Model-based fault diagnosis for a vehicle chassis system

Transcription

1 9 Ameican Contol Confeence Hatt Regenc Rivefont, St. Loui, O, USA June -, 9 WeB3.3 odel-baed fault diagnoi fo a vehicle chai tem Xian Zhang, Pieluigi Piu, embe, IEEE AbtactBaed on a lineaized 3-DO biccle model, thi pape compae two diffeent fault detection and iolation (DI) method fo the DI of a command input fault and an output eno fault within a vehicle chai tem. he fit DI appoach ue pait euation to decouple the two tpe of fault, while at the ame time, minimize the influence of the ditubance on the eidual. he econd DI method ue liding mode obeve deign, and b monitoing the euivalent contol of the obeve, in which the fault infomation i contained, achieve the detection and iolation of the fault. Lane change maneuve ae imulated, and the eult howed that, unde the given imulation condition, both diagnotic appoache can uccefull detect and iolate the two tpe of fault depite the exitence of a lateal wind gut ditubance. I. INRODUCION IH the inceaing peed of the moden vehicle, hand W -ling and tabilit iue ae of indiputable ignificance. Vehicle contol tem uch a VSC/ESP ae implemented to guaantee the handing and tabilit of the vehicle epeciall at high peed and when the vehicle i unde coneing maneuve. In the popula VSC/ESP tem, the contol tem utilize the infomation of the teeing angle fom the dive, the vehicle aw ate and lateal acceleation to decide the contol of the actuato, which make the diagnoi of the actuato fault and eno fault epeciall impotant. In []a hieachi- -cal model-baed DI cheme fo fault detection and iolation fo a vehicle tem i peented, and in the ubtem DI unit, the poibilit of etimating the tate of the vehicle ha been demontated fo a implified font wheel teeed biccle model baed on continuou time liding mode obeve. H. ennel [] developed a model baed eno monitoing tem fo ESP that wa implemented, and it i cuentl poduced in lage volume b Continental EVES. he monitoing tem i mainl ued fo detecting fault in eno onl. Since the field of DI ha een ignificant poge with epect to model-baed algoithmic appoache to eidual geneation, thi pape utilized thi elativel matue appoach to contuct the DI cheme fo fault detection and iolation of a command input fault and an output eno fault within a vehicle chai tem. A pait euation eidual geneation method i peented a bai of the DI cheme, and compaed with a linea liding mode obeve baed appoach. B monitoing the euivalent contol of the obeve, in which anucipt eceived Septembe, 8. X. Zhang i with the echanical Engineeing Depatment, Clemon Univeit, Clemon, SC 9634 USA (coeponding autho to povide phone: ; xianz@clemon.edu). P. Piu i with the echanical Engineeing Depatment, Clemon Univeit, Clemon, SC 9634 USA ( piup@clemon.edu). the fault infomation i contained, the detection and iolation of the input fault and output fault i achieved. he analtical elationhip between the fault and the euivalent contol i analzed, and the fault ae futhe decoupled uing tanfomation. he pape i oganized a follow. he odel Deciption ection decibe the nonlinea vehicle chai model. In the Diagnotic Appoach ection, two DI method ae peented, one uing the claical Pait Euation, and the othe uing Sliding ode Obeve. Simulation ae then caied in the ubeuent ection, whee both DI method ae veified. a b L V x V f S II. NOENCLAURE ditance fom cente of gavit to font axle ditance fom cente of gavit to ea axle wheelbae aw velocit fowad velocit lateal (idelip) velocit lip angle of the font tie lip angle of the ea tie font axle teeing angle Spung ma Unpung ma US otal ma of the vehicle k c h Supenion tiffne N-m pe adian of oll Supenion damping N-m pe ad/ of oll ate Height of CG fom oll axi III. ODEL DESCRIPION A biccle model of the vehicle chai tem that include olling motion i conideed. ig.. Biccle model. he vehicle model i deigned to have thee degee of feedom (3-DO), thee ae: idelip velocitv, aw ate, and oll angle. he input to the tem i the teeing angle /9/$5. 9 AACC 6

2 of the font wheel. he meaued output ae aw ate and lateal acceleation a [3], [4]. he lip angle and ae given b f V a V b, f V V x x () whee = degee ea teeing pe degee oll. he nonlinea vehicle chai model i expeed uing the following tate pace euation: h co( ) V Izzo Ixzo co( ) a b f h co( ) Ixzo co( ) I xxo h h in( ) Vx in( ) () h in( ) h Ixzo in( ) V in( ) hv x h c hg k co( ) in( ) in( ) he onl input to the model i actuall the teeing command coming fom the dive (ince the longitudinal peed, i.e. thottle poition i aumed to be contant). Howeve, the foce-lip angle elation of a tie can be bet modeled accoding to the Pacejka tie model, which lead the lateal foce f and to be teated a input. hen, futhe aociating the lip angle with the teeing angle b () would finall eult in the nonlinea vehicle model whee the teeing angle i the onl input. IV. PROBLE ORULAION hi pape deal with the detection and iolation of the following et of fault: ault on the teeing angle command (actuato fault). he effective teeing angle doe not coepond to the commanded teeing angle. Ou objective i to detect a contant eo of. degee o highe. Yaw ate fault (eno fault). Ou objective i to detect a bia of 5% o moe fom the nominal value of the aw ate. he longitudinal velocit of the modeled vehicle i et to a contant value of km/h. A wind gut ditubance up to 5N i alo conideed to be acting on the tem. We aume alo that the lateal acceleation i meauable and fault fee. o both aw ate and lateal acceleation eno a 5% white Gauian noie i conideed. V. ODEL LINEARIZAION A the vehicle model i imulated unde the aumption of contant longitudinal velocit of km/h, which i a ve high peed, the teeing maneuve i bounded to be a mall teeing angle input. B lineaizing the tem model aound V and, we ae expecting good appoximation of the nonlinea vehicle model. he nonlinea model in Section 3 can finall be lineaized and put into tandad tate-pace in the fom of x AxBu CxDu (3) (4) whee u x V i the tate, and i the output. A can be veified b imulation, the lineaized model peent good appoximation of the nonlinea model unde mall input cae. he popoed diagnotic algoithm ma be baed on thi linea model. Howeve, when lage input i fed into the tem o when the aumed contant tem paamete, vehicle longitudinal velocit vaie, modelling eo iue would thu aie. o deal with thi iue, multiple lineaized model can be contucted in the Lineaized odel module, poviding the poibilit of moe pecie appoximation of the eal nonlinea model at an time b electing appopiate lineaized model accoding to the tem opeating egion., VI. DIAGNOSIC ALGORIH DESIGN A. it method: Pait Euation (PE) Vehicle + Chai + Nonlinea odel a Lineaized odel ig. PE baed DI cheme. a _lin _ lin Reidual Geneato and Evaluato ig. how the Pait Euation baed DI cheme, whee i the input fault, and i the output fault. he command input goe into the lineaized model, which geneate the output _, a lin _. he Reidual Geneato and lin Evaluato take the output of both the nonlinea and linea model and then geneate and evaluate the eidual to make a deciion on the peence of a fault o not. he lineaized model given b (3) and (4) can be expeed in the geneal tate pace euation fom a x AxBuE pe D (5) CxDu p D whee p i the fault vecto, and i the ditubance. 7

3 he tem given b (5) can be expeed in tem of tanfe function in the feuenc domain a: Y() () U() S ()() p S ()() (6) D Whee () CIA BD S () () (7) and () () () p p p U() Y() he eidual ae given b [5]: R ( ) R ( ) W( ) Y( ) ( ) U( ) W( ) S ( ) p( ) S ( ) ( ) p () () () () () D p () () () () () D w w S w w S () Ou objective i to deign w ij (, i j,) uch that the eidual have deied epone to the fault and ditubance given b z kl ( k,; l,,3), i.e. R () z () z () z () 3 p () R () z () z () z () 3 p () () Note that decoupling the ditubance would put etiction on the futhe decoupling of the fault. hat i, if we z () w () S () w () S () and et 3 D D z w S () () () 3 D D D (8) (9) w () S () fo decoupling the ditubance, it i not poible to futhe decouple the two tpe of fault fom each othe. Hee, fit the poblem of decoupling the two fault i conideed, then, b adjuting W (), the influence of the ditubance on the eidual i minimize. o decouple the two tpe of fault, we deign: z () z () z () z () () hen, b neglecting the ditubance, the econda eidual become R () p p R () () whee, can be elected to adjut the tanient epone of the eidual to the fault, and the tanfe function of the ditubance to the eidual, i.e. z 3 (), z (), a well. 3 uthemoe, the tead tate value of the eidual would be identical to the magnitude of the coeponding fault itelf. om (8) and (9), b neglecting, it follow that: w () w () z () z () S w () w () () () z z () Once the matix W() i detemined, it i poible to evaluate the influence of the ditubance on the eidual b calculating and analzing z 3 (), z (). 3 ig. 3 epeent the Bode plot of z 3 () ( z () can be 3 plotted in a imila wa) when. he maximum of the magnitude of both z 3 () and z () ae eached at feuenc 3 (ad/ec), with the value -db and -db epectivel. Note that z 3 (), z () depend onl on, 3 epectivel, which can be elected independentl. ig. 3 Bode Plot of z () when 3 Balancing between the epone of the eidual to the fault and the pupoe of minimizing the magnitude of z and z (), the time contant ae finall choen to be 3 3 () and. B. Second method: Sliding mode obeve (SO) hi appoach i baed on a Dedicated Obeve Scheme (DOS) and ue the two output to build two liding mode obeve, each uing one output [6],[7]. In thi cae the fault infomation i included in the euivalent contol of the liding mode obeve, and b it magnitude, it i poible to achieve the fault detection and iolation [8]. Since one output i fault fee ( a ), the liding mode obeve uing thi output i obut to the output eno fault and thu can be deigned to onl detect the input fault. he othe obeve which ue the output infomation including eno fault ( ) can be ued to iolate the output fault. a Vehicle Chai + + Nonlinea odel DI (SO) Scheme S Obeve I Euivalent Contol S Obeve Euivalent Contol ig. 4 Sliding ode Obeve baed DI cheme. Reidual Evaluation 8

4 ) Deign of SO I ake the fit output, i.e. aw ate eno meauement he tem tate-pace euation ead [9] x=ax B( uu) E D () = C x+ m x, and define the new tate vecto of the tem a x. Intoduce the tanfomation Let V x matix uch that: x B appling the tanfomation to (, we obtain x = A x +A +B ( uu) E d =A x +A +B ( uu) E (3) d m whee A A B E d A, B, E d A A B E d Conide now the obeve I epeented b x = A x +A +B u Lv =A x +A +Bu v (4) whee v i an auxilia input defined b v ign m (5) Define the eo a e, e x x m, then e m ign A e A e B ue e (6) d Convegence condition ae given b [], []. When i lage enough, it can be hown that e afte a hot tanient. he euivalent contol v can be obtained fom (6) a: e v A A B E (7) e u e d On the liding manifold e e x x A LA e A LA (8) B LB ue LE L d d he tead tate value of e afte the tanient can be expeed a: e k k uk k u dot (9) whee k, k, k, k ae coefficient paameteized b L u dot. B ubtituting (9) into (7), we get A B A A A k E A k v k u k e u d dot () B adjuting L, it i poible to make k and k dot elativel mall, o that the euivalent contol of the fit liding mode obeve will be mainl contituted b two pat (neglecting the deivative tem and ditubance): a tem popotional to the input fault u, and a econd tem popotional to the output fault. ) Deign of SO II ake the econd output, i.e. lateal acceleation eno meauement, we have a. he tem tate-pace euation ead: x=ax B( uu) E d () =Cx+D ( uu) d C, D, ae the econd ow of CD,, d given b (5). d epectivel, a Define = D u, m =C x, and conide the new tate vectox, whee x V. B pefoming the tate tanfomation imila to that in the fit cae, we can ewite () a x = A x +A +B ( uu) E d =A x +A +B ( uu) E () m d D d u whee A, B, Ei, j,ae ome contant matice ij i di obtained b pefoming the tanfomation. Similal to the fit cae, the obeve II i contucted and it euivalent contol can be finall obtained a: v A k B A D ua k D u e u udot (3) A k E A A k d d dot d Whee ku, kudot, k, kdot can be adjuted b tuning L.In pactice, the tem u i ve mall, o thi tem can be neglected. If, b deign, the coefficient of the ditubance and it deivative ae made elativel mall, then the euivalent contol of the econd liding mode obeve would be popotional to the input fault u. hi i poible becaue of the fee paamete L. om () and (3), we have then v A k B u A k A k uk (4) e u ue e v A k B A D u k u (5) e u ue o decouple the two tpe of fault, conide the following tanfomation 9

5 v v e u e k uk k k ue e ue eu u k u k ue ue k ue e k ue k (6) (7), will each contain onl one fault hen the eidual (neglecting thoe mino tem), thu achieving the fault iolation. which i a contant. degee deviation fom the nominal input. Since the thee i no output fault, ta below th, while exceed th at 5, indicating the input fault occu. In ig. 8, a 5% bia fom the nominal value of the aw ate occu at the aw ate eno fom 5, which contitute the output fault (p fo eno fault without ditubance and p w/d fo fault with ditubance). Note that thi fault i popotional to the nominal value of the aw ate, o the fault eall occu at when the aw ate i elativel lage. exceed th at.7. VII. SIULAION RESULS o ou imulation poce, we conideed a ditubance acting on the tem a epeented in ig. 5: ig. 5 Ditubance time hito A. Pait Euation appoach he imulation eult unde diffeent fault/ditubance condition uing PE-baed appoach ae hown in ig. 6~ig. 8. In all cae, the dive i doing a paing maneuve, i.e. fit changing to the left lane, and then changing back to the ight lane. ABLE I PHYSICAL PARAEERS USED IN HE PRESEN ODEL Paamete Value Ditance fom cente of gavit to font axle a.4 m Ditance fom cente of gavit to ea axleb.4 m owad velocitv x km/h Spung ma S kg Unpung ma US kg Supenion tiffne k 47 N.m/adian of oll Supenion damping c 3. N.m pe ad/ of oll ate Height of CG fom oll axi h.35 m ea teeing pe degee oll -.95 degee f ig. 6 how the cae when no fault i peent, whee the two eidual, with o without the ditubance, ta within the uppe and lowe thehold. o the fit eidual, the uppe and lowe thehold th. ; fo the econd eidual, th.. In ig. 7, an input fault (p) occu at.5, ig. 6. Reidual unde no fault condition. ig. 7. Reidual unde input fault (contant. degee). ig. 8. Reidual unde output fault (+5% fom nominal value). We define the fault ignatue a

6 if th if th if if th th he DI ule i impl a tated in able. ABLE. AUL SIGNAURE OR PE SCHEE ault pe No fault Input ault Output ault Both ault B. Sliding ode Obeve appoach Simila imulation eult uing SO-baed appoach ae hown in ig. 9~ig.. ig. 9. Reidual unde no fault condition. he ame DI ule fo the PE baed appoach can be applied. Compaed to the PE method, the eidual uing SO method peent chatteing when the two method have compaable tanient epone. Note howeve, that, when the actual vehicle peed i not a contant km/h an moe, the coefficient matice in (5) will change, cauing phenomenon model eo fo PE-baed appoach. On the conta fo the SO method, which i a time-vaiant appoach in natue, the coefficient matice in () and () can be updated with time accoding to the eal time vehicle peed. VIII. CONCLUSION hi pape peent two fault diagnotic appoache fo the fault detection/iolation of a vehicle chai tem in the peence of actuato fault and output eno fault, and unde the influence of wind gut ditubance. Both appoache ue the ame lineaized model fom the nonlinea vehicle chai model a thei DI bai. In thi pape, the elationhip between the fault and the euivalent contol i analzed. Simulation ae caied fo both appoache. A the imulation eult howed, unde the ame condition, both diagnotic appoach can uccefull detect and iolate the two tpe fault depite the exitence of the ditubance. uthe wok will account fo the model eo and accommodate the opeation egion futhe awa fom the lineaized point, making the DI tem moe geneal and obut. ig.. Reidual unde input fault (contant. degee). REERENCES [] P. Piu, G. Rizzoni, A. Soliman, S. Ambeka, B. ua, and L. Jalic, ASE Intenational echanical Engineeing Conge & Expoition, Olando, loida,. [] H. ennel, E. L. Ding A odel-baed ailafe Stem fo the Continental EVES Electonic-Stabilit-Pogam (ESP) --635, SAE Automotive Dnamic & Stabilit Confeence, o, ichigan,. [3]. D. Societ of Automotive Enginee, Inc., 99. [4] J.Y. John Wile & Son, Inc., 993. [5] J. J. Getle, ault Detection and Diagnoi in Engineeing Stem, 998, CRC Pe, ISBN: [6] S. E. uldoon,. Kowalczk, J. Shen, Vehicle ault Diagnotic Uing a Seno uion Appoach, IEEE, pp. 59~596 [7] P. Piu, Vehicle Chai onitoing Stem, Contol Engineeing Pactice, (3), pp , (3) [8] D. Bambilla, L.. Capiani, A. eaa, and P. Piu, Actuato and eno ault Detection fo Robot Via Second Ode Sliding ode Obeve, VSS 8, uke [9] P. ank, ault diagnoi in dnamic tem [] V. Utkin, liding mode contol in Electomechanical Stem, 999 alo & anci, ISBN: [] V. Utkin, Sliding mode and thei application in vaiable tuctue tem, 978 i Publihe, ISBN: ig.. Reidual unde output fault (+5% eno fault).