A Backup System for Automotive Steer-by-Wire, Actuated by Selective Braking

Transcription

1 A Bakup Sytem fo Automotive Stee-by-Wie, Atuated by Seletive Baking Alejando D. Dominguez-Gaia Laboatoy fo Eletomagneti and Eletoni Sytem Maahuett Intitute of Tehnology Cambidge, MA USA ohn G. Kaakian Laboatoy fo Eletomagneti and Eletoni Sytem Maahuett Intitute of Tehnology Cambidge, MA USA oel E. Shindall Laboatoy fo Eletomagneti and Eletoni Sytem Maahuett Intitute of Tehnology Cambidge, MA USA Abtat In thi pape we popoe an altenate appoah to impove Stee-by-Wie (SbW) eliability in whih we utilize Bake-Atuated Steeing (BAS) a an independent eonday bakup teeing ytem. In SbW ytem, omponent and module edundany i the ommon appoah ued to maintain the teeing funtion when a failue ou. Unfotunately thi add a ignifiant amount of omplexity and ot and, what i moe impotant, it i not poible to oveome unantiipated and ommon mode failue of the SbW ytem. BAS utilize the toque geneated by eletive wheel baking and/o aeleation to atuate the teeing mehanim. With thi appoah, if the pimay teeing ytem (SbW) fail unoveed o thee i a ommon mode failue, the teeing ak i deoupled fom the pimay teeing atuato and the wheel ae intead teeed by the toque geneated by appliation of aymmeti baking (o aeleation). BAS, a well a SbW, will be a heavy ue of powe eletoni, eletial atuato, eno and ophitiated ontol ytem, many of whih ae aleady available fom eletoni tability ytem (e.g., ESP), whih ae beoming moe ommon in paenge a. In thi pape we detail the haateiti of the BAS ytem and povide the model neeay fo deigning appopiate powe eletoni and ontol ytem. I. INTRODUCTION Safety itial ytem in a a, fo example, hydauli bake and powe teeing, equie a eonday o bakup ativation mehanim to pevent atatophi failue. Thee bakup mehanim hould be baed ultimately upon diffeentiated edundant ytem to avoid unantiipated and ommon mode failue of the main ytem. In a onventional powe aited teeing ytem, the mehanial onnetion between the dive and the teeing ak eve a the eonday teeing mehanim [1]. In a SbW ytem the eonday teeing mehanim annot ely on a mehanial link (e.g., the teeing olumn) between the teeing wheel and the teeing ak ine the goal of SbW i to eliminate uh a mehanial onnetion. Laking thi onnetion, SbW deign effot have foued on developing faulttoleant ytem baed on edundany, i.e., the dupliation of omponent and module at all level [1], [], [3], [4]. Thi olution i widely applied in aiaft, but it add a ignifiant amount of omplexity and ot and, what i moe impotant, it i not poible to oveome unantiipated and ommon mode failue. Theefoe, it i impotant to exploe altenative to laial edundany fo ahieving ytem integity. In thi pape we popoe an independent bakup teeing ytem, Bake-Atuated Steeing (BAS), baed on utilizing aleadyexiting ytem to implement eletive wheel baking and/o aeleation to atuate the teeing mehanim. Simila appoahe have been popoed by NASA, in ode to develop the tehnology fo futue aiaft deign fo emegeny flight ontol, uing engine thut to augment o eplae the flight ontol ytem [5]. BAS, a well a SbW, will ue powe eletoni, eletial atuato, eno and ophitiated ontol ytem, ome of whih ae aleady available fom eletoni tability ytem, (e.g., ESP), whih ae beoming moe ommon in paenge a. Hee, we detail the haateiti of the BAS ytem and povide the model neeay fo deigning appopiate powe eletoni and ontol ytem. Setion II of thi pape explain the undelying motivation fo developing thi new ytem. Setion III peent the dynami model of the ytem ued in the imulation. In Setion IV, the ontol tategy i peented. Setion V how ome imulation eult, ompaing the behavio of a model implementing BAS to that of a vehile with a onventional teeing ytem. Conluding emak and futue wok ae peented in Setion VI. The notation ued i lited at the end of the pape. II. SELECTIVE BRAKING AS A BACKUP STEERING SYSTEM FOR STEER-BY-WIRE Seletive baking i aleady ued in ABS a a mean of ontolling the vehile in the peene of kidding ondition, and in eletoni tability ytem, whih keep the vehile fom exeiing maneuve that ould eult in lo of ontol, e.g., ollove [6]. In tability ytem, eletive baking i ued a a mean of maintaining the yaw ate and the body lip angle of the vehile below the limit that ould eult in the lo of ontollability and tability. Howeve, uh ytem do not take omplete ontol of the teeing tak, they only help tabilize the a in an ovetee o undetee ituation.

2 A pomiing way to utilize aleady-exiting ytem to meet the need fo a eonday mehanim to maintain teeing apability, when an unoveed failue o a ommon aue failue ou in the SbW ytem, i to dietly ontol the oad wheel angle, (and thu, alo the body lip angle and the yaw ate), by utilizing the eletive baking apability aleady inopoated in vehile equipped with eletoni tability ytem. In the unlikely event that SbW fail, the teeing atuato i dionneted and the dive ommand (a indiated by the teeing wheel angle) i ued to geneate eletive baking (aeleating) foe on eah wheel [7]. The moment podued at eah wheel by the offet (at oad level) between the longitudinal ente plane of the wheel and the kingpin axi (the ub adiu) aue the font wheel to tun appopiately. It appea that uh a ytem, with appopiate ontol, ould exhibit dynami behavio imila to that of the pimay teeing mehanim (SbW). Thi ontat haply with onventional mehanial bakup ytem, whih equie a lage toque at the teeing wheel if the powe ait uddenly fail while tuning. In uh a ituation an unpepaed dive may loe ontol of the a. a b V l l V fl fl F ll F lfl V F l X CG Z V V f f F l F lf F f Y F III. SYSTEM MODEL In thi etion, we peent the model ued in the development of the ontol tategy. Fit, a two-tak vehile dynami model i developed. Thi model ha been augmented o that the diffeential longitudinal foe at the font and ea tie F lf, F l, a well a the oad wheel angle δ, ae available a input. A implified model fo the oad wheel atuato i then peented, in whih the dive ommand no longe podue any effet in the teeing ak. Finally, the oad wheel atuato model i oupled with the vehile dynami model to obtain the omplete ytem model in whih the ontol input ae only the diffeential longitudinal foe at font and ea tie F lf, F l. Thi implified model allow u to un fat imulation uing M atlab/simulink, giving u good inight to the pefomane of BAS. A. Vehile dynami model The vehile dynami model peented hee i developed in a manne imila to the development of the linea ingletak model [8]. We extend the linea ingle-tak model to a linea two-tak model by alo onideing the diffeential longitudinal foe ating at the font and ea tie a ontol input, and making the following aumption: No lateal load tanfe No longitudinal load tanfe No olling o pithing motion (on the body) The tie lip angle ae mall enough to onide the tie woking in the linea pat of the tie-lip angle haateiti (i.e., the lateal foe ating on the tie ae popotional to the lip angle) Contant fowad veloity No aeodynami effet A mall-angle appoximation i made fo the oad wheel angle δ Fig. 1. Vehile vaiable and paamete fo the linea two-tak model. Figue 1 define the geometi paamete ued in the tatepae epeentation of the vehile dynami model given by (1). A defined in the figue, all vehile vaiable and paamete ae poitive, exept fo the body lip angle β, and the tie lip angle α fl, α f, α l, α, whih ae defined a negative. The influene of the oad wheel angle δ (whih i no longe ontolled dietly by the dive), and the diffeential longitudinal foe at the font and ea tie F lf, F l, have been epaated. The longitudinal tie foe ae the new vaiable ontolled by the dive via the teeing wheel angle δ w. Equation (1) epeent the lateal motion and the otation aound the ente of gavity (CG). Equation () epeent the longitudinal motion of the vehile (thee i no longitudinal aeleation tem ine ontant fowad veloity i aumed). The lateal foe ating on the tie ae aumed to be equal at the ight and left tie of the ame axle. They ae epeented by equation (3) and (4). β = ṙ + C f ac f C f +C ac f bc δ + ac f bc 1 a C f +b C V F lf β F l (1) F lfl + F lf + F ll + F l = ()

3 F lfl F lf Refeene Computation N u Vehile model F F lf V Reduedode etimato t Ff Fig. 3. Cloed-loop ontol ytem blok diagam. Fig.. Top view of a implified oad wheel atuato. = F f = C f a (β + V δ) (3) B. Road wheel atuato model F l = F = C f b (β V ) (4) β ṙ = + C m V bc tm V + a t bc 1 b C V F lf F l β (6) The aumption made to develop the oad wheel atuato model ae ummaized a follow: The kingpin axi i vetial, and kingpin inetia and fition ae negleted Tie foe ae the only mehanim to geneate toque aound the kingpin axi, i.e., thee i no foe tanmitted fom the teeing ak Effet of upenion, teeing ak and olumn ompliane ae negleted Figue how a top view of a implified oad wheel atuato geomety, defining the paamete involved in the oad wheel atuato model given by (5). A defined in the figue, all vaiable and paamete ae poitive, inluding the ub adiu, diplayed alo a poitive fo impliity of the pitue, although it i negative in mot ommeial a. The oad wheel angle δ depend on the vehile tate β and and alo on the diffeential longitudinal foe at the font tie F lf. δ = β + a v C f t F lf (5) C. Coupled oad wheel atuato and vehile dynami model By ubtituting (5) into (1), the omplete vehile model (6) i obtained. The limitation on the longitudinal foe impoed by () emain the ame. IV. CONTROL SYSTEM Figue 3 define the tutue of the ontol ytem. The input efeene fo the ytem i omputed uing a linea ingle-tak vehile dynami model [8], whih i a implified model of the dynami behavio of a vehile with a onventional teeing ytem. The input efeene i intodued to the ytem in uh a way that the taking eo i zeo. The feedbak ontol law i deigned uing the pole-plaement tehnique, whih will yield a imila tanient behavio to that of the linea ingle-tak model. A edued-ode etimato i ued to etimate the value of the body lip angle, ine the only meauement available fo the ontol ytem i the yaw ate. Thi i due to the fat that in eletoni tability ytem, the body lip angle i etimated athe than being dietly meaued. A. Refeene omputation Equation (7) epeent the linea ingle-tak model. It define the dynami of a vehile with a onventional teeing ytem, in whih the teeing ompliane wa negleted. β = C f +C a C f bc + C f ac f ac f bc 1 a C f +b C V β δ w SR (7)

4 By etting β and ṙ to zeo, a elation between δ w and the vehile tate β and i obtained (8), whih i the input efeene to the ytem. β = C f +C ac f bc C f ac f ac f bc 1 a C f +b C V 1 δw SR (8) Equation (9) yield the appopiate value of the matix N u that make the ytem tak the efeene input. N u = t + a t B. Feedbak ontol law 1 C bc bc 1 b C V (9) Equation (1) give the tutue of the feedbak ontol law [9], whee N u i the zeo teady-tate eo matix gain and F i the tate feedbak matix. ] [ β = F F l [ Flf ] [ ] β + (N u F ) (1) The pole plaement tehnique i ued to ompute the value of the State feedbak matix F, mathing the pole of the loed-loop ytem with thoe oeponding to the linea ingle-tak model. The tutue of the matix F i uh that only the diffeential longitudinal foe at the font tie F lf i affeted. The tutue of the matix F i given by (11). [ ] f11 F = (11) f 1 C. Redued-ode etimato A edued-ode etimato i ued to etimate the value of the body lip angle. Equation (1) and (13) yield the value of the etimated body lip angle ˆβ. β = ( C L bc + [( t ) ˆβ + ( bc ) L ( + a t D. Individual tie foe omputation ) 1 L b C V )] [ ] F lf (1) F l ˆβ = β + L (13) Leat quae etimation i ued to ompute the individual tie foe that will eve a the efeene to the individual wheel bake ontolle. Equation (14) give the value of eah individual wheel foe a a funtion of the diffeential longitudinal foe at font tie. F lfl F lf F ll F l = 1 F lf F lf F l F l V. SIMULATION RESULTS (14) The imulation wee aied out fo diffeent value of the ommanded teeing wheel angle δ w, fo diffeent value of the ente of gavity peed V, and fo diffeent value of the ub adiu. The eult of the loed-loop ontol imulation wee ompaed with expeimentally veified imulation data fom a a with a onventional teeing ytem, whih wee povided by Fod Moto Company. The numeial value of the geometi paamete ued in the imulation model oeponding to the povided data ae hown in Table I. Although defined a poitive in Figue 1, the value of the ub adiu ued in the imulation ae negative beaue mot ommeial a have negative ub adiu. TABLE I VEHICLE PARAMETERS USED IN THE DEVELOPMENT OF THE SIMULATION [deg/] MODEL. Paamete Value a 1.46 m b 1.71 m 1.55 m C f 19 N/deg C 19 N/deg 37 Kgm m Kg. m,.1 m, -.5 m,.1 m t.5 m SR 17 β [deg] δ [deg] Expeimentally veified Fod imulation data fo a onventional teeing ytem Fig. 4. Body lip angle β, yaw ate and oad wheel angle δ, veu time fo a 45 tep in teeing wheel angle δ w, and 1 km/h vehile peed V.

5 , F f F l, F -5-1, F f 5-5 F l, F Expeimentally veified Fod imulation data fo a onventional teeing ytem Fig. 5. Lateal foe ating on font and ea tie, F f, F l, F, veu time fo a 45 tep in teeing wheel angle δ w, and 1 km/h vehile peed V Expeimentally veified Fod imulation data fo a onventional teeing ytem Fig. 7. Lateal foe ating on font and ea tie, F f, F l, F, veu time fo a 45,.7 Hz inuoidal teeing wheel angle input δ w and, 7 km/h vehile peed V. [deg/] β [deg] Expeimentally veified Fod imulation data fo a onventional teeing ytem Fig. 6. Body lip angle β, yaw ate and oad wheel angle δ, veu time fo a 45,.7 Hz inuoidal teeing wheel angle input δ w, and 7 km/h vehile peed V. Figue 4 and 5 how the eult fo one of the imulation aied out, oeponding to a tep in teeing wheel angle of 45, and a vehile peed of V =1 km/h. The dahed line oepond to the expeimentally veified behavio of the vehile with a onventional teeing ytem, while the olid line how the imulation eult of a model of the ame vehile implementing the BAS ytem. In Figue 4 the body lip angle β, the yaw ate and the oad wheel angle δ ae epeented veu time. It an be een that the hape of the yaw ate of a a with a onventional teeing ytem δ [deg] i mathed almot pefetly, while the mathing of the body lip angle in not pefet. The imulation eult fo the body lip angle have le ovehoot than the veified data, while the teady-tate value i bigge. Thee eult ae expeted ine the model efeene ued in the loed-loop imulation i a vey implified model of the dynami of a a. Figue 5 diplay the lateal foe ating on the tie, F f, F l, F, while oneing. Again, the mathing between the expeimentally veified data and the imulation i not pefet. In thi ae, the expeimentally veified data diplayed fo, F f, F l, F oepond to the aveage of the lateal foe ating on the tie of the ame axle. In a eal a, although having imila value, the lateal foe developed by the tie of the ame axle ae not exatly the ame. Figue 6 and 7 how the eult oeponding to a 45,.7 Hz inuoidal teeing wheel angle input δ w, and 7 km/h vehile peed V. Again, the diepany between the expeimentally veified data and the imulation i expeted ine the model efeene i a implified vehile dynami model. TABLE II STEADY-STATE VALUES OF THE TOTAL FORCES ACTING ON THE TIRES F tfl, F tf, F tl, F t FOR A 45 STEP IN STEERING WHEEL ANGLE, 1 km/h VEHICLE SPEED V, AND DIFFERENT VALUES OF SCRUB RADIUS. [m] F tfl 6, 57 1, 344 6, 519 3, 877 F tf 6, 57 1, 344 6, 519 3, 877 F tl 6, 891 1, 64 6, 65 3, 384 F t 6, 891 1, 64 6, 65 3, 384

6 Table II how the eult oeponding to the the teadytate value of the total foe ating on the tie F tfl, F tf, F tl, F t, alo fo a tep in teeing wheel angle of 45, and a vehile peed of V =1 km/h. It i vey impotant to note that a the abolute value of the ub adiu deeae, the value of the total foe ineae almot linealy. Thi eult i vey impotant and ha to be handled aefully in the implementation of BAS ine the adheion limit of the tie i vey impotant fo the feaibility of the ytem. VI. CONCLUSIONS AND FUTURE WORK Thi analyi indiate that within a eaonable envelope of ub adiu and baking foe, Bake-Atuated Steeing an be ued to tee a vehile with dynami behavio imila to that of a a with a onventional teeing ytem. Implementation of the popoed ytem, a well a SbW, will ely heavily on powe eletoni, eletial atuato, eno and ophitiated ontol ytem, ome of whih ae aleady available in eletoni tability ytem. The imulation eult obtained in thi pape wee obtained with a implified vehile model. The next tep would be to develop and evaluate a moe auate model inluding featue uh a a moe auate teeing geomety, teeing ytem ompliane, load tanfe, a oad model inluding fition oeffiient and a non-linea tie model. The implementation iue of the ytem ae anothe impotant piee of futue wok that need to be addeed. ACKNOWLEDGMENT The autho would like to aknowledge oeph Neal at Fod Moto Company fo poviding the vehile dynami data. Thank ae alo extended to Robet Hammett at the Chale Stak Dape Laboatoy and Dougla Milliken at Milliken Reeah Aoiate fo helpful diuion and omment. Thi eeah wa uppoted by the MIT/Induty Conotium on Advaned Automotive Eletial/Eletoni Component and Sytem. NOTATION a: Ditane CG to font axle b: Ditane CG to ea axle : Ditane between wheel on font and ea axle CG: Vehile ente of gavity C f : Font axle equivalent oneing tiffne C : Rea axle equivalent oneing tiffne F : State feedbak matix F lfl : Longitudinal foe ating on the font left tie F lf : Longitudinal foe ating on the font ight tie F ll : Longitudinal foe ating on the ea left tie F l : Longitudinal foe ating on the ea ight tie : Lateal foe ating on the font left tie F f : Lateal foe ating on the font ight tie F l : Lateal foe ating on the ea left tie F : Lateal foe ating on the ea ight tie F tfl : Total foe ating on the font left tie F tf : Total foe ating on the font ight tie F tl : Total foe ating on the ea left tie F t : Total foe ating on the ea ight tie : Yaw inetia L: Obeve gain m: Ma N u : Zeo teady-tate eo matix gain : Yaw ate : Yaw ate efeene : Sub adiu SR: Total teeing atio t: Mehanial tail V : CG peed V fl : Font left wheel ente peed V f : Font ight wheel ente peed V l : Rea left wheel ente peed V : Rea ight wheel ente peed F lf : Diffeential longitudinal foe at the font tie F l : Diffeential longitudinal foe at the ea tie α fl : Font left wheel lip angle α f : Font ight wheel lip angle α l : Rea left wheel lip angle α : Rea ight wheel lip angle β : Body lip angle β : Redued-ode obeve tate vaiable β : Body lip angle efeene ˆβ : Etimated body lip angle δ: Road wheel angle δ w : Steeing wheel angle REFERENCES [1] W. Hate, W. Pfeiffe, P. Dominke, G. Ruk, and P. Bleing, Futue eletial teeing ytem: Realization with afety equiement, SAE Tehnial Pape Seie, Pape -1-8,. [] P. Dominke and G. Ruk, Eleti powe teeing,the fit tep on the way to tee-by-wie, SAE Tehnial Pape Seie, Pape , [3] R. Iemann, R. Shwaz, and S. Stolzl, Fault-toleant dive-by-wie ytem, IEEE Contol Sytem Magazine, vol., no. 5,. [4] R. C. Hammett and P. S. Babok, Ahieving 1 9 dependability with dive-by-wie ytem, SAE Tehnial Pape Seie, Pape , 3. [5] T. Tuke, Touhdown: the development of populion ontolled aiaft at naa deyden, Monogaph in aeopae hitoy, no. 16, NASA, [6] BOSCH, Diving-Safety Sytem. Robet Boh GmbH, nd ed., [7]. Guldne, M. Kug, S. Bakau, K. Balzuweit, H. Smakman, C. Ebne, M. Gaf, A. Shedl, P. Mehe, R. Die,. Heinih, S. Millap, B. Muay, D. Kukenkamp, and M. Bye, Bak-divable tee-by-wie ytem with poitive ub adiu. US Patent Appliation Publiation, Deembe 3. [8] W. Milliken and D. Milliken, Rae a vehile dynami. Soiety of Automotive Enginee, [9] G. Fanklin,. D. Powell, and A. Emami-Naeini, Feedbak Contol of Dynami Sytem. Addion-Weley, 1994.