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1 401 FUZZY CONTROL OF A SPEED UMTER Mr V M Thum. Mr P SchArer and Proressor W Schehlen UnverstlU Sluttgart Germany 93ME034 Abstract F.,.",,., '., 14c E.ro1"a Comm... l, (EC) "".,,,,,.etl conlrolfor Ae lmllollon of ",c&,,.." oa 14. E.ro,... roeu. Toll., ".,..t,m,'.rs co... 1 of aft.d."... PD co,,'roller. a n.r. 14. ",.alt"" "," ka,.. oar.01 "'lf,ctor, com,.",tllo,a.rpcne"ccl tln r. n.- ",f."" lac...,a 'zpcn.,," k... t 10,m,ro.. A. t.",.. So... /..,... "..,.ellfor ndo,..., of a Faz:,-c.o,.c-C"alroll.r (FLC) for lmll'", A. lract,,.ct," 1"''''ct. A.,.per. Sm.,lou of. co"lroll.r.. 1A 0 d lwo,.,.,.,ndl.,,,,, "'0_.."", A", FLC... k,.,..,,,,,.11..,.'fll,... l ar coalrol n. ",nlt,., coalrollo. Wl' k tluctwct. 1 ntroducton Lqal ~uou by the Europe&ll CommllllllY (5) requre tbat Crom the October every Dewly released tnack lu 10 be equpped Wth a devce tllat lmts tbe nwumum vehcle speed to ~5:m/ h. Sucb a speed mau u a amlat CUDctoa lke a crule coalro. t s mportadl to DOte boweftr. lhal t does DOl allow lbe..juce,peed 10 be rased above the upper lmt oc 85:m/ h. Today" speed lmlen are bued OD adaplve PO coolrol law. t sbows, however lba, experenced drvers ( alu outperform l... dnces wtb respect 10 nde smoothd_ ad eflaency. Tbe reason Cor lbas s lbal!hue are several system propertes wllch are qute dfltulllo balldle wth convenloda codlrol stratepes, e.,. wery larle varuodj of system par&melen due 10 ch&llpn, truck loads, Ulbly DODloeat CpDe &ld drve lrad behavour, luoo dslurb&llces due 10 road Opool)' U weu as ar resstallce Corces add wnd oouences. T1e llledloo 10 ~corporate drven' experence nto lbe conlrollaw leads 10 the dea oc Wnt; a F.::,.L<>9(. C..,,.lcr (FLC) Cor ths problem. The Cuny OCc approach to nclude human reasonoc ad experence m CCllOl systems u beed suc.-lully appled a a.,de varely oflecbdcal products, _ e.c. Zmmermann (4). The baac theory of Cuny leu &ld Cuuy loc< s preseated by Zadeb (3), Lee (. a the Colown, _loos oc the paper some CUDdarneJllalaspects for tbe development of a Fuzzy-Lacc Controller a coouollll, and lmlne truck speed are preseoted. 2 Speed Control Devces and the Smulaton Envronment Tle dnces lhal are already avalable D a truck and can tbal can be ullzed 10 realze a $peed control are (1) a coouol udl, (2) the Cuel njecloo pamp, &ld (3) a servomotor. The codtrol unt usually CODSSl3 of a ClO coouoller wbch executes the procrama for tbe Anl-Lock.Braknl System as well as Cor tbe Tracton Cootrol-Syatem. For the alter the coatroller.. &CCCS 10 a servomotor.b,ch as connected Wth lbe fud lljedon pump Cor controlo, the edpne Orque. The system can be used 10 dowdload yet anolher prot;ram to lbe tdtro codtrauer, n order 10 awe the eryomotor ala Cor speed control. Fcure,lustrates lhe funcllonal rdalonahp betfteq the fuel njectod pump, the accelerator pedal and tbe servomotor. The elont;ated hole _res that the 8CfYOmotor wll DCYU be able 10 move the external lever oc the Cuel OJectlon pump further DW&rds Cull load thao tle drver.no The 'prne couplnc ellablealbc speed lmter to reduce the drver',

2 '-=::::;ct ~' 7,'.~ ~,_... f Sprlne couphnc "'N f"u functonal lallom' t..wffn lu.1,njftl"'" 'Ulllp. ac.. lnad. ~... and w.. OOOt w'"'",1.hed the nh,cle.j'ftd... ~da tbe _red Ot muunun, pumtlwd ep«d The mulalloll at lhe tnod hebav"",. S "-d on a mockl hal c... be.. KW 'ft... lrrw Ol a D,1e M~a proc_ n. flc call be hnh'" to an "lsln, llmulallon p"",am 'mpkrrwnl... 'D C D lhe f'lc broutll'. oolylll1tpf.al... at...,n ord to lac,hla'e...,mpkmedlalkw OD a nuclo CODlroln '0 lh... tblcle u...tal ne upab.htlh 01 lhe mulaloon.1... r..-,le 10 run tbe "PC"... 11a '0 a batdwatc-.n.lhr-1oop ttup. 'D wb,ch tbe... 1 wrvomolot S eoduol... by We flc lub.oulln. darcclly. 3 Defnton of the Desgn Parameters A rl(, COSS'" or the lollowan, luneloonal bmk. lor.mb dh.,a paramel... ba~ to be choaea accordlllc 10 lbe apl'laulloll. fuufcatoo nlen.e,", Th. U.leallOll.1,e.la.. rrw&&ll.ts tbe pul >a"ables. t.anslormt br la> nude.&l1ft 'D'O d_.e'~ num"'''. and p."".des tl", UlJ.lcatlOft or tbe ulsr 'lpul data.nlo CulSt '''Y data.. K_\8dp Due: The knowled,;. bate DOl ooly coftwn nlurmalloa abovt lbe syu.m lbat b.. 10 br codtrolled bul atao.alormallon about h~ w,.ttd beha.lour at lbe complett.,.un. t COftSUU ol a ~at. kj. and a ",. kt Tht dala bue provde tt.. dtl.ocs ntchlar. to roahlt the lan",.lc control rul.. and the fm! data man'pulallon The ruk "- d..."bes b~ cod"ol Olojftll..,. h~ a tl or lall,u'''1c cootrol rules 3. Oec:.oa M.kn,; Loltc: Th.. ruaulon..... kt,del at a rlc' t.mulal...,t dcclslod makla, b~ _ftc runy loc< 4. Del"ufcaloa ntar..,a: ThS.att,lau accompluhellhe dtl.u.lactlol1 b~ lornun, a nt"...,.. 1 u... 1 or,.::, c,m.clr... F urtlotttnc>h t rtttaallot... the dllc","... tpul dala ''" COD_ val.. ror tbe ""'cn 01 a FLC " rttommtnd.bk 10 totlstrurl a mplr coetro! a,or'lbm,. lw ~Dft'D' As... as the 1"",lAllO luncllorlln,.1 fa.,ly mrlr to rnlaahtr and 1.0 n...,f, b~ Luor tontrolkr coasuu(\ 3.1 F\Jzzfcaton nterrace A llfer (rldlfcatlod ~alot). a,"" ~.,. - /wll,...,lt.....'... (~ Tt".ulcallOO 1dha>d a euy to.mrtnw.l and " fhowt to be,",lo.nl lor tbe applacalqa ndtr.n_tl,atroa T1e 11m coatrolkt ftlslof haa btca "-,...,th tlw dtralon (4,,/, ) or the wltlck.r-/ lrom lbe ca... apctd '.,t) A.apul nt.abk. tle.. ~'peed... p.t.

3 llt _ d coa'ro'ln ~,he "hcle uceleracon b., beea added aa MCOnd nput varable. Tha cadt to."b a,_ d_ a DPUt.pace uad a oae d/dellloaal output.pace.,_&folcr Output = /(/n,..,,ln,..,2) Th. dkrellallod. U doac accot~ll' to the po.ab~ r~,e.o l all Yarablc:a. Tba can be <lone n a Y",), atbltat)' faaboa. Uowe<ow be ' cornel Co ad apphc&lloll a real tbe lldyldua ran,cs of.,ad> '&be abould he rcaouted.. b,bjy A pomhle w"h be aucro proccslor bell, used n order to mnmze,,.."'m OddD, etron durn, djyoll operalons. 3.2 The Knowledge Base ""'"' memmnbp (Ulc&1Ol are,he mc»1,u table ypc o( membe,.bp (ullclona (or l.ednlcal applcalons. 0mca (6). Bellc_.,"u",lat abaped memben'up (uncloal b.ve beell cbo.en unlcormly. As =,""ample, be fff'/ toatcl)' pmllloded lll",..uc vanable rklla. ol the controller depcted,ure :!a. The plol Ullhe l'trr',,' m,mkn4., (DOJl) of,be speed de'falon ddt". 10 be nsu... c vat/abes </v.n (or t(auft. d...ok (M adm_ble...d,., dv'pl (or pael.ve dn&1lod. rcspcc\vrly OOM ~ -.P K Mf" lal aloc' --' (..,.""1. :1>1 FPN 2: ParlltoG1A, olull"" (a)..d HMOrMtor.pt.d (b) ll,he frsl SlCc lpu connaller. hlple roam )'pe.. hcb olcn (rom lhe proc_.ute 10 a O4PU dcaaoa haa beell appled.. Mote SOphulcaled 1e Jpa lke pnclct... rua Uft ~ leell UCd la th.. enm\qatoa. la the am pe CAlC of the fjru COllltolter ~ _ la",&k llpg YWabc.".,ulaoDed laco,b.. lll",tl;c wal_ compl"", rule base a,vell by: "'" #1: F rkll""::d,, _' TEN HMHm"or lpt.d=-.pl laje #:1: F ult""::d,,.ok THEN laje #3: F rkllu:d...p1 THEN urthwrjolor p",d=-m.dk unlotfll1f",..ptlcd=-nj 'lm l1l..'(1, -.ok, uad D...P are 1pcCl.a)' (_ 6"," 2b). ;D~..at_ 1M MCW... uro, &ljd pos.l..e scr..omotor speed. U The Decson Makng Logc t\t Lust_ PrH.d Op.ral.r baa been chc.ct.. tbe (DY ll(creace mechantsm. lellce. the output of the 11.,.,t a lapalc nalc a tudpy _upled..lb tle ~p fullcuoa of the addressed lllsulstc value Q, 01p11&...nable ol tb naj.. Lt The FUzzfcaton nterface obt&ded by Onuoo (5/ & s.uftcal& rot techacal applmollll 10..,p~nl he lncusl/c l.sollt lapatc O&lplll var&ba by (uu)' lasctoa.a. TblS. tbe manbcnhp (uncllom or theac lasuslc....,. JqJc polo", mpd, a ccpee ol mcmbenbp ol ooc Co the ~l crup values. ThU., llulu.ted!pre 211. ~ Co raaltl Controller Wth One nput Varable r au 1M rou-a, Rmql!ont a paramect «tjw dacrba a fthcle..th a mass of 11.5 Ons and an ~... ol170 lap bu beat.-d. For tbe uam"'oa of the rohuaeo- of the /jllal con roller. parameler ou u.. beat coodracced. 11M alla&ou lund -.J1y from 801m!" and Vlet _.. d"tlled _t SSl:m/ h ard, Co tle Culln EC repl.,om. 403

4 Fcur.: 3 Jhoon lbe raull or lh. lm lmulalon. Tbe LlUck speed approaclla YK from below bul L ovmbool.s and OSClllaltS contnuoualy around YKL due to a bd"ty control aclon or tbe FLC. Anotber poublly to depc ~ ~...,'M'.. /_... 1 "' 1 /':, /',s~~~~----' '--~~~:--~~'----~--~~ ~~,, f. 'j~\ \ \...,, fs~ ~----~;~' --~ ~o o 151M 30! \.. f, \ \ \!, \,! \ Fcur.: 3' Oscllatn, t)'lem beha.. lour ca..-l by Lb. conlrol actons o( Lbe lnt FLC Lhe oyalem beha.. ou, s to plot Lhe.. hck.peed &lanol th. (uel njeclon pump le.. e, poallod Th. plot ll lcu,e 4 Jhoon a ml cycle beb... our whch ndcales Lhe nonlne.r cb.racur or Lhe lyaurn. Tht (ollowd, / 1 ) 12.o~ ~ F,Ur.: 4 Plot or the veblcle epeed &lalnol Lh. (uel nj<ctlod pump k Lbods h... bftn.pphed orde, to oblaln lon "L1stYlne results (). lne, parttlolllnc of the Dptll and DUlpU y...ble:a n Ofoler n allow more lubtl. conuol,cllogs around _, (~) tbe ntroducton oaoaes o( lknc. n lh. lnculstlc values arouad cldla,' = 0... t~ _res dd nol y.eld moro.labl. behavour al Lbe.. hcl. &peed. Oaly Lhe frequency althe OKl&lOD wu reduced but Lhe amplude 'tmllll<1! &lan laadnuable value. Snce lo.. tllfacto,y ""ulla could he obwoed.,th a.. ncle npu ( :. &not... Oput.. arah". be.d<kd La the a,otlthn. (or the follownc... mlnallollo 5 Controller Wth Two nput Varables A. a _d aput...,.ble Lhe dervalon of Lhe.. ehcl. peed baa been <bo.n By utendnl h. npu.pace La a lwo dmmaoftal lpaee l a _ poaable La de,... mote aophlsucated lall'llc COlluo rules NOt', DOl only one proc_.. ar.b~. be examned n the F par of a ruk bu mor..., a <omblnahon or 'to proc.. varables a..- La <orne La mnre approprate clccaona Tha aha nc,.... Lhe Dumber of rules ~urtd to ohtan a compkte rule tl,"111$, l S aha feubl" La ntroduce a lne, parlll_lo,; of Lhe OUlpul ".flab...,b hneualc.. &1_. Thr lral rlpermealllowl a... 7 promlae rtaull. Feur.: 5 exllbla bow the ruck lpeed a approaduo,; tt rrom below. As 100 u the truck apeed comes nto Lhe sealt... raac" of the colroler the &moual olrjtclcd fuel s hene reduced aad the... bcle.peed reachea net.thoal o..nlloot The prohkmo, howe..." lhu... arsnl wtb ths conlroler are euy n d"", to ll radlcallltalqr to bold.. wt al "7 CfCUllllaaC.. hea.. y conlrol aclon wll be hllered by any lnd o( dlllu,baace auch u l\oy Cn'" (rom lhe.peed oborf'llas

5 ... (...'A : 15; ~ \ ~=~ 30 o S, (- Flun 5: Plclure perfecl speed CODtrol of tbe lnl FLC wtb lwo npul v&lables. _, road bumpa or wnd forca. TbenCore, the controller bu to be made more capable DC <lealnl wth ta.! _d condtod. 6 mprovng Dsturbance Behavour Tha CCton be restrcted to treaunl wtb dsturbances from tbe external envronment onlt. nle dstllr Maca an represeated by allm&1e opa wth 20m ea"b and & nclnaton DC ±O.5<k,reu wbch tbe Wce bu to pad after reacbnc 'nc. Feur. S depcte a Carly rouch rde oc the truck dunn, the smulaton caused by tbe trool reactlolls oc the lta coauollu to tbe uncftd road. h-~ ~ (=:.. x~\._'m 10 V -l (4cpw1 A' '\-.J\/'.f\J\N\..J--..., f-3O -... r-t ~J ~~ ~r ~O o 1$ &- 30 Fpre 6: Aur-ve beb... our of the FLC durn, dsturbances mpaclol 00 the vebcle. Pnocpally, there an _vera! JlC*bltes to nduce tbe anstrly of a FLC n a cerlan ana or &lound lhe... red )'ttem~: (1) Aaotbu U.pul varable, pven by the o&ecraloo of lbe vebcle peed, can be..., (2) the DCUstc nput varabla u wd u the Otpul varables can be parttoned n a fner fashon around ~ desred.tate n order to obtan DOR.ubtle conlrol aclou n ths area, (3) tbe ln",slc rules &lound lhe 4ared l)'ltem.tate can be Cormulated more "soft)' wbch meam that even C Cor example a devalon Cram tlet OCCUft, lbe conlrouer should oal)' react very sowl)" (4) tbe frn, stren,lb oc lhe rules lbal are dealnt; ";111 all smau devateu Crom _t can be reduced, thereby deausne lbe control acton. Ulal a tral and error tralq)' a controller.. u developed lbat shows a much smoolher bebavlour, lt;ure 7. of 1M webcle durde lbe dsturbances compated to lbe rde llustrated n lpre 6. The trad~ff for less.. "resslve ()tro behavour s a lchtly dower approacb of the wct speed toward Vet n lhe becnnlnc. However, as t wll be sbowu later, bs beharour lat11aupuor to a conyelltona PD conlroller. 1 Comparson: FLC - Conventonal PD Controller Tle PD C01lrokr ued rot compan- correspoods to commercal.peed lmter conlrollen used by many lruck lwa(aclum1. Duro, the comparaon, (oar dtreraat parameter sels, representn, Cour dtre~nl vehcles, have 405

6 t~~ ~~ , dqroe) ];S~ ',==~--..'.."... ~ TS~ r ~ LD DUo 1_) )0 Foeur. 7 Smootb rd. or tb... bde despu. ext.rnal dsturbaoc.. ~n loaded wthout modfcatloo or the coctrolk~ Two or tb. rour tuatlons aba/ he pruented Yl(anously As t S the mast dffcult taak ror a truck p«d COCtroll.r to react ll an approprate r&&boon to a rut chall,' 10 the lchnaton or the road. a stuaton wll be &bown where tb~.ehlde. arter r.acb,ol.ltl. 11 lnt Co up a "ope.,tb +3Jt,rtU 10dnallOn. thea 10 dowll a dope.,tb tb. aame lteepneu.b,ch.. rollowed by a plln road. Th. frst parameter.. descrbes a truck.,th the masa of 3S 10M and an encno y.rlloo.,tb 490 hp. Fp,1t 8 how the performance of the FLC here.. the behavour or the con.. ntlooal J>D collroll.r lhowo ll,ure 9 The luperor performance or the FLC t aa/~at a tb.. tuatoon The J>D COllol.r S r rnor. U,,'Sh 10 U rtf>ore to de.allom 1ft the truck l,thl fronl.k :--,----- _1Uw'1 :110 TS~ _r ~ LO o S ".1 J(J F'eure 8 Performance or the FLC. truck wllb 3S ton. 490 bp _."'-_.-..u _/,.... -,..,r- -.. ' " '" --r ~,---v _-....., "----_. -~ ~ ~. TS~ ~ ~~ ~U o U (_ )0 Feur.9: Performance of the PO COQlloler. truck."h: 3S tom, 490 hp The _d patanwter Nt defnes a.. bd. wth lbe mua of 15 tona, equrred.. lb a 170 br enl'ne Tlt FLC COClroled rde a d.pcted n leu.e 10. tbe PO conlrolled "d. CU he Mft D lcure AClln. the PD 406

7 coallolln ;. DO matcb Cor tbe FLC dm 10 tbe slu"ahnae oc tbe PD coalrol. j..,...t,-1w\f...,., :', ~ ~ S -/:r'.,-;.-,-_-_--..-_-_.-:.-. oj:/ -_.-.. ~..-.:,.. _~_- -~-. _.-:-~_- 10 eo. --.,dopwj ~S~ ~ ~~ o S t \.1 FSU~ 10: PerCormaocc or tbe FLC; truck wth: 6 lolls,,d bp.... ~'- -~,...,., :! (de :"::':~-,, /---y--~.---'_ '. 1! ',... (bw~ -30., : \ "~~_._-- ",;..- -_1'-'1 ~~ ~~------~ ~ ~ o S' [., 30 Fpre 11: Pcnomluacc oc tbe PD codtroller; truck wtb: 6 loll, ld hp. Ala result t au be DOted tbat altboueb tbe PD codtroller bas baed developed to matcb a varety oc dfferent..akla. the FLC shows a much better pnformaoce, albet u deve!opmed Cor a sdele parameter set only., J & The Nonlnear Characterstc of a FLC tle Cuuy Jose COQtrol that was dneloped rcpraenu a ltatc rdatollsbp between tbe output varable &Ad the two nput varabla, 11.1 bcbayour au therecore be vsualjcd by plottne the Donlnear characterstc, pte 12. Ta YJual1uaa mula tba1 ClDy occ an be uaec as a COol Cor despde complcated DonlDur -...., -l l Fpn 12: Nonlnear characterstc or tbe FLC. coatroll&wa wthout USDe matbematcal system models. Tbe control law Col lows Crom decson rlles that can 407

8 t,., Cormulaled n a more or lea nlulft.a". FUll" occ thudore p... d.. a promanc approach to tbe dts"n oc controllen Cor lechalcal.",tems.th comphcaled lructure 9 Concluson A FUlly.l.o&c.Conlroller Cor,peed lmlen ed a!ruch.u d~1oped and ll performance was compared 10 con~enuonal PD conuollen The mult. ha" *a prnen~d n ht predeces,ml: tdlonl. n summary lb. r"k>.. ml: advanla,es of fuu" 1o"C can t,., enumeraled. Thurm (2) The controller can b.. d"'cned.,thoul a malhemaueal model or the 'Ylltm fl a quu nlu,u~e proc... poaable to 'peclf), the control t,.,havlour v,. the lncullc control rules The FLC.ho a cnfcaall), hcher robualnem tban a PD controlkr The developmenl process can t,., conduc~d n a "r), shorl lme.p... Addtonal nput or outpul yarabla can t,., added " the alcorltbm wlboul bolherldc aboul malhem. llcal complexl)'. Fuzz), occ a a promllnc tool to derve nonhnear control... for complu syllfflls 10wever. there are alan lome daadvanlac" to t,., polnled OU' A. larce Dumber or dea,n pararnc~ bu 10 t,., apecl'ed w,thoul a formal methodol"". TMre a DO malhematcal proof for the lablly or a FLC coolrokd.yatem avalable ),el C the rules cannot be cenerated tbeorcucally th.,. hav. 10 bt denved from t:lperl knowled,e ThS knowledce h.. to be quantfabk for aucc_fullmpl.~ataton D th" VeW of tbe promldc results l would t,., or ale,esl 10 'DV.. tl,.1< furlbe, DO be follo..,n, pro... ms Tbe... of more npul varables. u fot llsullce the <urr.nl "bck load. n o,d.r 10 d... ve mo'e Opb, sucaltd con!rol,ul.. lard.,., aoullofll lke fun,. Josc procaoon tba,.,., capable of proctssln, lar,. rule acts mpl_ton of & paralkl funy procas as an adaru" (oouoll., whch opumll.,. the nu" fully 1'""'_ ac(o,dnc 10 ts curreal perform... ce. References lac. C.C. F... ~ _ c-arollor S_ F_.-l.etw-c-cr./or P... Pat:.. : EEE Tr S,..._ 104_. -. C'Mnoeuo. VcoL:U"':. _/ApnlteJ 1'1 ~.V.M.: E..c.,.,(. p..., , Tac c_ r... R..,....,... F~"""'''W..ftftMt STUD-to. UN_, of s... 8 ol ~... h."k..1r. z-a. LA.: F_.s.u. h'... c-arl... C'M$\. pp.3j.ju 14) ZOo,_..J. F..,y Sd ~..d t. A"L- '''Of. Bo.,~ K... AndtaZ'C P.t! ls R tnh/ewc... ru.. _lj,l... 11P2... C,,'... ~_ , -._ ~_...,... "" F"""-U A... LlaU do.. Earot-,odwa C"'...-ucha Nr.L.19, OS 1m ",...., C... 80M. 0--~.. _. J_ r.n 408

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