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8/14/2019 artigo elepot

1/7

SCOS O IS OCS, O O6 19

Mathematical Modeling and ComputerSimuation o a Separatey Excited

dc Moto wit ndependetArmatue/Fied Contol

ISAAC AVITAN, ICOR KORMIN R

tt mahemil moel f paaely excited d mor KLa3 araure inducance ccent 3 ( H)pvidig in-ep epti maj pyic asomai, Kf eld nductance gan (- )eelpe Te mod i implemeed cmpute imlin ce i cmbi wh SEX opimiio pcede, i u Kl eld nductnce ccent 1 (/A)o paamr etma a lae model veicti Te mel i K12 eld nductnce coecent 2 (H)gge or eelpme mcpco ol K eld nductance ccent 3 (z'mH)pe piig adal iblity a elI pimizig m Kml agnetc saraon limpefmace ccent AA)

O Km magnetc saturation lmicoecient 2 (A)KU unsaated eld inducnce

A core area m2)ccient 1 H)

B ux densy (Weberm) KU unaturaed eld nducanceD vscous dampng ccent

coecien 2 Dm + DL) ( . mrads) Kx, u ccient

1 (Mx)

DL oad vscous dampng coecent KXux coecent 2 (A)motor voage consant (V s)

483

@ motor (N . rads) Kg

Dm motor vscous dampng coecien N mads) Ktmotor orque constant (N'mW A)

ack EMF or generaed voltage (V)fa aatre opeatng frequenc (Hz)f ed operatng equenc (Hz)H magnetc ed intensty A sm)Hk agnec eld intensi sauraton

imt (A tusm) aatre curent (A)iamx maxmum aae curent (A)

ed curent(A)

steady-se eld current A)k magnec satraton curent lmt A)J moment o neia Jm + JL) (g m2 )JL oad moment o ineria @ motor (g m)m Motor moment o nera (g'm)K consnt rcon torque oss

coecent (' )Kil ron torque loss ccent N'm)K ron orque loss ccent 2 (W rads)KLal aare nducance coecent (A)KL amare nductance coecent 2 (mH)

Manuscipt recev Sembr 989 Jn 22 1I. Atn wih Adn Dlopmn a p Rerh, Raymond

Coran Gn NY.V Skom th he Dprmn of El gng Sate

Uety o N or Bghamon IEEE Log Nm 7

Ky

suM

NPPPRaR0

RbcRfR0

Tf

02786/90283$0

sa orque oss coecent (N mArad/s)

mean length o e ux pah (m)aare inducance H)eld nducnce (H)saated eld nductance (H)unsaturaed eld nducance (H)mua nductance H)nme o paae arare

pahs (- )numer o s (- )nume of moto oles (- )power input W)power output (W)armare wndng ressance 0aature wndng resistance@20C 0bs conct ressance 0ed wnding ressance 0eld winding esisance@20C 0avalae torque q TL Ts (N'm)vscous dapng toque oss (Nm)

consant rcton torque oss (N'm)iron torque loss (Nm)

1990 IEEE


2/7

484 IEEE TRANSACTONS ON DUSTAL RS, VO 37 N.6 ER 19

TgTL

Ta

bwmZmu8m

generad toqelod oqe @moorotal ore loss Td + Tyaue widing empeueed winding atresry torqe ossppid ue voltagebaey volagebrush coc volge dropapplied eld voltagebsh conct volge op @50 Abush conac voage drop @5 Amoor angulr velociynber of armre conducorsmotor eciecymeabiliye air permebiiysurated reaive peabiityusarad relaive pemebliygec uxmoor sh aglar displcemen

I

(N'm)(N m)

(N m)))(N m)(V)(V)(V(d/s)(- )

%(Hm)m)(HIm)(m)(d)

INDEPENDEN raure nd eld coro of dc moorcn ze the advantages of seres nd shut dc achines,povdg hgh saring ores and precis sed egioder a vrey of sha lodig codios. This pprochwhich s appied o a sh dc moor aks advantage of loweld crt (they g i ecoocy fesie) andfactes lmtless oaon uuder the commio crveli s is show i Fg

Power contol icit for impemeng e cotol separtio techqe is show in Fg 2,

The applcio of scial prdres corporag hecool sepaion technque provides g opporuiies formaizato of eblty and eciency of indusrial dcmoos Sicaly ehos of l dcopg cool po

vide he means for indede acess to the veliy andtoe of e moo I itio an rre/eld creato opizng he eciency ccien of the moor may beestabishd and atan rogho its oron

Developme of such predurs reure n-deph knowege of the electomechcal ansfomtions whn hemoor dynaics of majo contol canels and ierrelatonof nueros physical facors and vables A ahemicalmode povidig adeue descripio of these pesseswod serve s a basis for smlaion d aalysis of the dcmoor

Alogh heory of dc machies is wel esablished [3]681 esg reseach he are of mhematc descpto of dc moors oers simplsic modes sevg primaly he neds of seadysae linear sigleput sigleoupu conrol.

MO Ptr rut: eivlen dyamic circi of sep

ratey ecied dc moor s show in Fg . Lower case lees

Q []Fg 1. S-qe ea ee d moo

have e employed o emphsze nstaneous vales oftimevrying uaiies.

Armatur ls The voage io of he armaturecrci der dymc codiios is give by

1

Brushntat vlta rp commato macnesch he one uder discussio ere ests a voltage dropdue o he coc wee he shes and the comor1]3] As the carbo bsh sldes over he codcvesface of he commaor lm ha is nessary i provdig brcaio for prope brsh functos is fod Thism has some of he popries of a delecc erl usreslg i an appet brushcouor interface sis

anceFuher he coc lm resisance s geeraly cosiderd

onlne and is ieced y any varables a caus i oucuate sch ct desiy temraure pressrerotoal speed rake ange coaio and maeacomposiio For simplcy a piecewise linear epessionfor the rush-conact VOlage drop s a cion of ararecure is proposd s is show in Fig 4

Then he volage eaion of the armatre circit udedymc codiios (ee (1 incsive of e bsh-cotacvolage drop my be ewre a

/t Va - R g Vbc (2)

where e l-coact essance is epresend as

(3)Fl ls The voltage euon of the eld crci der

dyaic condiios s give by

(utual nutan De o he dependen dalwind

igs of the arare nd eld mal idctance (tsforer eec) is eced o conrie to the overall eldloop Therefor 4 may be wite o iclude e mutalidctace s

ant r saturatn The mgnetzion proty ofhe moor is cio of he ferromgec meil used in

he cosrcio of he oto and may represeted y heeaoshp bewee he desity B and he mgetic eldesy H

hs relioship between B and H s onliear mlival-


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ATAN AND KMN MATMATA MDNG AND MPT ATN 485

Choper

icut

FU5

--------H-BdgCt

s

r----

PlzE

i snUber ! i i

_________J

D ,,,, RnD ypntctzSb

Fig 2. Sepay td d moo w y Atug j' Crol

g 3. Dm il cut of a paatl eit motor

5 0 []Fg 4 ecw o ofh ta oltg dop.

u, histoy denden (hysesis) and on m dndn[]-[6], [3]. This is the comunded by e complexiyof he sha of motor's maic sucues Fo smplicitynglectig th yseesis ec n th maeal a piecewislinearzaion of h magnezation cue may adequateyepsned by he BH chaacerscs of g. 5 [5]

Th pwise lneized cuv consiss of a inea ionin th ang B < B < Bk havng a so uo and wolea potions fo th nges B Bk eac aving aslo ' Thn lnazed BH cur may d-scib by 6) fo he unsaua egion H < H > andby 7) fo h saurad rgion H > H

(6

BH

g Piwi lto f H

(7)

Furhe we can elate h eld nducace o h rme

abiliy by 8 for h unuaed gion and by 9 fo tesaurat egion [5

Lfu uNzA / L

Lfs slo2AL

(8

9

Hence h volag quaio fo he unsauaed eld coisee 5 may expssed as

fudifdt vf Rff Mda dt (10and fo th saurated eld col

Lfdfdt vf Rff Mdadt

Ahouh te cts of magneizaon are wll undrsto

hee aps to lie ex mateial on th mahmaicaodeing of d inducance as i ins sauaionTheefoe he following mel is poposd co wih heansnt cts of magnizaon Dn t eld inducanc


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486 I RSAONS ON NUSRIA ERONCS, NO BR

gain KLf' where, for he unsaturatd rgon

KL=Ku\(1 K2lva for he saturated region

KLf 1

12

where Kf s governed by the magnetic saturaton eldcunt imt ik dened as

Then rewring 5 to ncud he magnetc saturaon we

get

Armaur an l nuans ae non-near nctonsof th appied ed current and the scic eects of frequency of oration on hysteress [7]. From he nducanccuvs supped by he manuactrer, the inducancs aremodeed as

a 1/ [ 1 + KafKa + Kada] 16Lf= 1/ [ (1Kfli(KLf2+Kfdf)]. (17)

Armaur an l rsan can vay neay withtmau down o 38.5K. Then th amatue and edressances may reprsented as

R R02.5 Temp255 18Rf Rf 2345 + emP 25.5 9

Arap pesent a he amatre cols can be expressed as a nction of the amatur and ed cuens andh amatu and ed nductances. However the oowingequaton o the ar-gap ux which reects exermnta daasuppd by th manuactrer was empoyed n the mode:

2

Bak m n he amae is a nction of ts anguarvelty a voltage constnt and th magntc ux per poe as

represnted y21

where the votage constnt is xed by h desgn of thewndng nd is gven by

22

Gnra rqu s a nction of the armature curent atorqu consant and he magnetc x r pole a shown by

2

whe h toque constnt K s numrcay equ to thevoage constant Kg in the SI system which s expressedwth th folowng units

2rqu l he dc motor s not an ideal energy con

verer due to ntern loses tha rsut n hat gnaton

The osses can b catgorizd nto th folowing groups[8[,

lral amatr coppe d copr, rush contact lrman:eddy currents hysteress stray load Mhanal stckton couomb con vscous dmp

ng, wndage shorcircut.

Armaur ppr l ppr an brushnalral lsss do not rprsnt a diect torqu oss;

raher they resut n a voge drop wh n u resus nreduced gnrated toru Thes a accounted for in thenegatve feedack of the armatre and d ccits

urrns an hsrss lsss are ncons of uxand motor roational speed Both eddy cuents and hysteressconbut to th heatng eect o he motor hat ncrsswth motor roationa spd and these losss usuy determine he maxmum speed that may b obtaind m an incore amaure Stang om a mde rommended y hemanufacuer that consders ux only and accountng forrotationa sd th ecragnetc torque oss s modedas [6, [[1]

25

Sray lss s due to amaue eakage ux esutng om

dstod magntic eds therby causing eddy cuent andhysteress osses n the amatre suoundng ion [6 [8],12] Stay loss s a nction of amatue cunt and motorrtationa speed nd may b rpresented as

26

Skn s ony present sandst therore it s nottan into account in the dynamic anayss

ulmb rn rqu lss incudes factrs thatpruc a mchanical drag on the motor such as beang andbrh-comutator ntfac con he cton torque ossis consdered to be constantly applied and may be rprsentedas

(27)

Vsus ampn an wna rqu lss ncude afacors hat produc a mchaca dag on the moor and aeprtona to the rotational s squared and seed of thmotor resctivy. owever since windge s ypcalymuch smale hn vscous dampng, it s repesented as paof h viscous dmpng toqu loss as foows

28

Shrru ls occu when the brush cosses oom one commuor segment to an adjacent commuatorsegment thereby creatng an insntaneous shot crcuit connecton twen he ends o h co. he eect of shot-circut curent s a contrbution o a component of oss thatncases wh motor s d and apars a a vscous drag onhe amature as we a imsng a maximum seed lmtatonon he moto 9. For hs anaysis th ects of shortcuit

osss a assumed to neglgbe and are hereore gnoredThen the al rqu lss may wten as

29


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AvrA AD KORMN: AHEAICAL ODLG AD OPUT SIUON 487

nd he avaiable torque my be given byTa = Tg - L - . (30

The motor elocty equon under dynic condions isgiven by

Jdw/dt 'Fnlly, he motor ecenc my represented s

when lOPout/Pin

u 1.72 WTLPi = i + iff

31

32

(33

(34

Conentional models, or simplcy generlly linerzhe moor chrcteristics nd/or consider some o he vribes in the sedyste regme oly [3]5] [8] [10][13.Hence noniner chrcerisics such s rmure inductnceL eld inducnce f bshconc voge drop c ndsry lod loss re viewed s constns or simpy ignoredom ormlion Additionlly lhogh mutul inducnceM nd mgneic coe surion KLf re generly discussed[3]5 [10 hey re either no rtionzed o prcicoulon or re simply ignored due heir nonner rnsen behvior Alhough hese smplicions cn be justidin mos prccl moor pplicons lner mels re ncpble o e combined eecs o e/eld conrol encountered in numbr o cropressorbsed conrol pplicons

Fig 6 shows convenonl model o he dynmic equions o se excludng e eecs o b, M nd K fFurer, nd f re considered heir sedysteconsn vues.

Oeral blok diaram o he mhemicl mel, shownin Fig. 7 summrizes he ll mtemicl ormultion o

he modl represenng the equons o he physc rnsormtions nd inecton o prticur elemens o the mel

OPU IUAIO AD UThe developed memicl mel ws mplemened n

computer code, smulting he overll moor rormnce geneting he ruired resnse vrbles. Althoughmel congurion s dene simulon o pculrmoor implies specicon o the mel preers.

The ollowing prmeers o te seleced moor e supplied by he nucrer:

m 2phsP 4polesZ 90 conducors,

JEU = 6.1bm in2

R0 = 0018 ! @20CR/ = 101 ! @20CKx1 8.73E5 MxKx2 666 A

where subscrp EU denoes english uns o mesuemenSimlation conditons reect he emrue o the motor nd equenc o oion Temp nd TemPf eprsenthe mue nd eld windng emrurs respecely I

l-

Fg 6 Cnvl l bok dag

v

-Fg l bok da

prcicl terms i my qute dcul to mesure Temp'hereore Temp is esmted s ollows Knowg t stedy ste

R" (d/dt)/iThen i olows rom 8) h

TemPa "

d

/dt

)/i

35

(2545/Ra+ 2345 (36

Additionly knowing th pek ed curren

R" f/55. (3

Then i olows om 19 t

TemPf" /i 2545/Rf - 2345 (8

The opering equences re se to 0 H or boh hemure nd eld

Determnsti parameters reec he eld nd rmreinductnce cciens nd he bushconc volge dop.Given he rmre nd eld nducnce chrcersics eccens o the rmure nd eld inducnce equons re

esblished s ollowsK 003618/AK2 = 9693/m

KL 00I620/AKf 00I2/m


6/7

488 RSCIOS O USRIL LEROS OL 37 O6 CEBER

KLa3 7H H KL3 5.88E 5H' H

For the moor-bsh combnion unde consideon, vlues fo e s-conc volge drop e seected s follows[1]:

0 = 8 Y 28 Ynknn aramr e nehe gven no cn be d

ecy deved These prmees wee viewe fctos

esponsble for he ccurcy of e smuion esuts ndwee esmed y mnmzon o he dscrepncy beweenexpement nd smlted d he esmon ws cedou in he fom of nonlner les sques predure mpemented v SIPEX opmzon oune 1415

he folowng vues e found o gve e es coespondence o cu esuls

D = E 5N . raM 24H = 5 N m

K2 67E 5W ra

KJ = O5N mK = . A/AK2 5E A ,

K = 2.5 HH,K 6 N m/A2 rd/s K2 = 2. V

rmn and muain ns wee desgned o nvesigte e pl nd combind eecs of e vons ofme nd eld voges on he motor fomnce heepemens perfomed nd smul nclude the folowing

Sep npu ppe to te ed sep inpu ppled to e rmre step npu pped to the ed nd mueFgs 8 hough show e dynmic responss of he

models s epesned by Fgs 6 nd 7 denoted on Fgs 8hough Fg 1 s Me A nd Moe B sctvely ncompson w the followng exrmenl dt

Feld curent versus me rme cuen vesus me moor sd versus ime

A Dcussin RulFs s cey seen n Fgs 8 ough e

conventonl me espons gety ders om he ctlmoo esponse n he nsen se s esclynoceble n Fg 10 whee sep npu s simutneouslypplied o boh he ed nd mue Addionly ecusehe convenon me ignores te eecs of muul nducnce nd mgneic core son e eld simpy behvess sode sysem t is ndependen of mue nuence (Fgs 8 nd O his esus n o moo ouputnsen chctescs (sedFgs. 9(c) nd lOc; me cuenFgs 9(b nd O(b

he eec of manc cr aurain s cerly ilused y e eld cuen cuves o Fgs. 8 nd O

Smlon of the eec of voge steps smulneousy pped o he d nd me shows h he mgneicson phenomenon s ccurey mele n he poosdmel nd s esu rmre cuen nd motor speed

Field Curent. amps5 --r 1 20

pY1 /10 I /5

60 0 80 40

Te (s)300

Actal roposd CoetionalFg 8 28 p l'

360

3Field Cur _ :p=8 __

8 /,/ l -

18 ,_400 41 40 4 40 475

e s)- tu Propoed Cvetoal

aArmure Crren mps1000

800

00

00 200/490

_200i- , j -00 4 40 4 40 475

Te s)ua ropod Coeo

Moto Speed RP1600 -

400

100

000

800

00

90

I 00 415 430 4 40

475

ua ooed oetol(c)

90

i 28v p re: () f; c w


7/7

AA A SKR: H G R S 489

Fild Curent, amps25 ----------

f- I j j 60 120 80 240

Tme (m)300

- Actua Popoed(a)

) Conveio

360

12 00 _m ureu en.ap s _ _o 60 0 180 240

Tme (ms)300

al Propoed ) Coenoal(t)" 000 Mor Speed. RM500 'fI -"(lj'000

50 f

60 20 80 0Time ms

300

Al - +- roosd Conl(C)

360

360

Fig 10 258 sinp to eld ad armare a If; ; ) wm'

responses correlate reasonably wel wih eximenta data( Fig. O(b) and (c. Further, changes in the matude o

the voltage steps applied to he eld and/or armare result ina predctabe eect on he smulaed responses o he motor.

Additionally he eecs of mutua ndutane ae clealyvisible in ig 9a); a sep volage applied to he armaureesults in an nial eld weakenng evdent in he esponse ohe acual and proposed model motor. The actuaproposedmoe el cuen coelaion may e improve y inceas-

ing the ccien M However ecessive mutua inucanceadversely aecs the eld co reacon whch resls neduced eld current hereby esutng in educe airgapu

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