sensorless speed dynamic modeling of an induction motor withinput-output feedback linearization controller and adaptive nonlinear,NMC2007 - 11th EEE nternational Multitopic Conference, 2007.

[II] O. Elmaguiri, F. Giri, Digital backstepping control of inductionmotors, EEE nteational Symposium on ndustrial Electronics, p

221-226,2007,2007.[12] S. Chaouch , L. Chri, A. Makouf, S. Nai, S. Med, Backsteppingcrol nalyi o t dieret sed sesorles proes orinduction motor, 5th nteational Muli-Conference on Systems,Signals and Devices,SSD'08,2008.

[13] W. Jia-Jun and H. Jie, Torque and ux direct backstepping conrolof induction motor,Proceedings of the World Congress on nelligentControl and Auomation (WCCA), p 6402-6406,June 2008.

[14] Y. Ho Hwang, K. Kwang Park and H. Won Yang, Robust AdaptiveBackstepping Control for Eciency Optimization of nductionMotors with Uncertainties, EEE nteational Symposium onndustrial Electronics,p 878-883,2008.

[15] Y. Tan, J. Chang and H. Tan, adaptative backstepping control andfriction compensation for AC servo with ineria and loaduncerainies,EEE Trans. on industrial electronics, Vo.50, No. 5,pp.944952, October 2003.

Sensorless Speed and Flux Control Scheme for an Induction Motor With an Adaptive Backstepping Observer

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