Anti-lock Brke System With Semi-Model Bsed Controller Using Wheel Pressure Sensors Knghyun Cho ), Seibum Choi ), Kimo Son 3), nd Jongkp Kim 4), ) KAIST nd 3, 4) Hyundi Motors Corportion,) Deprtment of Mechnicl Engineering, KAIST, Dejeon, 3-7, Republic of Kore Phone: (+8-4) 3-44, Fx: (+8-4) 3-4 3,4) Hyundi & Ki Corporte Reserch & Development Division, Seoul, 37-938, Republic of Kore Phone: (+8-) 3464-769, Fx: (+8-) 3464-4 E-mil: ) khcho8@kist.c.kr, ) sbchoi@kist.c.kr, 3) kimosohn@hyundi.com, nd 4) ckkim@hyundi.com The Anti-lock Brking System() must gurntee to shorten the brking distnce nd keep the stbility of the vehicle s soon s possible during the vehicle brking. To do this ork, the trget slip(ccelertion) must be knon to control ech four heel long the rod conditions. Hoever, it is difficult to determine the optiml trget slip becuse the rod friction coefficient is unknon. In this study, the Anti-lock brking system using dditionl four heel pressure sensors hs been proposed. The rod friction coefficient is clculted by using the heel dynmics nd vehicle longitudinl dynmics. The system is controlled by semi-model bsed controller hich is the combintion of the semi-feedbck control nd the feedbck control. A vriety of simultions re crried on to verify the performnce of the proposed system using CrSim progrm. They re compred ith the system designed ithout four heel pressure sensors. The simultion results sho tht the proposed lgorithm mke the brking distnce be shorten nd the stbility of the vehicle be improved. Vehicle Dynmics, Active Sfety Systems. INTRODUCTION The Anti-lock Brking System hs been equipped on most vehicles to gurntee the longitudinl stbility of the vehicle. The bsic function of the system is control the pplied brking torque by modulting the brke pressure. It prevents four heels from locking during the vehicle brking. It must gurntee to mke the brking distnce s soon s possible nd keep the stbility of the vehicle simultneously. In the brking control systems, there re to vribles to be considered for controlling four heels: heel longitudinl slip nd heel ccelertion.[] The trditionl uses heel ccelertion to control four heels.[][3] These systems hve mny complicted threshold-bsed control rules, so it tkes long time to pply to vriety of vehicles. Therefore, mny reserches hve been performed for the trnsition from rule-bsed control to model-bsed one becuse of tuning simplicity nd robustness.[4][][6][7][8][9]. Most model-bsed systems ssume tht the optiml control trget (desired heel slip or speed) is knon. These systems consider the control issue in s only trcking problem. Actully, it is impossible to define the control trget exctly long vriety of rod conditions becuse the rod friction coefficient is unknon nd it is hrd to kno one using only equipped sensors such s n y rte sensor nd longitudinl ccelerometer. In this pper, semi-model bsed nti-lock brking system hs been proposed. The system uses four heel pressure sensors dditionlly to clculte the rod friction coefficient from the heel dynmics nd the longitudinl vehicle dynmics. The control trgets of four heels re obtined from the estimted rod friction coefficient. Therefore, it cn improve the implementtion problem hich is min issue of the model-bsed control system rchitecture. The rer heels re controlled by reference heel ccelertions bsed semi-feedbck controller. And the front heels re controlled by n dptive sliding mode controller bsed on longitudinl heel slip (heel speed). The performnce of the proposed system is verified by simultion using CrSim progrm under vriety of rod conditions. Also, they re compred ith results of system designed ithout for heel pressure sensors. The pper is orgnized s follos: In Section II, the estimtion scheme of the rod friction coefficient is described. The proposed control lgorithm is presented in Section III. To different simultion tests re performed in Section IV to verify the performnce of the proposed lgorithm. Concluding remrks re given Section V.
Fig. Vehicle ongitudinl Dynmics Fig. 3 Wheel Dynmics Fig. Reltion Beteen Force nd Pressure. ROAD FRICTION COEFFICIENT ESTIMA- TION In this section, the norml forces nd brke torques re clculted to estimte the rod friction coefficient. Four heel pressure sensors, hich hve been used for regenertive brking system in the hybrid vehicles or n ACC(dptive cruise control) system recently, re used to mesure the pressure of ech heel. Using heel dynmics bsed on these prmeters, the rod friction coefficient is obtined.[]. Norml Force Clcultion The norml forces of the vehicle re clculted by the longitudinl vehicle dynmics. It is described in Fig.. When the vehicle is decelerting, the norml forces of front nd rer heels re clculted s follos: mglr cos mghsin mxh Ferohero Fzf () mgl f cos mghsin mxh Ferohero Fzr () here, F zf nd F zr re the norml forces of the vehicle, m the totl vehicle mss, l f nd lr the distnce from C.G. to front nd rer heel, the heel bse length, g the grvity ccelertion, the rod elevtion, h the height of C.G, nd Ferohero the moment of ero effect. Here, ssume tht the rod surfce is flt, i.e., nd irdrg is negligible, i.e., Ferohero. Then, () nd () re pproximted simply s follos: mgl mxh Fzf (3) mgl f mxh Fzr (4). Brke Torque Computtion The brke torques re obtined by the reltion beteen force pplied to four heels nd cylinder pressure s described in Fig.. The force pplied to brke disk pd is obtined s follos, FB bfc bfbn bpba () here, FB is the brke force, b the cliper friction coefficient, Fc the clmping force, F BN the norml brke force, PB the brke pressure, nd A the cylinder re. The brke torque is computed s follos, TB FB rd kbpb (6) here, TB is the brke torque, rd the disk rdius, kb represents the brke gin hich is determined by the specifiction of brke cylinder. In this study, the brke gins of front nd rer heels re Nm/MP nd 7Nm/Mp..3 Rod Friction Coefficient Estimtion The rod friction coefficient is clculted by heel dynmics. It describes dynmicl representtion for heel driving on the rod s shon in Fig. 3. The moment blnce eqution is obtined s follos, I RFx TB (7) here, I is heel inerti, the heel speed, the rod friction coefficient, R the heel rdius, nd Fx the longitudinl tire force, nd Fz the norml tire force. Also, the reltion beteen the longitudinl tire force, Fx nd the norml tire force, Fz is represented s follos, Fx Fz (8) In (7) nd (8), the rod friction coefficient is obtined by normlizing the longitudinl tire force using the norml tire force. It is presented s follos, Fx I TB (9) F RF z The obtined in (9) oscilltes in ccordnce ith heel cycling pttern cused by the brking opertion such s pply-hold-dump. Therefore, it must be limited by rte limiter to obtin the mximum rod friction coefficient. z
Fig. 4 Block Digrm of Control Algorithm The rte limiter is implemented s follos: mxts if mx pek mints elseif min () otherise here mx nd min re the mximum nd minimum rte limittion of nd T is the smpling time. The mximum friction coefficient, s pek represents the mximum brking force obtined during the brking. It is used to obtin the control trgets of the rer heels. It cn solve the implementtion problem mentioned bove. Also, it enbles ll heels to be controlled under ech estimted rod friction coefficient. Therefore, it gurntees the lterl stbility of the vehicle under vriety of trnsient conditions of the rod friction, especilly such s the split friction rod condition. 3. CONTRO AGORITHM In this section, the control schemes of the front nd rer heels re described. And the control strtegies on the split-friction rod re presented. The block digrm of the proposed control lgorithm is s shon in Fig. 4. 3. Rer Wheel Control The rer heels re controlled by heel ccelertion bsed rules. Hoever, the reference ccelertions re obtined from mesured heel pressure signls, nd the error beteen mesured nd reference signl is lso used for control. It orks such s P-type controller. Therefore, the rer heel brke system is not considered s simple open-loop controller (only rule-bsed system) but semi-feedbck one. The vlve commnd to control rer heels is presented s sum of vlve dump commnd nd vlve pply commnd s follos: Vcmd Vdump Vdhold Vpply Vhold () here, Vcmd vlve dump commnd, Vdhold is the totl vlve commnd, V dump the Vpply the vlve pply commnd, the vlve hold commnd for dump, nd V hold the vlve hold commnd for pply. The dump nd pply vlve commnds re obtined by the difference beteen estimted heel ccelertion nd reference heel ccelertion. The commnds for the vlve dump nd pply opertion re represented s follos: V dump dump if dump () otherise pply if pply Vpply (3) otherise here, is estimted heel ccelertion, dump the reference ccelertion for dump nd the pply reference ccelertion for pply. The reference ccelertions, dump nd pply re obtined from the clculted mximum rod friction coefficient, mx ith dditionl mrgin. For exmple, the reference ccelertions, dump nd pply re determined s follos: dump mx..7g (4) mx () pply..g here, mx mens the mximum ccelertion during brking on the driving rod using the rod friction coefficient estimted in (). mx pek g (6) The vlve hold commnds determine hether the vlve dump/pply commnds re pplied or not. The commnds of the vlve hold re s follos: if Vdump Vholdth for t t Vdhold (7) otherise if Vpply for t t Vhold (8) otherise here, Vholdth is threshold for dump hold, t time threshold to keep smll dump commnd, t time threshold to be redy to strt pply commnd. The pply-hold-dump commnds mke cycling ptterns
of the rer heels round the pek friction slip point. 3. Front Wheel Control The front heels hve no direct cycling ptterns like one of the rer heels becuse it mkes the ride very hrsh on high-friction surfces. They re controlled by n dptive sliding mode controller bsed on the longitudinl heel slip(heel speed). The trget speeds for preventing heels from locking re obtined from controlled rer heel speed ith dditionl slip mrgin. The vlidity of the control trget is gurnteed by n ssumption tht the rer heels re controlled ner pek friction point through cycling-pttern. Therefore, the desired heel speed, Fdes is represented s follos, Fdes R (9) here R is rer heel speed, n dditionl slip mrgin. In (7), the chnge rte of brke torque is proportionl to fluid flo rte, nd flo rte is proportionl to control vlve opening. Therefore, the brke torque rte is proportionl to the vlve commnd nd then it becomes the control input.[] Using (7), the system model to design the controller is defined s follos: d T B RFz () I I dt The stte-spce representtion is described s follos, x x u d x x / I () here, x d, u T B, d RFz x I dt Here, the term, d, ssumes tht it is the disturbnce, hich is clculted by (3) nd (9). The control objective is to trck the desired heel speed, Fdes ith trcking error s smll s possible. In this study, the sliding mode controller is proposed nd the dpttion mechnism is used to estimte the disturbnce, d In cse tht the informtion of d is totlly unknon, the dpttion mechnism does not ork ell becuse it is fst time-vrying prmeter. This mkes the trcking performnce very poor. Hoever, the nominl vlue of d dn cn be clculted using (3) nd (9) in this study. Therefore, the stte-spce representtion () is obtined s follos: x dn d () Iu Here, d d dn is the error beteen the ctul disturbnce nd the nominl disturbnce. To design the sliding mode controller, the PD-type of sliding surfce is defined s follos, S e e, (3) here, e x xd is the trcking error, xd being the desired heel speed, Fdes nd the tuning prmeters. The im of the sliding mode control is to force the system stte to the sliding surfce, S nd then mintin it on the sliding surfce. Therefore, the sliding surfce, S must stisfy, SS (4) And (4) cn be stisfied using () S KSS, KS () From (), the control l is obtined s follos, u u ˆ ff ufb I dn d xid e Kse e (6) feedforrd feedbck Here, the disturbnce error must be estimted using the dpttion mechnism. Our dpttion l is designed s follos: d ˆ K, e e K (7) here, K is tuning prmeter of the dpttion lgorithm. The control l (6) nd the dpttion l (7) gurntee the stbility of the system. et s define ypunov function, ˆ, K V S d d K (8) The derivtive of (8) is s follos: V SS d dˆ ˆ d d K (9) The disturbnce error, d ssumes tht it is vrying sloly becuse the nominl vlue, d n is trcking the ctul disturbnce, d. Therefore, the derivtive of d is nerly equl to zero, i.e., d nd (9) is reclculted using (3), (6) nd (7) s follos: s V SS d dˆ dˆ K S (3) K Therefore, it proves tht the system is stble. Using Slle s invrint set theorem, the symptoticl stbility of the system is lso proved. If e, only e mkes S in (3) nd S mkes S. Substituting (6) into (), bove reltion mkes d d ˆ. Therefore, the equilibrium point nd d dˆ re symptoticlly stble. 3.3 Split Friction Control In, the lrge pressure difference beteen left nd right-side heels mkes vehicle be unstble. It cuses spin-out of the vehicle or mkes controllbility of vehicle loss. Although the rod friction coefficients of both sides re different, the difference of the pplied pressures must hve some limit condition. The heel pressure sensor is very useful to pply the limittion becuse the heel pressures re mesured directly.
3 Front eft 3 V V Pb/ Vdes Pb/ Vdes Fig. Mu-Slip Curve nd Split-Mu Pressure Control Tble Simultion Cse Specifiction Cse kph Friction trnsition high(.8 ) to lo(. ) Cse kph Split friction left(.8 ) - right(. ) Tble Brking Distnce Without pressure sensors With pressure sensors Cse 67.83m 6.4m Cse.m 96.7m It mkes the vehicle more stble on split-friction rod. The proposed control method is s follos: PF Vcmd Vpply Hcmd if Ph Pl Pth Vcmd (3) Vcmd otherise here, Vcmd is vlve commnd, V cmd the vlve commnd of lo pressure heel, V pply Hcmd the vlve pply commnd of high pressure heel, Ph the pressure of high pressure heel, Pl the pressure of lo pressure heel, th P the threshold of pressure difference, nd PF the lo pss filtering. In (3), the vlve commnd of the high pressure heel is reclculted using dc component of lo pressure heel ith pply commnd of high pressure heel. It mkes the vlve commnd of high pressure heel be to ork like vlve commnd of lo pressure heel ith dditionl pressure mrgin. In cse of rer heels, the threshold must be loer thn tht of the front heel to prevent the vehicle from being spin-out. Using this scheme, the vehicle cn be stble under the conditions hich hve lrge difference beteen left nd right-side friction such s driving on the split-friction rod nd full brking on the cornering driving. The description is shon in Fig.. 4. SIMUATION A series of simultion hs been performed to verify the performnce of the proposed lgorithm under vriety of conditions using CrSim progrm. They re stndrd test conditions consisting of vriety of rod friction coefficients nd vehicle velocities. To sho the contribution of this study, to controllers re compred through vriety of simultion tests. They re shon in Tble. The proposed lgorithm is compred ith one ithout four heel pressure sensors in []. 3 Rer eft V Pb/ 3 Rer Right Fig. 6 Cse. High To o: ithout Pressure Sensors 3 Front eft 3 Rer eft V Pb/ Vdes V Pb/ 3 V Pb/ 3 Rer Right V Pb/ Vdes Fig. 7. Cse. High To o: ith Pressure Sensors The results of the control ithout heel pressure sensors re shon in Fig. 6 nd 8. And the results of the proposed control re shon in Fig. 7 nd 9. In figures, to subfigures t the top represent front left nd right-side heels, nd to subfigures t the bottom represent rer left nd right-side heels. The steering heel ngles for cse re compred in Fig.. In cse of the lgorithm ithout heel pressure sensors, the rod friction coefficient cnnot be estimted, so the detection of the friction vrition such s friction trnsition(cse) nd split-friction cn be slo or cnnot be detected properly. At the moment chnging the rod friction coefficient from high to lo mu in Fig. 6 nd 7, the proposed lgorithm shos tht the heel slip is smller thn tht of the lgorithm ithout pressure sensors becuse of fst detection of surfce friction trnsition. In cse of driving on the split-friction rod in Fig. 8 nd 9, lthough the pressure difference beteen left nd right-side heels nd the steering ngle re similr to both lgorithms s shon in Fig., the brking distnce of the proposed lgorithm s shortened. The results of the brking distnce re compred in Tble 3. From ll simultion results, the proposed lgorithm shos the improved performnce hen it is compred ith the lgorithm ithout pressure sensors in terms of the similr stbility of the vehicle nd shorter brking distnces. CONCUSION This study hs proposed ne Anti-lock Brking System control lgorithm using four heel pressure sen- V Pb/
3 Front eft V Pb/ Vdes 3 V Pb/ Vdes Hoever, the proposed system shos some chttering of the front heel pressure. It must be improved in the future ork becuse it cn mke the rid hrsh on high-friction surfces. 3 Rer eft V Pb/ 3 Rer Right Fig. 8 Cse. Split Mu: ithout Pressure Sensors Front eft 3 V Pb/ Vdes 3 Rer eft V Pb/ 3 V Pb/ 3 Rer Right V Pb/ Vdes Fig. 9. Cse. Split Mu: ith Pressure Sensors SWA[deg] - -4-6 -8 - - -4 Steering Wheel Angle ithout Pressure Sensor -6 Time[sec] ith Pressure Sensor Fig.. Steering Wheel Angle Comprison in Cse sors. The proposed control scheme is considered s semi-model bsed control system becuse the combintion of the rule-bsed nd model-bsed controller is used. The min issue of the model-bsed control system in hs been improved by using the estimted rod friction coefficient. Therefore, it is considered s more prcticl control lgorithm. The estimted rod friction coefficient enbles ll heels to be controlled under ech estimted rod friction coefficient. It gurntees the lterl stbility of the vehicle on the split friction rod condition mking the brking distnce shorter. The rer heel brkes re controlled by semi-feedbck controller, nd the front ones by n dptive sliding mode controller. The simultion results sho high performnce under vriety of rod conditions. The brking distnce hs been shortened hile keeping the vehicle stble. V Pb/ REFERENCES [] Svresi, S., Tnelli, M. nd Cntoni, C., Mixed Slip-Decelertion Control in Automotive Brking Systems, Journl of Dynmic system, Mesurement, nd Control, vol. 9, pp. -3, 7. [] SAE, Antilock Brke System Revie, Society of Automotive Engineers, pp. 9-, 99. [3] Wellsted, P., nd Petit, B., Anlysis nd Redesign of n Antilock Brke System Controller, IEEE Proc. Control Theory nd Applictions, vol. 44, no., pp. 43-36, 997 [4] Yu, J., A Robust Adptive Wheel-Slip Controller for Antilock Brke System, Proc. of the 36 th IEEE Conference on Decision nd Control, vol. 3, pp. 4-46, 997 [] Petersen, I. et l., Wheel Slip Control in Brkes Using Gin Scheduled Constrined QR, Europen Control Conference, pp. 46-, [6] Buckholtz, K., Reference Input Wheel Slip Trcking Using Sliding Mode Control, Society of Automotive Engineers, no. --3, [7] Johnsen, T. et. l., Gin-scheduled Wheel Slip Control in Automotive Brke Systems, IEEE Trns. On Control System Technology, vol., no. 6, pp. 799-8, 3 [8] Solyom, S., Rntzer, A., nd udemnn, J., Synthesis of Model-Bsed Tire Slip Controller, Vehicle System Dynmics, vol. 4, no. 6, pp. 47-499, 4 [9] Mirzeinejd, H., nd Mirzei, M., A Novel Method for Non-liner Control of Wheel Slip in Anti-lock Brking Systems, Control Engineering Prctice, vol. 8, no. 8, pp. 98-96, [] Cho, K., et. l., Design of n Control Algorithm Using Wheel Dynmics, Koren Society of Automotive Engineers Annul Conference, pp. 76-76,. (in Koren) [] Choi, S., Antilock Brke System With Continuous Wheel Slip Control to Mximize the Brking Performnce nd the Ride Qulity, IEEE Trns. on Control Systems Technology, vol. 6, no., pp. 996-3,. ACKNOWEDGE This ork s supported by the Ntionl Reserch Foundtion of Kore (NRF) grnt funded by the Kore government(mest) (No.-99).