A COMPARISON OF TWO ROBUST CONTROL TECHNIQUES FOR THROTTLE VALVE CONTROL SUBJECT TO NONLINEAR FRICTION

Transcription

1 Advnce in Coputing nd Technology The School of Coputing, Infortion Technology nd Engineering, 6 th Annul Conference 0 9 A COMPARISO OF TWO ROBUST COTROL TECHIQUES FOR THROTTLE VALVE COTROL SUBJECT TO OLIEAR FRICTIO Jcob L Pederen, Stephen J Dodd Delphi Dieel Syte Ltd, Pr Royl, London, United Kingdo CITE, Univerity of Et London, United Kingdo Jcobpederen@delphico, tephendodd@pceconcou Abtrct: Throttle vlve for internl cobution engine uffer fro coniderble nonliner friction in their echni tht i difficult to odel nd ubject to ignificnt vrition due to chnge in teperture nd wer over the lifetie The tic lip friction coponent i prticulrly troubleoe Thi preent chllenge to control yte deigner when it i iportnt to obtin precribed dynic repone to reference input poition chnge The contribution of thi pper re ) the coprion of two different robut control technique (liding ode control nd oberver bed robut control) ied t overcoing thi difficulty nd b) new iple but ccurte nonliner friction odel for iultion The control yte perfornce uing thee technique re copred with one nother nd with the perfornce ttinble with conventionl PI controller Introduction: The throttle vlve, n eple of which i hown in Figure, i n eentil coponent on both petrol nd Dieel internl cobution engine They re ued inly for controlling the ir-to-fuel rtio by pplying vrible contrint to the ir pth DC otor Ger yte Throttle plte Poition enor Throttle body Figure : Throttle vlve Thi i chieved by opening nd cloing the throttle plte which i driven by DC otor through ger yte The poition i eured by poition enor ttched to the plte Throttle vlve uffer fro coniderble nonliner friction in their echni tht i conidered difficult to odel nd i ubject to ignificnt vrition due to chnge in teperture nd wer over the lifetie The tic lip friction coponent i prticulrly troubleoe nd cue controller liit cycling (Artrong-Helouvry nd Ain, 994) Thi preent chllenge to control yte deigner when it i iportnt to obtin precribed dynic repone to reference input poition chnge The tte of the rt controller i PI governor with eure to overcoe the ttic friction Thi cn be chieved, for eple, by injecting n dditionl ocilltory ignl to the control vrible tht produce correponding torque jut ufficient to overcoe the ttic friction, nown dither The plitude nd frequency of thi ignl depend on the echnicl coponent nd their wer Thi e the t of coiioning the controller tie conuing The robut

2 Throttle poition feedbc Tooth wheel Advnce in Coputing nd Technology The School of Coputing, Infortion Technology nd Engineering, 6 th Annul Conference 0 9 control ethod preented in thi pper re intended to overcoe thi liittion Throttle vlve odelling: Liner throttle vlve odel: The DC otor drive ger trin tht i connected to the throttle plte nd poition enor, odelled in Figure + V In - R L e K e I DC otor J Coil pring Figure : Throttle yte odel D J D On both ide of the ger there re oent of inerti, J nd J, nd inetic friction (ie, vicoe friction) coefficient, D nd D The DC otor i odelled in the tndrd for: di vin t L R i t Ke dt t () where i, R, L nd Ke +5v 0v re, repectively, the rture current, reitnce, inductnce nd bc EMF contnt Rerrnging (): di dt L v i R K in e The torque produced by the DC otor i () i t K [ ] () t where Kt K e i the otor torque contnt To iplify the odel, J nd D re referred to the right hnd ide of the ger uing (4) where nd re, repectively, the nuber of teeth on the input nd output gerwheel Thi reult in the iplified echnicl ubyte odel of Figure J D Figure : Siplified echnicl yte odel The correponding torque blnce eqution i J D (5) where the yte inerti nd inetic friction re / J J J g nd D D / D ec/ rd, the coil pring contnt i [/rd], the ger rtio i / nd the DC otor torque i [] Rerrnging (5) yield D J (6) The tte for the throttle vlve odel re choen i, nd The eureent re y i nd y The tte differentil eqution cn be fored fro (), () nd (6): = A + B u 0 b V in (7)

3 Advnce in Coputing nd Technology The School of Coputing, Infortion Technology nd Engineering, 6 th Annul Conference 0 9 where 0 R / L, K / L, e K / J, D / J t 4 / J nd b0 / L The eureent eqution i y 0 0 y C y 0 0 (8) The correponding bloc digr i hown in Figure 4 Ger yte Ger yte Figure 4: Liner throttle vlve odel Additionl nonliner friction nd hrd top odel: Additionl refineent to the odel of ection 0 re preented here They re ) hrd top, ) initil coil pring torque nd ) nonliner friction odel Hrd top The throttle plte h liited rnge of ngle, uully fro 0 to bout 90 Thee echnicl poition contrin re clled hrd top Thee re odelled by pplying retrining torque proportionl to the ditnce by which the ngulr liit re eceeded, uing reltively lrge contnt of proportionlity, hown in Figure 5 Figure 5 Hrd top odel (MthWor Inc) Hence, when > H the retrining torque i H K nd when < L it i L K Initil coil pring torque The coil pring i pre-treed in the fctory to eep the throttle open in the ce of n electricl filure To odel thi, contnt torque i dded, equl to Initil pring onliner friction odel Through tie, the throttle vlve on vehicle will be epoed to oiture nd dirt tht infiltrte the echnicl yte Thi will reult in n incree in the friction between reltively oving coponent The clicl friction odel of bidirectionl echnicl yte, uch the throttle vlve under tudy, illutrted in Figure 6, coprie three coponent: i) K inetic friction which i function of velocity: inetic inetic (9) ii) Stedy (Coulob) friction: ign (0) tedy tedy iii) Sttic (tic-lip) friction (Ppdopoulo nd Chpri, 00): tic () where nd e,, 0, 0 e e ign e e,, 0, 0 i the eternlly pplied torque, i the brewy torque

4 Advnce in Coputing nd Technology The School of Coputing, Infortion Technology nd Engineering, 6 th Annul Conference 0 94 Trnition ection totl friction inetic friction tedy friction ttic friction Figure 6: Clic friction odel (Ppdopoulo nd Chpri, 00) Thi, however, h the drwbc of inccurcy round zero velocity nd therefore n iproved verion will be ued A generic friction odel w propoed by (Mjd nd Sin, 995) which include ore relitic continuou trnition between the brewy torque nd the u of the inetic nd tedy torque coponent of (9) nd (0) The nonliner function ued, however, i reltively coplicted but the uthor hve produced ipler verion ipoing leer coputtionl dend, follow: y () totl inetic tedy ttic t Figure 7: Friction odel nd it coponent The following contnt preter re ued: 00 nd 000 ttic nd, were found uing the Siulin Preter Etition tool Finlly, Figure 8 how iultion of the friction odel to be incorported in the ubequent iultion where tedy, inetic re define by (9) nd (0),, y t (), nd ttic A B ign (4) where A B, B nd together with re defined in Figure 7 Figure 8: Friction odel iultion - Throttle vlve control: Stndrd PI control totl Figure 9 how the tndrd PI control loop including control dither to void the liit

5 Advnce in Coputing nd Technology The School of Coputing, Infortion Technology nd Engineering, 6 th Annul Conference 0 95 cycling error tht would otherwie be cued by the tic-lip friction coponent Figure 9: Stndrd PI control loop Oberver Bed Robut Control OBRC i control technique tht cn be pplied to liner nd nonliner plnt with diturbnce (Dodd, 007) & (Stdler et l, 007) Figure 0 how the generl bloc digr of thi chee Figure 0: OBRC bloc digr (Dodd, 007) Here,, y, d nd u re, repectively, the plnt tte, eureent, diturbnce nd control vector Thi bloc digr tructure reult fro the following Firt n oberver i fored with odel tte, ˆ, nd n etite, u ˆ e, of the diturbnce referred to the control input tht i equivlent to the cobintion of d with the theoreticl diturbnce equivlent to pretric itche between the odel nd the plnt Then u ˆ e i ubtrcted fro both the plnt nd the odel input Thi convert the proble of controlling the uncertin plnt to tht of controlling the nown odel Hence the odel tte controller hown in Figure 0, tht repond to the reference input vector, y r, i deigned lie ny other tte pce controller A wide rnge of plnt odel i poible with rn t let equl to tht of the rel plnt but in the yte under tudy, the liner throttle vlve odel of Figure 4 i ued Applying the odel tte control lw u r y ˆ ˆ ˆ (5) r where r i the reference input cling coefficient nd i, i,, re the tte feedbc gin, nd dding it equivlent bloc digr to Figure 4 enble the cloed loop trnfer function to be derived with the id of Mon rule, yielding: Y b (6) Y r where: b r / L J R / L D / J / L t t e t J L J L J R D D L J L J t R L J L J L J The Dodd 5% ettling tie forul (Dodd, 008) i ued to obtin non overhooting cloed loop repone with ettling tie, T, by chooing the cloed loop chrcteritic polynoil T T T T (7) The gin cn be found by equting (7) with the denointor of (6) The oberver i lo deigned uing the odel of Figure 4 but with dditionl

6 Advnce in Coputing nd Technology The School of Coputing, Infortion Technology nd Engineering, 6 th Annul Conference 0 96 diturbnce etition (referred to the control input), hown in Figure u Figure : The oberver Equting the deterinnt of Mon rule to zero then yield the oberver correction loop chrcteritic polynoil follow: 4 q q 5 q q q q q q q 5 q q q q q q q q q 4 (8) where: q / L, q t / J, q R / L, q / L, q5 D / J nd q6 / J 4 e Agin the Dodd 5% ettling tie forul i ued to deign the oberver to hve correction loop ettling tie of T o : To To 4To (9) To 6To Equting (8) nd (9) then yield 0 / To q q 5 50 / 4T o q q q q q q q / 8T q q6 q 4 4 q q q q T q q y ŷ Sliding Mode Control (SMC): It i well docuented tht liding ode control (SMC) cn chieve robutne in liner nd nonliner yte (Utin et l, 999), (Dodd nd Vitte, 009) There re ny vrition on thi thee, oe of which re deigned to eliinte the control chtter of the bic verion In thi invetigtion, the boundry lyer ethod i eployed, equivlent to high gin output derivtive feedbc control yte Since the high gin i finite, n outer integrl control loop cn be dded, reulting in the cloed loop yte of Figure Figure : Boundry lyer bed SMC with n integrtor to reove the tedy tte error The low p filtering with tie contnt, T, i introduced to void plifiction of filter eureent noie t high frequencie Agin, the Dodd 5% ettling tie forul i ued to deterine the three output derivtive weight, w, w nd w, uing the foreentioned filtering h negligible effect on the cloed loop dynic, yielding ettling tie of T follow: Y Y w w w r where T /6 Then (0) w, w, w

7 Advnce in Coputing nd Technology The School of Coputing, Infortion Technology nd Engineering, 6 th Annul Conference Siultion: 4 Preter: 4 Throttle vlve The following preter re found by lbortory tet nd the Siulin Preter Etition Tool: K 006; K 007 ; R 5 ; t e L 00 ; J 000 ; 009 ; Initil pring 7 ; t yte dely 000 ; 869e 05 ; 05 ; inetic 05 ; 054 ttic tedy 4 Conventionl PI control loop The controller gin were djuted to yield T 0 without overhooting: K 8 nd K I 7 The qure wve dither plitude nd frequency re, repectively, u V nd f 0 Hz dither dither 4 Oberver bed robut controller A ettling tie of T 0 w ued to clculte the tte feedbc gin: 05, -065 nd To iie the robutne, the iniu oberver correction loop ettling tie w found to be T o 005 Attepting to reduce thi further reulted in undeirble ocilltory behviour Oberver gin: 97, 49776, nd Sliding ode controller The output derivtive filtering tie contnt, T 00005, w et to reltively ll filt vlue to void liiting the high gin A ettling tie T 0 w elected to deterine the derivtive feedbc weighting: w 05, w nd w To iie the robutne, p the yte gin w et to K= 500 Beyond thi, the yte repone bece ocilltory Step repone coprion In ll three Siulin iultion, tiff nuericl integrtion lgorith w eployed to cter for the two robut control technique The PI control loop w tuned to chieve non-overhooting tep repone with the pecified ettling tie but thi entiled uch tie nd effort, in coprion with the SMC nd OBRC Figure how the uperipoed repone uing ll three controller with reference input coencing t zero, tepping to rd t t nd returning to zero t t 7 Since they pper very cloe together on thi plitude cle, difference in perfornce re de ore viible by plotting the poition control error (Figure 4), defined y t yidel t, where yidel t i the tep repone tht the yte i deigned to chieve idelly Figure : Step repone

8 Advnce in Coputing nd Technology The School of Coputing, Infortion Technology nd Engineering, 6 th Annul Conference 0 98 Figure 4: Step repone error It i evident tht the PI control yielded the wort error A epected the robut control ethod yielded better repone but the SMC h ller error thn the OBRC 4 Rp repone control coprion Since the throttle poition dend i continuou during the norl opertion of n engine ngeent yte, the econd reference input ued for perfornce coprion rp up t rd / fro zero t t nd t t 5 rd / to zero t t 7 rp down t, reining zero therefter The reult re hown in Figure 5 nd 6 Figure 6: Rp repone error Depite the control dither, the PI control loop i dverely ffected by the tic-lip friction A for the tep repone, both the robut controller iprove on thi but the SMC perfor better thn the OBRC 5 Concluion nd Recoendtion: It i rerble tht even without control dither, the robut controller perfored better tht the PI controller with the control dither Furtherore, it i recoended tht firer coprion be crried out by pplying control dither with ll three controller The different plnt odel uch the ultiple integrtor (Dodd, 007) hould be conidered in ce thi perit ller vlue of T o nd therefore higher robutne Finlly, eperientl wor currently in progre will be publihed lter Figure 5: Rp repone 6 Reference ARMSTROG-HELOUVRY, B & AMI, B (994) PID control in the preence of ttic friction: ect nd decribing function nlyi Aericn Control Conference

9 Advnce in Coputing nd Technology The School of Coputing, Infortion Technology nd Engineering, 6 th Annul Conference 0 99 DODDS, S J (007) Oberver bed robut control AC&T DODDS, S J (008) Settling tie forule for the deign of control yte with liner cloed loop dynic AC&T DODDS, S J & VITTEK, J (009) Sliding ode vector control of PMSM drive with fleible coupling in otion control AC&T MAJD, V J & SIMAA, M A (995) A continuou friction odel for ervo yte with tiction Proceeding of the 4th IEEE Conference on Control Appliction PAPADOPOULOS, E G & CHASPARIS, G C (00) Anlyi nd odel-bed control of ervoechni with friction IEEE/RSJ Interntionl Conference on Intelligent Robot nd Syte STADLER, P A, DODDS, S J & WILD, H G (007) Oberver bed robut control of liner otor ctuted vcuu ir bering AC&T UTKI, V I, YOUG, K D & OZGUER, U (999) A control engineer' guide to liding ode control IEEE Trnction on Control Syte Technology, 7, 8-4