A quarter-car suspension system: car body mass estimator and sliding mode control

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1 Aville online Proei Tehnology 7 ( 3 ) 8 4 The 3 Ieroerin Conerene on Eleroni Engineering n Coper Siene A qrer-r penion ye: r oy eior n liing oe onrol Ervin Alvre-Sánhe* Fl e Ingenierí Meáni Eléri, Univeri Verrn, on Univeriri, Xlp C.P. 99, Méxio Ar The prpoe o hi pper i o preen ro onrol hee or qrer-r penion ye ner ro irne proile. Here liner heil oel i preene in orer o eign liing oe onroller h llow voi he ine ro vriion over he r oy. Novely o hi pper i given y he lgeri eior e o in he r oy o he qrer-r ye, he rel how h he in onrol ojeive n e rehe: he penger oor. Keywor: liing oe onrol, ive penion, ilion. Inroion An iel penion r ye hol e le o iole he r oy ro he perrion ine y he ro. In generl, he penion ye n e liie, e on he exernl power inp, pive, eiive n ive. A pive penion ye i onvenionl penion e in lo he oeril vehile n oion o r oy i vrile je o ro oniion. The ei-ive penion ye h he e eleen o onvenionl ye, he per h wo or ore elele ping re n reqire high ore low veloiie n low ore high veloiie, n e le o ove rpily eween he wo. An ive penion h n or h llow iprove he penger oor e hi eleen i * Correponing hor. Tel.: ; x: E-il re: erlvre@v.x The Ahor. Plihe y Elevier L. Open e ner CC BY-NC-ND liene. Seleion n peer-review ner reponiiliy o CIIECC 3 oi:.6/j.proy.3.4.6

2 Ervin Alvre-Sánhe / Proei Tehnology 7 (3 ) ple in prllel wih he per n he pring eween he r oy (prng ) n he wheel (nprng ). Typilly, ive penion ye inle or h pply iionl ore. Thee iionl ore re eerine y ee onrol lw ing ro enor he o he vehile. Vrio onrol regie h pive onrol preene y Ngroho e l. [], y onrol in Rnjr-Srine e l. [] n opil onrol evelope y Pheg e l. [3] hve een propoe in he p yer o onrol he ive penion ye. In hi pper he ro onrol eign propoe, e on he liing oe onrol ehniqe y Uin [4], llow he ppreion o he ro perrion over he oy o r, inreing he penger oor. Alo, e on he lgeri pproh propoe y Flie e l. [5,6], prng eior i preene.. Sye yni A qrer-r penion ye hown in Fig. i e o ile he onrol ye. The yni eqion o he penion ye ing Newon or Eler-Lgrnge ehoology, preene y Feh n Alvi in [7], re o he ollowing or were,,,, n enoe he, ine n he ping re o he prng n nprng eleen, repeively. The ro vriion re repreene y r n he vrile n re he oy n wheel ipleen, repeively. The ye i eqippe wih n ive per ple eween he prng n nprng e o exer he reqire onrol ore. Soe o he ro vriion re inroe ing he npe nrl reqeny o he ye. r r () () Fig. A qrer-r oel o penion ye In orer o oin he npe nrl reqenie o he nperre ye he preer,, n r re eql o ero in () n (), oining he ollowing hoogeneo eqion (3) (4) j Propoing he olion n (3) n (4) n e wrien in he ollowing or e e j

3 Ervin Alvre-Sánhe / Proei Tehnology 7 ( 3 ) 8 4 (5) where A i he lle ine rix o he ye. The eerinn o rix A i given y A 4 ) e( (6) Eqing (6) o ero n olving or he wo npe nrl reqenie re oine. 3. Sliing oe onrol eign The in i o onrol eign i o provie he eire yni ehvior o vehile ner ro vriion. Aoring o Chve e l. in [8], he liing oe ehniqe llow lill he onrol ojeive i he nex liing re i e (7) where repreen he eire vehile ehvior, n re poiive onn o e eerine. Diereniing he eqion (7) one (8) n repling ro () he eon erivive o he prng ipleen, he yni o he liing re i given y (9) When, he o lle eqivlen onrol n e oine () whih reri he ye yni when he liing re h een rehe. To ore he ye yni o reh he liing re he ollowing rive onrol i e () where L i poiive onn. Finlly, he liing oe onroller, given y he o he eqivlen n rive onrol i he ollowing () A eq Lign n Lign

4 Ervin Alvre-Sánhe / Proei Tehnology 7 (3 ) Sprng eior The i ie o he lgeri eior i e on he ieniiion eho propoe n nlye y Flie e l. [5, 6,9]. In orer o oin he prng eior, he ierenil eqion () i erie in noion o operionl ll ollow F (3) where,,, re he ye iniil oniion. In orer o eliine he epenene o nnown onn, he eqion (3) i ierenie wie wih repe o he vrile, reling in 4 U U F (4) Now, liplying (4) y - one oin h 4 U U F (5) n rnoring o he ie oin le o he inegrl eqion 4 (6) By olving (6) i i oine he ollowing eior or he nnown prng 4 () I i evien h he nowlege o he prng n nprng e ipleen n he onrol ore i reqire. 5. Silion rel The ilion rel were oine y en o MATLAB/Sylin, wih he Rnge-K neril eho n ixe inegrion ep o. The neril vle or he he qrer-r penion, preene y Arele e l. [], n he onrol preer re hown in le.

5 Ervin Alvre-Sánhe / Proei Tehnology 7 ( 3 ) 8 4 Tle.Pree: Qrer-r penion ye n onrol Preer Vle Uni Sprng ( ) 8 g Unprng ( ) 8 g Spring ine ( ) 8,79 N/ Dping onn ( ),3 N / Tire ine ( ) 7, N/ Tire ping ( ) N / Conrol preer (,,L),3,. The ro perrion proile i hown in Fig.. One n noie he hree ieren plie n reqenie ing over he qrer r oel. The ir wo ignl repreen py ro n he hir ignl eween 6 n eon repreen pee reer in he ro. Fig.. Ro perrion In hi ilion, he eire poiion or he prng i onn vle o 5. The ree ipleen ver he onrolle ipleen or he prng i hown in Fig.3. Fig. 3. Dipleen o prng : ree v onrolle In Fig. 4 one n noie h he nprng ipleen oille even in he onrolle ye, hi i ee he liing re only reqire h he prng ipleen rehe he eire vle.

6 Ervin Alvre-Sánhe / Proei Tehnology 7 (3 ) Fig. 4. Dipleen o nprng The prng eior ehvior i hown in Fig. 5. One n noie h he eior rehe he prng vle o 8 g in ll ie o o. eon, whih llow ing i in new ro onrol hee wih preer ieniiion. Conlion n rher wor The pper preen onrol opion or n ive penion ye. The propoe liing oe onroller i ro ner ro vriion n he ilion rel prove h lgeri eior i n ville eleion or e ino onroller eign. The rher wor i irely rele wih he lgeri eiion o pring ine n ping vle. One hving he preer eiion, he onrol hee ol e ipleene i in rel qrer-r penion ye. Reerene [] Ngroho, P. W., D, H., Li, W. H. & Alii, G. A new pive y-hyri onrol regy o ei-ive penion wih gneorheologil per. In Y. G & S. Sh (E.), 4h Inernionl Conerene on Copionl Meho (pp. -9). [] Rnjr-Shrie, B., Solni, M. n Roopie, M. Conrol o Aive Spenion Sye: An Inervl Type - Fy Approh. Worl Applie Siene Jornl (): 8-8,.

7 4 Ervin Alvre-Sánhe / Proei Tehnology 7 ( 3 ) 8 4 [3] Pheg, T., Gi, A., Se, C. Conrine opil onrol: n ppliion o eiive penion ye, In. Jornl o Sye Siene, Vol. 4, No. 7, pp , Jly. [4] Uin, V.I., Glner, J. Shi J. Sliing Moe Conrol in Eleroehnil Sye, n Eiion, Tylor & Frni Grop, 999. [5] Flie, M. n Sir-Ríre, H., "An lgeri rewor or liner ieniiion", ESAIM: Conrol, Opiiion n Cll o Vriion, 9: 5-68 (3). [6] Flie, M. n Sir-Ríre, H., Cloe-loop preri ieniiion or onino-ie liner ye vi new lgeri -ie Moel ro Sple D, H. Grnier & L. Wng (E.) (8), p [7] Feh, M.M., Alvi, S.S. Ipene onrol o n ive penion ye. Mehroni 9; 9, p [8] Chve, C.E., Belrn, C.F., Vlerrno, G.A., Chve, B.R. Ro Conrol o Aive Vehile Spenion Sye Uing Sliing Moe n Dierenil Flne wih MATLAB, MATLAB or Engineer - Appliion in Conrol, Eleril Engineering, IT n Rooi, Dr. Krel Per (E.),InTeh. [9] Flie, M., Mrqe, R., Delle E. n Sir-Ríre, H., "Correer Proporionnel-Inegrx Générlié", ESAIM Conrol, Opiiion n Cll o Vriion, 7: 3-4 (). []Arele, J.J., Mrin, J.P., Clle, G.T. Moelo, ieño y onrión e n no e pre pr el nálii e l heión en l evlión en penione e vehílo livino jo l nor eropen ho orer nrer oiion (EUSAMA). 8º Congreo Ieroerino e Ingenierí eáni, Ore 7.