Behavior Modeling and Simulation of Double Wheeled Electric Vehicle Drive

Transcription

1 Nadi BOUHETATA, Mohamd BOURAHA, aaadj GHAOUTI Univsit of scincs and th tchnolog of Oan (USTO) BP 55 E M naou Oan, Algia Bhavio Modling and Simulation of Doubl Whld Elctic Vhicl Div Abstact. Th pincipl of th lctic vhicl is v simpl: instad of an intnal combustion ngin with ful stod in a tank and whos pow is tansmittd to th whls though a gabo, lctic vhicl (EV) is powd b a taction sstm consisting of a cntal o twowhl div supplid b battis, whos spd is contolld b an lctonic contol dvic. Th populsion sstm considd in this wok is two diving whls. It consists of two pmannt magnt D motos (PMDM) dictl coupld to th a whls of th vhicl foming a motowhl (diving whl). Each motowhl is supplid b a static convt which is powd b battis. Th two sub sstms (soucconvtmoto) a coupld to an lctonic diffntial in od to compnsat th tndncis of diction of th vhicl and maintain a stad spd b adjusting th diffnc in spd of ach motowhl accoding to th diction in th cas of a tun. Stszczni. W pojazdach lktcznch stosuj się nikid sstm podwójngo napędu z lktonicznm stowanim. Sstm składa się z dwóch silników pądu stałgo bzpośdnio dołączonch do tlnch kół. (Modlowani właściwości i smulacja pojazdu lktczngo z napędm na oba koła) Kwods: Elctic vhicl, Elctonic diffntial, Pmannt magnt D moto, Yaw at contoll. Słowa kluczow: pojazd lktczn, lktoniczn mchanizm óżnicow, podwójn napęd. Intoduction Th lctic vhicl can b motoizd in vaious was accoding to th mchanical simplification dg of th chain of taction. In th oldst vsion, th latt can b mad up of a singl moto associatd with a clutch and a ga bo and in th most advancd vsion, of fou diving whls fo th dict div. In this pap w psnt an intmdiat solution justifid b tchnical and conomic considations. It is psntd b a stuctu of spd contol of two idntical pmannt magnt D motos ach on associatd with a fid atio gabo coupld to a a whl of th vhicl, thus foming a diving whl. Th two diving whls a contolld spaatl b a static convt and thi spd is managd b an lctonic diffntial. Stuctu with Two Indpndnt Motos Th multimachin multiconvt stuctu (MMS) poposd in this wok is that of th contol of two idntical and indpndnt PMD motos. It is psntd in th figu blow wh ach moto is associatd with a fid atio gabo coupld to a a whl of th vhicl, thus foming a diving whl. Th unit is contolld b a static convt; it is a BUK chopp tp that allows vaing th moto spd b adjusting th dut ccl. Both diving whls a managd b an lctonic diffntial to offst th chang in spd in th cas of a tun. P afg afg P I acc I acc Elcton ic Fig. Two diving whls taction chain stuctu Elctic Vhicl Modling I a I af I a I af f f H g H d U a U a g d Th lctic vhicl is a compl sstm composd of an assmbl of sval componnts of vaious tps (mchanics, lctic, thmal, ) in intaction. Th analsis of th EV as a sstm thn quis a modling of th vaious intvning componnts in od to hav a complt modl. Kinmatic Modl Gnall, an igid bod moving in spac is animatd b si dgs of fdom, th in tanslation and th in otation. Th vhicl is thus gadd as a bod povidd with th fam Rv ( O, v, v, zv) in which w associat th intial fnc point of positioning R ( O,,, z). i z i i i i i Fig. Psntation of th Vhicl in th atsian Fam Ointation Equation Using th appoimation of th biccl modl, th sting angl δ and th adius of cuvatu R G of th vhicl path a connctd to th distanc btwn th font al and a al b [6]: v tan R G Fig.3 Biccl modl in th intial fam Position Equation s z s v s RG i G 8 PRZEGĄD EEKTROTEHNIZNY (Elctical Rviw), ISSN 3397, R. 88 NR a/

2 W assum that th vhicl pfoms small unifom ctilina motions. To dvlop th simplifid quations, w tat two tps of motion (tanslation and otation) btwn two momnts t and t t. Th small angl appoimation allows us to pss th lationship btwn δ and th spd of otation spd, (φ: vhicl ointation) as wll as th lationship btwn th diffntial of th sid coodinat of th cnt of th a al of th vhicl and th latal dviation φ as follows []: V V Fig.4 Kinmatic modl of th vhicl Dnamic Modl Th gnal fomulation of th dnamic quations maks it possibl to psnt th following vaious otations: Pitch ( ): q is th otation spd aound ais. Roll ( ) : p is th otation spd aound ais. Yaw ( ) : is a otation aound z ais. Fig.5 Vaiabls of motion and spds of th vhicl attachd to th ais sstm Modl of th Effots Applid to th EV Th vhicl psnts a load which is chaactizd b a ctain numb of toqus. () v ao slop acc Th figu abov illustats th vaious focs highlightd fo modling. Fo this pupos, th aim of th modling that w sk to wok out is to appoach as much as possibl th al bhavio of th lctic vhicl. So, th finalit of th wok is not to las th most pcis possibl modl b intgating th maimum of paamts, but to hav a satisfacto modl b its pcision and its complit. Fo this pupos, ctain mo o lss act modls a ncssa. Ths concn th kinmatics and th dnamics of th vhicl [6]. F (, i j) v Pitch Spd (q) : Baing sistanc focs, vij (, ): Vtical action focs, cij (, ): ntiptal focs, p(, i j) : Populsion Focs, with: ( i, f and j g, d) : Etnal sultant focs following, : Etnal sultant focs following z, z h Yaw Spd () Roll Spd (p) (a) (b) Fig.6 atal viw (a) fom blow (b) diffnt focs applid to vhicl Baing sistanc toqu: osponds to th sistanc against th dfomations of th ti du to th contact whlgound, th vhicl displacmnt spd, ti pssu, th natu of th gound and th condition of th bandag. () F M av av M a a Mg Wh M av, Ma, and av a a th masss and th toqus caid spctivl b th font and a whls. Thus th baing toqu is: MgF R (3) adh Aodnamic toqu: Is th toqu cosponding to a st of focs td on th vhicl bod and which sists to th pntation into th ai. Ths focs a: : Th tail foc. It opposs th populsion of th vhicl. : Th lift foc. Tnds to ais th vhicl. z : Th dift foc. Tnds to tilt th ca. (4) Fao ai S ( Vvh Vwind )² (5) V ( V V )² vh wind Thus th aodnamic toqu td on th vhicl is givn b: 3 (6) ao ai S R Toqu latd to th slop: Whn th vhicl movs on an inclind lvl, its wight baks up into two componnts, nomal and tangntial. Its toqu is givn b: (7) MgR sin slop p Ra al Font al Foc latd to acclation: F acc psnts th dnamic tm of acclation o dclation of th vhicl. dvv (8) Facc M M Finall, th total ffot of sistanc to th advanc of th vhicl is: (9) Fv M g( sin p) ai SV Modling of th hain of Taction Th dsign of an lctic div sstm is a ath dmanding task. It psnts a st of lmnts dsignd to achiv a tchnological pocss, consisting of an lctic moto powd b a voltag souc though a static convt, a movmnt mchanical convt and a sstm of contol and gulation. Each moto is quippd with a fid atio spd duc and attachd to th whl constituting a diving whl [4]. PRZEGĄD EEKTROTEHNIZNY (Elctical Rviw), ISSN 3397, R. 88 NR a/ 9

3 Th mchanical quation of th unit is givn b th following pssion [3]: dm () J fm m with: Jvh () J Jm and vh N N Batt d hopp Fig.7 ontol stuctu of th taction chain of a diving whl with buck chopp Modling of th Static convt Th static convt is an lmnt of connction btwn th moto and th souc. Th choic of its stuctu iss fom th usd moto. It is slctd such as th maimum pow qustd b th moto is covd b 5% of th atd output pow of th convt and accoding to standad IS33 NEMA (National Elctical Manufactus Association), it must suppot 5% of th atd cunt fo on minut duing (acclationsdclations) [5]. Th convt usd is a vsibl cunt BUK stpdown chopp contolld using th compaison of a sawtooth fnc signal having piod qual to th piod of chopping and givn amplitud V ma with a contol voltag V c. Th point of intsction of th two signals imposs th duation of th conduction of th chopp. ^ t () Vds V ds T T V c f (3) f c ^ T V ds Vf (4) Uav fc Vdc V ^ dc V ds Vdc (5) Ho ^ V ds V ds : Sawtooth signal T c : Duation of conduction U av : Avag load voltag Actuall it is notd that th is a dla Tc btwn th contol momnt and its ffct on th convt. B intoducing th avag dla T c th tansf function of th chopp is givn b th following pssion [3]: o (6) H () t h s Ho Aft appoimation on obtains th following lation: d V dc c dc V vh u f V ontol Diving whl Ho (7) Hh() s s o Modling of th PMDM Th lctic moto is th fundamntal stuctual lmnt of an lctic div sstm. It is chosn on th basis of calculation of th load pow P ch quid b th divn mchanism so that th moto atd pow P n =. to.3 P ch. oncning hating ffct, a going bond th limiting tmpatu b involvs a duction of 5% of th moto lifspan. In man cass, th chcking of th cition of hating of th moto can b don b th toqu: (8) n q with n : Ratd toqu of th moto q : Equivalnt toqu quid b th load (9) q n t c i i Th ovload cition nsus that th stall toqu dvlopd b th moto cds th toqu quid b th load. () dc ma Accoding to th motion quation, th quid toqu is obtaind b th following pssion: dm () t () () t J j with: J : Th total otational intia j Thus th dnamic modl of th PMDM is dfind b: dia () Ua RaIa k d (3) kia Jm f Ua m( s) (4) m sm s m k Jm with: a : Elctic timconstant Ra RaJ m : Elctomagntic timconstant R a k Fom th lctical and mchanical quations of th pmannt magnt D moto th stat quation modl is psntd as follows []: (5) A Bu di a R k a a a ia U a a (6) d k J a J Th moto spd contol is don b a PI contoll. Th chopp is contolld b a logical function that dtmins its dut ccl f If Ia (7) ki If kp ( f m) Iacc p (8) di f kp ( f m) ki ( f m) PRZEGĄD EEKTROTEHNIZNY (Elctical Rviw), ISSN 3397, R. 88 NR a/

4 . Fo f and b placing in th modl (3) on obtains th following total stat quation: df dia kk p k p ki k i p ki J a (9) J f dm k m J J Th Elctonic Diffntial Bhavio of th vhicl whn tuning W will consid that th vhicl is in a pfctl cicula tun allowing it to chang its diction of olling b 9. Fig.8 Yaw at of th vhicl whn taking a tun As th aw angl is changing in th sam wa as th angl swpt in th tun b th vhicl w hav th aw at. This spd is zo in both stats A and D bcaus th vhicl is in a staight lin situation; in addition it is constant duing th two stats B and sinc th vhicl is th in situation of tun. To mov fom stat A to stat B, th vhicl will hav to undgo an acclation of aw in ntanc of tun and convsl it will nd a dclation of aw at it of tun. At th ntanc of th tun th div opats th sting whl. Th font whls chang diction whil th vhicl is still on a staight lin. This puts th font tis in situation of dift and th poduc guid ffots dictd towads th intio of th tun. Th a whls a zo dift sinc th vhicl has not statd its aw motion. Th a guid ffots a null. Duing th tansitional zon th vhicl is otatd which is gaduall difting th a whls. f A δ δ dv B R Fig.9 Vhicl stuctu in a tun δ R Th modl of th lctonic diffntial In th cas of a staight lin, ach diving whl is contolld b a static convt with th sam spd fnc. But in a tun this spd is diffnt bcaus th A V vh D B Succssiv ointations of th vhicl cntlin fom th R G D two whls will not hav th sam spd. This diffnc is managd b an lctonic diffntial that allows us to calculat th diffnc in spd in od to b abl to appl it in th contol. As th aw angl is changing in th sam wa as th angl Vd Vvh Vvh (3) Vg Vvh Vvh Vd, V g : a spctivl th lina vlocit of th ight and lft whl. V vh : lina vlocit of th vhicl. Vvh : th diffnc in spd btwn two diving whls Thus: dv Vd vh( RG ) (3) dv Vg vh( RG ) v (3) RG tan Thn th angula vlocit of ach diving whl is givn b th following pssion: dv v tan d vh v 3) dv v tan g vh v dv tan (3) g d vh v with : fo ight tun : fo staight lin : fo lft tun Tabl. Gomtical paamts of th vhicl M Vhicl mass 5kg v v Whlbas, m d v Distanc btwn th diving whls,3 m R Radius of th whl,3 m Simulation Rsults Th simulation modl of th vhicl is psntd fo two cass of diffnt applid loads, th fist cas dtmins th bhavio of vhicl dnamics und th influnc of th vaiation in spd in a staight lin (acclation and dclation), whil th scond cas is usd to visualiz th bhavio of th vhicl duing a doubl tun on land whil nhancing th opation of th lctonic diffntial. as : Th vhicl dnamics in staight lin On flat gound in a staight lin, th sstm is subjctd to a spd stp of km/h du to th action on th acclato b th div in od to dfat th focs of intia (figu.). At t = sc th div doubls its spd b pssing mo on th acclato (figu.5). In both situations, th two diving whls otat in th sam angula vlocit so that th spd vaiation dvlopd in th lctonic diffntial is zo. To pfom a shutdown at t = 4 sc, th two diving whls un as a gnato und th influnc of th intia of th vhicl so that ng is movd b dissipation. PRZEGĄD EEKTROTEHNIZNY (Elctical Rviw), ISSN 3397, R. 88 NR a/

5 Vhicl lina vlocit 45 4 ina vlocit of vhicl Vvh Vd=Vg 35 3 Vvh (Km/h) 5 Vvh (km/h) Fig. ina vlocit of th vhicl in staight lin km/h Aodnamic Toqu Fig.5 lina vlocit of th vhicl with chang of consign km/h and 4km/h ao (Nm) w (pm) Angula vlocit of vhicl Wvh Wd=Wg Fig. Aodnamic toqu V vh =km/h 5 pnt (Nm) Toqu latd to th slop Fig.6 Angula vlocit of th vhicl with chang of consign as : Vhicl dnamics in a tun Th vhicl ngags in a doubl tun (on th ight thn on th lft) with a spd of km/h (figu.7). 5 Vhicl dnamics in doubl tun Toqu latd to th slop Baing sistanc toqu Fig. ina vlocit Vvh (km/h) 5 5 Vd Vg Vvh Vf (Nm) Fig.7 Vhicl dnamics in doubl tun.9 Elctonic diffntial Fig.3 baing sistanc toqu Rsistiv toqu vaiation spd (km/h) (Nm) Fig.8 Vaiation spd on th lvl of th diffntial Fig.4 Rsistiv toqu to ovcom fo taction In this cas, th spd of th diving whl which is clos to th cnt of tun is low than that of th most distant. This mans that thi aw at is constant (condition B and figu.8) and th lctonic diffntial has compnsatd th vaiation of spd (figu.8). PRZEGĄD EEKTROTEHNIZNY (Elctical Rviw), ISSN 3397, R. 88 NR a/

6 onclusion Th intst of this wok is to psnt th stuctu of EV in th atsian coodinat sstm and giv th modl of th vaious pats which constituts it (kinmatic and dnamic). As it allows studing a populsion topolog basd on an intmdiat motoization constitutd b of a chain of taction to two diving whls dfind b a multi machin multi convt sstm. Th moto contol is povidd b two buck chopps and a PI contoll. Th vhicl bhavio is psntd b two cass, in staight lin and tun, wh w toud th dnamics of th aw at of th vhicl whn tuning. Th simulation sults show that this stuctu allows poducing th lctonic diffntial which contols th otational spd of th diving whls with high pcision in od to pass th tun as fficintl as possibl. onsidd ssntial, it is pat of th sstm quipmnt thus nsuing stabilit and good stabilit of th vhicl. As pspctiv, this wok ma b subjct to pactical implmntation fo spcific applications such as pandd spacs, nclosd o closd (aipot, ai tminal, milita aa, golf cous... tc) fo a lina spd not cding th 5km / h and caing two popl. REFERENES [] Bouchtata N., Bouahla M., Mnad A., Epimntal stud of potction and contol applid to Pmannt Magntic D Moto, PRZEGĄD EEKTROTEHNIZNY (Elctical Rviw), ISSN 3397, R. 87 NR / [] R. Jaabalan., B. Fahimi., Modling and Analsis of Switchd Mod DD onvts fo Vhicula Pow Sstms, IEEE5, Univsit of Tas at Alington. [3] Takuo K., Kazua T., Diving haactistics of an Elctic Vhicl Sstm with Indpndntl Divn Font and Ra Whls, IEEE, TRANSATIONS ON INDUSTRIA EETRONIS, VO. 53, NO.3, JUNE 6. [4] Hoi Y., Futu vhicl div b lcticit and contol sach on fouwhlmotod, IEEE. TRANSATIONS ON INDUSTRIA EETRONIS, V5, NO.5, OTOBER 4. [5] John.., Jams.., Elctic Vhicl Tchnolog Eplaind, ISBN , Ofod Books Univsit, Ofod, UK [6] Aiman N., ontibution au dévloppmnt d un simulatu pou ls véhiculs élctiqus outis. Thès d doctoat, Univsité d Tchnologi d BlfotMontbéliad. UTBM, Blfot, Fanc. N 85, 8. [7] Rajsh R., Vhicl Dnamics and ontol Univsit of Minnsota, USA ISBN , 5 [8] G.ivint., V.Hoga., D.Stica., M.Ratoi., M. Albu., Hbid Elctic Vhicl Epimntal Modl with AN Ntwok Ral Tim ontol, Advancs in Elctical and omput Engining, vol., no., pp. 7,. Authos: d N.BOUHETATA, Univsit of Scincs and th Tchnolog of Oan Mohamd Boudiaf BP 55 Al Mnaoua, 3 Oan, AGERIA, Nadil4@ahoo.f; d M.BOURAHA, Univsit of Scincs and th Tchnolog of Oan Mohamd Boudiaf BP 55 Al Mnaoua, 3 Oan, AGERIA, Bouah3@ahoo.f; d.ghaouti, Univsit Scincs of and th Tchnolog of OanMohamd Boudiaf BP 55 Al Mnaoua, 3 Oan, AGERIA, Glaadj@ahoo.f; PRZEGĄD EEKTROTEHNIZNY (Elctical Rviw), ISSN 3397, R. 88 NR a/ 3