Controller design of a new active front steering system

Size: px

Start display at page:

Download "Controller design of a new active front steering system"

Lilian Cobb
6 years ago
Views:

1 WSEAS RANSACIONS on SYSEMS Delng Cen, Cenglng Yn, nu Zng Conolle degn o ne ve on eeng e DELIN CHEN, CHENLIN YIN, IANWU ZHAN Inue o Auoove Engneeng, Sool o Menl Engneeng Sng o ong Unve No.8 DongCun Rod, Mnng D, Sng C P.R.Cn E-l dde: endelng_@ol.o Ab: - An AFS ve on eeng on e b o C-EPS olun ele oe eeng e develoed. Bed on e el odel o eenl oonen, e AFS onolle degned oveng o un: n EPS uo un ued o edue e eeng oque equeen o e dve; n AFS uo un ued o oene e eeng ngle o eeng e nd vele bl. In on o e onvenonl bl onol, bo e del ngle nd e e ee ed bk o AFS onolle nd e bl eone been oed LQR lne qud egulo. In ddon, e ne unene ve been ken oun n e LQR onolle o ovde e onol obune. Fnll, HILS Hde-n-e-Loo Sulon e ee ondued o deone e eone o e degned AFS onolle. Eeen nde e ooed AFS e n ove vele bl nd oene e eeng eon oque eevel. e-wod: - Ave on eeng AFS, Ele oe eeng EPS, Lne qud egulo LQR, Sdel ngle, Y e, Vele bl Inoduon Ave Fon Seeng AFS e ve been nodued o ove ndlng bl unde dvee od ondon. In on o onvenonl eeng e, e enl lnkge beeen e eeng eel nd e on eel o n AFS e oleened b n e ngle ugen oo. eeoe, ll ul on eel ngle, n ddon o e eeng ngle oed b e dve, n be led o ble e vele bede ovng vele eeng eone nd vodng l ndlng uon. Ye, e dve n ll eeve noon bou od on nd vele bl del oug e enl lnkge ou e ddonl onol n e ee-b-e SBW e. Addonll o e enned dn bevo o e eeng e nd vele blon, e AFS e ould lo ovde n oved eeng oo b edung eeng eo []. eeoe, e oque ne equed o l nul oe o eonble level. e eng AFS e ued e oell vlble dul oe ed eeng e e ol volue lo ould be ded o e ouu equeen. en n ddonl lo onol vlve uull ued eulng n ole onol one []. ne develoed AFS bed on olun ele oe eeng e C-EPS. eeoe, e onuon n v e eeng o b ueong eeng ngle nd lleve e eeng oque equeen o e dve b e EPS uo. e uo n ovde deonl onol o e vele dve nd edue e engne lod n on o e dul oe ed AFS e. Fueoe, ole dul e nd dul del n be elned. eeoe, o oo e nluded n e AFS e. One ovde ugen o e eeng eel ngle, le noe n e EPS e ovde e oque ne. e gol o e o develo n AFS onolle, no onl el enue e vele eone oebl ng e dve ene, bu lo el even e vele o llng no n unble e. Mo bl eee ued onl e e o ove e vele ndlng bl due o e dule oed e del ngle eueen [3, 4]. eoell, e lel oon o e vele debed b e nd del ngle. In ddon, e del ngle onol n oene e devon oung o e e onol. eeoe, e del ngle ll be eed nd ued o AFS e onol ogee e e. ISSN: Iue, Volue 7, Novebe 8

2 WSEAS RANSACIONS on SYSEMS Delng Cen, Cenglng Yn, nu Zng o eve bee vele bl, e e ee o dvng vele ould be ed bk. e lne qud egulo LQR n be ued o nd uble e eedbk nd oe e onol. LQR been del ued due o le dol oe nd eved ol onol o e loed loo. Hoeve, LQR degn ovde e ol gn, unon o e e e. Unounel, oe ee unene e n e vele e, nd eul n odel nu. eeoe, loug oe neen obune oee e, e ll LQR onolle no obu enoug o e unene nd nno gunee e bl o e ul e [5]. eeoe, e ll LQR onol ould be oded o oveoe e lon. e unene eng n e oble unde ondeon nlude unodeled dn, ee eubon nd eenl dubne [6]. A been nodued n e leue o L. none, n ve 4WS e degned l unene. Hoeve, e e e degned onl o e e e ne unen l eed e e A. I ndeque o e on eel eeng vele, eell e AFS vele. eeoe, LQR onolle degned ee ooed R ee unene nd led o e AFS onol e. e e ogned ollo. Fl, e uue nd odellng o e develoed AFS e debed. en e onol e nludng e EPS uo nd AFS uo degned bed on e odel n eon 3. In eon 4, del o e AFS onol been eened. o evlue e degned onolle, de-n-e-loo ulon HILS e debed n eon 5 nd HILS e e nll ondued n eon 6. Conluon o e e ued n eon 7. Suue nd odelng o n AFS e e AFS e e develoed bed on olun ele oe eeng e C-EPS. eeoe, o oo e nluded, llued n Fg.: one n e ognl EPS e ovde e oe ne o l nul oe o eonble level, ee e enen-gne nonou oo PMSM ovde ugen o e eeng eel ngle. eeoe, e e n be dvded no o : EPS uo nd AFS uo. Fg.. Suue o e ve eeng e. EPS uo A DC oo ued EPS uo o ovde e n oque o u oque e gven uen nd onollble oque. e ele equon o DC oo [7]: R dd & E d ud ee R d e ue ene, E e ue bk e onn, d e DC oo uen, ud e oo enl volge, d e ngul oon o e oo. e n oque o e EPS uo led o e eeng e b o nd o eel. e dn o e DC oo en n be gven b: & d d B & d d d d d d ee d, B d, d e e ne oen, dng oeen, oonl ne o e DC olun, eevel; e oo oque onn, e eeng eel ngle, d e ge o o e DC oo o e eeng olun.. AFS uo A PMSM ued AFS uo o ovde e n ngle o ee oo oonng onol ell o nge o e ge one. e PMSM odel n be debed lon nd Pk noon [8]: 3 L & q N λ & Rq uq 3 ee L e o ndune, N e nube o ole, q e uen o q -oonen, u q e o volge o q -oonen, e PMSM eeng ngle, λ e gnude o e lu eed b e enen gne, R e ue ene. e oque odued b e PMSM n be eeed lon : ISSN: Iue, Volue 7, Novebe 8

3 WSEAS RANSACIONS on SYSEMS Delng Cen, Cenglng Yn, nu Zng 3 N λ q 4 e ugenon eeng ngle o e AFS uo led o e eeng olun oug lne ge en, on n Fg.. e lne ge en ke e o ele e vble eeng o VSR nd odue ueoed eeng ngle. Fg.. Se o e lne ge en u, e ueoed ngle : 5 ee e ge o o e eeng olun o un eel o e lne ge e, e ge o o PMSM o e ng o e lne ge e, e ge o o o-o-o eel, e ueoed ngle o e eeng olun. e PMSM dn n be debed [9]: && B & 6 ee, B, e e ne oen, dng oeen, oonl ne o PMSM olun, eevel; e oonl ne o eeng olun, e dleen o e k nd e od, e du o e non..3 Seeng en Seeng en e lo nluded n e e, u eeng olun, k nd e od. e dn equon o e eeng e bede e EPS nd AFS uo n be eeed [9]: && B & d d dd d 7 d && B & lk 8 & B & lk lk M 9 ee, e e ne oen o e eeng olun, e on eel, eevel;, e oonl ne o e eeng k nd e od, e on eel, eevel; B, B, B e dng oeen o eeng olun, k nd e od, on eel; e eeng ngle o e on eel, e o e k nd e od, l k e leng o e eeng knukle, d e oque ovded b e dve, M e ene oen o e on eel. Equon 7 debe e dn oon o e eeng olun; Equon 8 eeen e dn o e k nd e e od. Equon 9 debe e dn o e on eel. In Equon 9, e ene oen o e on eel e deend on e longudnl velo. Wen e vele dven, ll del ngle uon o lne vele odel, e ene oen o e on eel n be led : M d β γ v ee e oneng oeen o e on eel, d e neu l o e on eel, γ e e o vele, β e del ngle o vele, v e longudnl velo, e dne o gv ene o on le. Wen vele ove lol on d l nd nge deon, lge oun o eeng oque equed due o e od lod on e e. e e oll nd nge e deon ulneoul []. e u ene oen deenng e deonl ngle o on eel n be eeed []: 3 μ M 3 P ee μ e on oeen beeen e e nd e od, e lod o e on eel, P e eue o e e. Ee e AFS uo odel n e-e o: & A Bu ISSN: Iue, Volue 7, Novebe 8

ee, e nu [ ] q M u u, e e gnen ] [ q & & &, nd e onol e e: ' ' 3 3 43 4 3 L R L N B l l l B N B k k k λ λ A ' / / L B ee /, / 3, / 4, / 43.

4 ee, e nu [ ] q M u u, e e gnen ] [ q & & &, nd e onol e e: ' ' L R L N B l l l B N B k k k λ λ A ' / / L B ee /, / 3, / 4, / Conol e onguon EPS onol un nd AFS onol un e nluded n e AFS e, on n Fg.3. Fg.3. Blok dg o e eeng e onol e EPS onol un n ele e eduon o eeng oque eeed b dve; le AFS onol un ovde e eeng ngle ugen o vele e nd bl. eeoe, e ugen ngle onol nd eeene k onol e oveed n e AFS onol un. 3. EPS onol un e n unon o e EPS uo e eduon o eeng oque nd oveen o eun-o-ene eone. ee o unon e no equed o ve e e e. A oe oun o oque ould be ovded o edue e dve eeng oque dung oneng, nd o eun e eeng eel o e ognl oon ool ou oveoo nd ubequen ollon o e vele g e eeneng g-lne od [7]. e EPS onol n oe eeng eo e o dve b vng qun o n oque deendng on vou velevelng uon, on n Fg.4. e ge uen o e oo deened bed on e dvng ondon o edue e eeng oque equeen. e ul uen geneed oug e dn o e DC oo nd e eeng olun, nd eued b e uen deeng un. en e onolle lule e onol gnl o ne e eo e beeen nd. Fg.4. Conol o e EPS un o ne e uen eo, PI onol ee eloed n e uen onol : τ dτ e e u 3 ee, e e ooonl gn nd negl gn, eevel. en e n oque deened nd delveed o e eeng. 3. AFS onol un In ode o onol e AFS un ondeng e VSR vble eeng o nd vele bl, n-loo onol nd n nne-loo onol e nluded n e onolle, on n Fg.5. WSEAS RANSACIONS on SYSEMS Delng Cen, Cenglng Yn, nu Zng ISSN: Iue, Volue 7, Novebe 8

5 WSEAS RANSACIONS on SYSEMS Delng Cen, Cenglng Yn, nu Zng C,v βd, γd VSR Reeene u d ub eedbk AFS - Mn-loo onol Inne-loo onol - Seeng e Fg.5. Conol o e AFS un vele β,γ In e nne-loo onol, PI onolle degn o k e ge ngle o e on eel d oenoee eung e dleen o e eeng knukle. In ddon, e ge ngle o e on eel deened n e n-loo onol b bo e eedod nd eedbk onol. e eedod onol deene e on eel ngle odng e deed VSR nd e eeng eel ngle. e bl ee e uled n e eedbk. en e ge ngle n be deened n e n-loo onol b e eedod nd eedbk onol. 4 Del o AFS n-loo onol In e n-loo onol, deen oenon ll be led o e on eel o eve deed e vble odng o vele e dn. eeoe, eeene odel en ebled l. 4. Reeene odel Aodng o e evou eee, led o-degee-o-eedo DOF vele odel genell deved o debe e vele lel dn, on n Fg. 6 [, 3]. kng e del ngle β nd e e γ e e o e e, e DOF odel n be debed : b β & v v β v γ b b & γ I I Iv 4 ee e eeng ngle onolled b e dve eeng ond nd e vble eeng o, / ; e vele, I e vele oen o ne;, b e e dne o e gv ene o e on nd e le, eevel;, e oneng oeen o e on nd e eel, eevel. b γ C v β M Fg.6. DOF vele odel odel eeen e vele dn bevo n e lne nge. Suoe e vele un onn du le o neul ee, e ge eone n be obned: v / b γ d / b / v / b 4 v b b b β / d b b v b / / / 5 en e eedbk onol n egule e oenng ngle eeene vlue: u b γ γ-γ d β β-β d 6 ee u b e eedbk oenon volge o e PMSM; γ, β e e eedbk oeen o γ nd β, eevel. o leen e eedbk onol ee, ue noon on bo del ngle nd e e equed. e del ngle n onol e vele devon oung o e onvenonl e onol. e e n be eued gooe, le del eueen eque eenve eno. eeoe, eon n eve n oon. e del ngle eon ung lel eleon gnl, been eed b You Aok, led. Aodng o e DOF odel, e vele lel eleon n be eeed : v & β γ b 7 v β γ v v v en, e euble gnl nd γ, e eed del ngle βˆ obned: & ˆ ˆ b β β ˆ γ v v 8 ˆ ˆ γ γ v ISSN: Iue, Volue 7, Novebe 8

6 WSEAS RANSACIONS on SYSEMS Delng Cen, Cenglng Yn, nu Zng ee, e e gn o eon. A ul n be oen o kee e obeve obu nd ee e del ngle el [4]. u, e del ngle n be ed bk o e AFS onol. e eedbk gn, n Equon 6 n be deened b lne qud egulo LQR. 4. LQR onol LQR n be ued o nd onol veo u o ne e o unon o good bl nd obune oee [6]. e o unon o e AFS onol ke e o: e Q e u R u d 9 e β β d ee e, u e onol nu, e γ γ d Q nd R e e egng e o e nd u. Mnng e o unon, n oed eedbk onol nu n be obned: * u lq R B P ee P e eul o e R equon P A A P P BR B P Q. LQR ovde e oed eedbk gn e unon o e e A nd B. And e e unene ve no been del n e lne e-nvn nonl odel. Hoeve, n o, u nlon eue, nol lod, nonlne, e vele ee [4]. A eul, e e ll no eo oll. Aloug oe neen obune oee e; e ll LQR onolle no obu enoug o e unene nd nno gunee e bl o e ul e [5].eeoe, e onolle ould be oded egd o ee unene o e vele. e e ee eeen e o on oue o unene n e vele odel [6]. e e oneng ne unene n be eeened b lne unon bounded unen [3]. * α α σ * α α σ ee σ, σ e e ove lng o eleng e gnude o e devon o e nol vlue α nd α. Conde genel e equon nludng eenl dubne: & A B u B γ β ee u nd e e onol nu nd eenl lel dub oe, eevel. en e unen lne e n be debed n e ollong e ee von: & [ A ΔA] [ B ΔB ] u B 3 ee A, B, B e nol e debe e e, ΔA, ΔB e eubed e eeenng e-vng ee unene. b v v A, b b I I v σ σ σ bσ v v ΔA σ bσ σ b σ I Iv v B, I v B, l I σ v v ΔB σ σ I I kng oun o e unene no e LQR onol degn o e nol e, e R equon nd o unon ll be eended. e R equon ke e ollong o: PA A P PΔA ΔA P PBB P φ 4 σ PBR B P Q o kee e e obu, P ould be onned : PA A P PΔA ΔA P PB B P φ 5 σ PBR B P Deooe ΔA, ΔB nd dene e e L, N ollo: ΔA LN 6 en e uen ondon o 5 n be eeed : PA A P Q λnn P σ BR B BB LL P φ λ 7 ISSN: Iue, Volue 7, Novebe 8

7 WSEAS RANSACIONS on SYSEMS Delng Cen, Cenglng Yn, nu Zng ee Q, R e e e e nol e ou unene. e e ϕ e eonble o e eenl dubne ejeon. e nenl dubne enuon ken no oun b e e λ. en ove dene oluon P ould be ound o degn e onol o gunee bl nd obune. Wen oluon P P > ound n e Robu R Equon 7, e e egng Q n be oded : Q PA A P P σ BR B B B P φ Q λnn λ PLL P 8 W e e egng Q, e o unon n be oded nd e onol gn n be obned. 5 HILS e degn o evlue e degned onolle, oe el-e ulon e eoed e degned eeng equen o e AFS e. e de-n-e-loo ulon HILS nege e ul ECU nd eel de e vul vele odel, ong loed loo o be uled n el e [7]. In e HILS e, bo e eeng ngle o e dve nd e oo e led o ove e eeng lnkge, oe dleen eued b e eno. W e eno gnl, e vele odel ede n e PC oued, en e nd del ngle gnl e en bk o e ECU e eedbk. u, e deed ngle n be obned o onol e oo. 5. Nonlne vele odel In e HILS e, o-k nonlne vele odel, been vlded gn e d n ou evou ud, eened o ule nd evlue e ooed AFS onolle. e odel deved oug negleng eve, oll nd oon, n Fg.8 [8]. e longudnl deon gnoed beue onl e lel bl o nee n ud. Hoeve, e e oen odued b e unblned longudnl oe oveed n e odel odng e ond. 5. HILS e Fg.7 o e eeenl equen de o n AFS un eve odule. e HILS e on o ee : e de nlude eeng e en, ECU, oo, d quon d, eno, PC; e oe nlude e nonlne vele odel n MALAB, e AFS onol log, nd o-oeng odule; nd nee lnk e de nd oe. Fg.7. Hde-n-e-loo-Sulon e Fg.8. Vele odel nd eenl oe e equon o lel nd oon o e vele odel e deved: & ν ν γ Fl F o Fl F 9 Fl F n F I γ& Fl F o Fl F n l F W Fl F b F Fl o F Fl 3 ee F ll, Fl, Fll, Fl F l e e longudnl oe on e on le, on g, e le, e g e, eevel; F l, F, Fl, F F e lel oe on e on le, on g, e le, e g e; v e lel velo; W e k d, F e ond oe, l e dne o e gv ene o e on on o ond oe. ISSN: Iue, Volue 7, Novebe 8

8 WSEAS RANSACIONS on SYSEMS Delng Cen, Cenglng Yn, nu Zng e oneng ne unen ondeed ung e nonlne e odel. A n e vele odel, e e oe o e eel n be oued b e e odel. In ode o ule e eone o e e, e nonlne Dugo odel eloed [9]. e led odel denoed [, ]: α nα F η, F η 3 μf [ ε v n α ] η, denoe e α n α η η η < deen e, η. η > ee e oneng ne o e e, α lo eeed, o on, e e eevel; e longudnl ne o e e, ε e od deon eduon o, F e vel lod ng on e eel, e l o, α e l ngle o e eel. Aodng o e nonlne vele odel, e eel n ndeenden l ngle: v γ α l n 3 v Wγ / v γ α n 3b v Wγ / bγ v α l n 3 v Wγ / bγ v α n 3d v Wγ / e nnneou vel lod F e u o e e lod nd lod ne. In ddon, e lod ne ued b longudnl nd lel eleon. en e vel lod o e eel n be eeed []: v & β γ Fl gb v& b 33 b W v & β γ F gb v& b 33b b W v & β γ Fl g v& 33 b W v & β γ F g v& 33d b W A e on oeen μ n on ee o oneng ne nd nee n e AFS onol, ued ee knon, o n be eed b oe en [, 3]. 6 Sulon eul e eone o e degned AFS onolle eed n e HILS e nd oed e onvenonl vele ou AFS onol. e lel eleon, been uled o e del eon, ued n e eul oon ned o del ngle. 6. oque n neuve In Fg.9, ne ve eeng nued e eed o 6 k/ ee e equed VSR e e e o o enl e. lo e eeng oque veu eeng eel ngle o e AFS onolled vele nd e onvenonl vele ou AFS. b, e e lel eleon nd e eone, eevel. I n be een, n ode o k e l e nd lel eleon, e eeng oque ovded b e dve edued b e oque oenon n ve eeng oeon. eeoe, e eevene o oque oenon b EPS uo oned. Seeng oque v. eeng eel ngle b Lel eleon ISSN: Iue, Volue 7, Novebe 8

9 WSEAS RANSACIONS on SYSEMS Delng Cen, Cenglng Yn, nu Zng Y e Fg.9. Reone o e oque n neuve. Lel eleon AFS vele v. eeene 6. Lne keeng eeng neuve e ne ve eeng neuve eed on e e od μ.5 e eed o 5 k/, on n Fg.. o deone e AFS eevene, l eeng eel nu on n e ovded o e AFS onolled vele nd onvenonl vele ou AFS, eevel. d Lel eleon onvenonl v. eeene Seeng eel ngle e Y e AFS vele v. eeene b Seeng oque v. eeng eel ngle Y e o onvenonl vele v. eeene Fg.. Reone o e lne keeng neuve. ISSN: Iue, Volue 7, Novebe 8

10 WSEAS RANSACIONS on SYSEMS Delng Cen, Cenglng Yn, nu Zng e AFS onolled vele een o eque lle oque e oon n b. Fgue nd e e e lel eleon nd e eone o e AFS onolled vele; d nd e e lel eleon nd e eone o e onvenonl vele. e eeene gnl o e oeondng nu deened b Equon 4 nd 5 e lo nluded n e. Reul nde bo e lel eleon nd e e o e AFS onolled vele ollo e eeene gnl n eonbl loe on n onvenonl vele. e u lel eleon devon o e eeene eone.8 / o e AFS onolled vele, le.56 / o e onvenonl vele. e u e devon o e eeene eone.4 deg/ o e AFS onolled vele, le.5 deg/ o e onvenonl vele. Lel eleon 6.3 Bkng on l od ue Dung bkng, ddonl oen ll be odued en e oe e led o le nd g de eel. en e ddonl oen ll eul n vele nbl. A ul ondon o e bkng eegen bkng on l deon od. o o e vele qukl oble n eegen, e l bkng oe ou lokng e eel e led o e eel. W deen deon ondon on e le nd g de, oen ll be geneed nd u e vele o e de ee e on oeen ge. In e o bkng on l ue, obl beeen bl nd bkng eone oble ung onl longudnl oe [8]. e AFS n oe e nbl ngle oenon uoll odng o e eedbk o e nd del ngle. o llue e eevene o develoed AFS e, e dve ve o ovde no bl oenon o e on eeng eel. e e ondued e nl velo o 6 k/. Fg. o e eul o g bkng on l od e od deon oeen o le de.5, nd g de.7. e lel eleon nd e e on n nd b.e ek e nd lel eleon o e AFS onolled vele e lle n e onvenonl vele. u, onluon n be dn e bl oved e AFS onol. b Y e Fg.. Reone o l bkng neuve. 7 Conluon In e, ne develoed ve on eeng AFS e onol been eened. On e b o e C-EPS en, e ooed AFS e n onol e EPS uo o oene e oued eon eeng oque ulneoul en e AFS uo oee. Sng e onuon eenon, el odel o e AFS e deved. Aed, e k o e AFS onolle degn oeeded n o : one e EPS uo onol o edue e eeng oque equeen o e dve, e oe o ovde e oened eeng ngle o eeng e nd vele bl. In on o e onvenonl bl onol, bo e del ngle nd e e ve been ed bk o ove e vele bl. In ddon, e e ne unene ve been del o ovde e onol obune. o deone e eone o e degned AFS onolle, HILS e ee ondued n ee e neuve bo e AFS onolled vele nd e onvenonl vele ou AFS. e eul ISSN: Iue, Volue 7, Novebe 8

11 WSEAS RANSACIONS on SYSEMS Delng Cen, Cenglng Yn, nu Zng o e ooed onolle n eevel lleve e eon eeng oque ell edue e devon o e deed eone. e AFS e n ove e vele bl nd neuvebl evdenl. Reeene: [] le, W., Renn,. nd Renel, W., Cone nd unonl o e ve on eeng e, SAE enl e, 4, No [] oen, P. nd Ek, M., Ave eeng - e BMW o od oden eeng enolog, SAE enl e, 4, No [3] Hok, M. nd Muk,., Y e onol o ele vele ung ee-b-e e, IEEE enl e,4, [4] Y, P., See-b-e lon o vele ndlng nd e, PD deon, Snod Unve, 5. [5] Dougl,. nd An, M., Robu lne qud degn el ee unen. IEEE non on uo onol, Vol.39, No., 994,.7-. [6] none, L., Plkov, L. nd Boko,., Degn o n ve 4WS e l unene, Conol Eng. Pe, Vol.3, No.8, 995, [7],.H. nd Song,.B., Conol log o n ele oe eeng e ung oo, Meon Vol.,, [8] n,w. nd lo,d., Adve onol o oo dve nvee nonlnee, Inenonl ounl o Conol, Vol.7, No.9, 999, [9] Cen, D.L., Yn, C.L. nd Cen, L., Sud on ve on eeng bed on e-e obeve, Cn Menl Engneeng Vol.8, No.4, 7, [] Song,.H., Boo,.S.,, H.S. e l., Model develoen nd onol eodolog o ne ele oe eeng e, Po. Inn Me. Eng P D:. Auooble Engneeng, Vol. 8, 4, [] Lu, Z., Ree on dn nl nd onol eod o ele oe ed eeng e o vele, PD deon, Huong Unve o Sene nd enolog, 4. [] M, S. nd Bgd, V.B., odegee-o-eedo oulon o vele ndlng oveen b ve eeng, Poeedng o e Aen Conol Coneene,. [3] M, S. nd oeng, D., Vele ndlng oveen b ve eeng, Vele Se Dn, Vol. 38, No.3,,.-4. [4] Aok, Y. nd Ho, Y., Robu degn o bod l ngle obeve o ele vele nd eeenl deonon, Elel Engneeng n n, Vol. 59, No., 7 nled o Denk kk Ronbun, Vol. 5-D, No , 5. [5] L, P., Cen, N. nd Sun, Q.H., Ol ollo u onol o 4WS vele bed on e eo, Cnee ounl o Menl Engneeng, Vol.4 No., 4, [6] Ad, N.L., jeou, A.nd Mee,., Robu e eedbk blon o uled ee vele, Vele Se Dn, Vol. 45, No. 3, 7, [7] Pk,. nd Heo, S.., Develoen o de-n-e-loo ulon e o ue n degn nd vldon o VDC log, Inenonl ounl o e oen Soe o Peon Engneeng, Vol. 4, No. 3, 3,.8-35 [8] uven,b.a, An,. nd uven, L., Coodnon o eeng nd ndvdul eel bkng ued vele bl onol, IEEE enl e, 4, [9] Hok,., uoo, H. nd N, O., Sdel ngle eon nd ve on eeng e bed on lel eleon d ene o euon ee o on/e eel. SAE Reve Vol.5, 4,.7-4 [] Dugo, H., Fne, C., Segel, L., An nl o e on oee nd e nluene on vele dn eone, SAE enl e, No. 7377, 97, [] k, B., Pk, Y.. nd, D.S., Degn o obeve o vele bl onol e, FISIA Wold Auoove Conge,. [] Alejndo, D. Dongue-, on. kn, oel E. Sndll., A bku e o uoove ee-b-e, ued b eleve bkng, 35 IEEE Poe Eleon Sel Coneene, 4, ISSN: Iue, Volue 7, Novebe 8

Introduction to Inertial Dynamics

Introduction to Inertial Dynamics nouon o nl Dn Rz S Jon Hokn Unv Lu no on uon of oon of ul-jon oo o onl W n? A on of o fo ng on ul n oon of. ou n El: A ll of l off goun. fo ng on ll fo of gv: f-g g9.8 /. f o ll, n : f g / f g 9.8.9 El: