IMPROVED HANDLING CHARACTERISTICS OF OFF-ROAD VEHICLES BY APPLYING ACTIVE CONTROL OF STEERING WHEEL TORQUE

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1 Sustinle Construction nd Design 11 IMPROVED HANDLING CHARACTERISTICS OF OFF-ROAD VEHICLES BY APPLYING ACTIVE CONTROL OF STEERING WHEEL TORQUE J. Kis, L. Jánosi Institute for Mechnicl Engineering Technology, Fculty of Mechnicl Engineering, Szent István University, Gödöllő, Hungry Astrct Driving speed of griculturl moile mchines hve een incresed in the recent yers, rising serious questions out vehicle hndling chrcteristics considering the high center-of-grvity, multi-mss configurtion nd rer-wheel-steering of these vehicles. The next genertion of steering systems on offrod vehicles will incorporte steering column mechtronic susystem which will generte tctile feedck for opertor. This pper presents our reserch work to utilize steering wheel torque to improve off-rod vehicle hndling chrcteristics. Keywords griculturl moile mchines, rer wheel steering, off-rod vehicles, hptic feedck, hndling 1 INTRODUCTION To gin productivity the weight nd speed of off-rod vehicles, prticulrly griculturl moile mchines is continuously incresing. Opertion on the field (or in some circumstnces t lest retin moility) nd hve sfe nd comfortle vehicle hndling on pulic rods hve contr verse requirements on vehicle design [] Good exmple for the contr verse requirements is the tire design nd pressure of griculturl tires. The design of the steering system is lso result of suoptiml compromise etween rod trnsport nd field opertion. Some vehicle hve rticulted steering Figure 1/ which llows only very limited speed, ecuse of the steering kinemtics. Self propelled forge hrvester or comine hrvesters re equipped with rer wheel steering, which hve severl enefits for the field opertion in terms of heder opertion, nd lso in mchine design in terms of ody clernce. This concept hs lso serious drwcks in terms of vehicle hndling in trnsport mode, ecuse of the stility prolems with rer wheel steering. In Steer-y-Wire (SBW) systems there is no mechnicl or hydrulic link etween hnd wheel nd rod wheels. The hnd wheel ngle is mesured y redundnt rotry sensors, processed y n electric control unit to otin rod wheel ngle, nd clcultes lso the set vlue for the ctutor control. [3] This concept enles decoupling the motion nd the forces of the rod wheels from the hnd wheel motion nd torque, which mkes possile to implement vrious driver supporting control systems. Using n ctive force feedck device on hnd wheel unit, the SBW system cn provide vrious type of hptic signls for the opertor. In this pper we investigte the stility conditions for the hevy-duty griculturl vehicle with rer wheel steering. Considering of SBW system with ctive force feedck, we present one method to emulte synthetic torque on hnd wheel, which corresponds to the idel ligning moment of virtul front wheel steered vehicle. The pper will provide informtion out the clcultion of the stte feedck gin, nd the stility of the modified system. The concept uses the stte vriles of the vehicle motion, which cn e estimted on vrious wys, nd these methods re not prt of this pper. INFLUENCE OF MODEL PARAMETERS ON STABILITY.1 Vehicle model For the investigtion of the rer wheel steering system, nd the hndling ehvior of the hevy-duty griculturl moile mchine we use liner single trck model. The model nd the resulting differentil equtions re derived in nd nlyzed for the front wheel steering system ut there is limited informtion out pure rer wheel steering systems [,,7]. The model shown on Figure 1/ is ody with 3 degree of freedom, wherey motion in z-plne is llowed. The differentil equtions for lterl nd rottionl motions re: Copyright 11 y Lortory Soete

2 Sustinle Construction nd Design 11 The model is vlid elow.g lterl ccelertion, nd elow 5 degree lterl tire slip. We investigte the vehicle under these conditions in rod trnsport mode. Assuming constnt velocity long x xis the stte vriles of the model cn e reduced to the rottionl speed r nd slip ngle. There re two lterl tire forces cting on the chssis, wherey longitudinl components re ignored. v f f f v F sf instntneous centre geometry centre instntneous centre f F sf v f d v s v r m geometry centre s 1 r r r F sr F sr v r Figure 1: Liner single trck models for front/rer nd rticulted steering Becuse vehicle ehvior is function of tire lterl force nd moments, therefore model ccurcy is significntly influenced y the ccurcy of tire models. There re widely ccepted nonliner tire models, e.g. the mgic formul to cover different spects of tire-rod interctions. Due to smll lterl slip, in our nlysis we use simple liner reltionship etween the lterl force nd lterl slip, nd ligning moment nd lterl slip. The constnt prmeter used in the model is the cornering stiffness (C F,R ). In our nlysis we don t consider the effect of suspension flexiility on lterl tire forces, nd so the elsto-kinemtic tril, ecuse we investigte system with no suspension nd very rigid steering linkge (hydrulic cylinders cting directly on the wheel). We ignore the fct lso tht most of the moile mchines equipped with rer wheel steering re designed with lrge cstor ngle nd mechnicl tril. The model consider only the effect of the pneumtic tril on ligning moments. Using Figure 1/ we cn otin the equtions for the tire lterl slip ngles from rottion nd slip ngle: Comining the eqution from ove we cn set up the differentil equtions for the single trck model in the form where the derivtives of stte vriles re on the left hnd side: Using these equtions we cn otin the stte equtions of the system in mtrix form x = A x + B u. 7 Copyright 11 y Lortory Soete

3 Sustinle Construction nd Design 11 The system stte vriles re x 1 = x =r nd the inputs re the steering ngles F,R. The differentil eqution system in mtrix form.. Stility of rer wheel steered vehicles Why pure rer wheel steering is not used in pssenger crs hs severl resons. One is tht the tire ligning moment cts on opposite direction, nd chnges direction in trnsient sitution. Therefore mechnicl force feedck cn not e relized. The other reson is, tht ecuse of the flexiility of the steering system nd the suspension, n elsto-kinemtic steering ngle creted, if lterl force is present. The opposite ligning moment increses this ngle, therefore there is no stle operting point for this sitution. Driving the vehicle on stedy-stte pth, the relized elsto-kinemtic steering ngle reduces the lterl force, which hs n impct on the rer xle cornering stiffness nd so on over steering ehvior of the vehicle..3 Modeling the mechnicl steering system To compre front- nd rer wheel steering, the single trck vehicle model is extended with the model of the steering system. In this model the inerti, viscous friction nd (s n externl disturnce) hnd wheel steering torque re modeled, nd it cn e regrded s feedck system. The differentil eqution used for the steering system model: The viscous friction is proportionl to the ngulr speed of the steering system. This prmeter cn e prt of the control system nd cn represent virtul friction to reduce system oscilltions. The ligning moment depends only on the pneumtic tril nd lterl force. The kinemtic reltionship etween hnd wheel ngle nd rod wheels re modeled with fixed rtio i S. Comining the equtions from ove, nd expressing the ngulr ccelertion the differentil eqution of the steering system: Sustituting the rer wheel steering ngle in the differentil equtions of the single trck vehicle model: This gives the stte equtions for the front wheel steering system in the following form: 8 Copyright 11 y Lortory Soete

4 Sustinle Construction nd Design 11 The stte eqution for the rer wheel steered vehicle : The difference etween the two system mtrix (A) re mrked old. We cn see the negtive feedck of the hnd wheel ngle on the yw rte chnge nd the ngulr ccelertion, which cses the system instility. In the following section we will nlyze the stility of this system in function of different model prmeters using the eigenvlues of the system mtrix. It is known, tht t given model prmeter set, if ll the eigenvlues of A hve negtive rel prts the system is stle. Figure shows the eigenvlues of the front nd rer wheel steered system t chnging model prmeters. Figure / shows the effect of incresing ground speed on the system pole loctions. Both pole pirs re slowing down, nd the dmping of the system is not chnging. Becuse of the incresing phse lg the system poles get positive rel prts, nd t 5 m/s the system get unstle. Figure / shows the effect of decresing rer tire cornering stiffness. The dmping of the fster pole pir is decresing, due to the decresing ligning moment. The slower pole pir get into the unstle region ecuse of the over steering. It is ovious if the pneumtic tril get reduced (Figure /c) the controllility of the system decreses, which shows over dmped poles t not chnging viscous friction. If speed increses higher viscous frction vlue is required to keep vehicle stle (Figure /d). This is one of the concept used in the following section to modify vehicle hndling chrcteristics. Figure /e shows the system poles of the rer wheel steered vehicle t incresing speed. It is ovious tht this system is unstle, ecuse it hs one rel poles in the right hnd plne. 3 ALTERING VEHICLE HANDLING CHARACTERISTICS In this pper concept will e presented to lter vehicle hndling using n ctive force feedck device which will generte virtul ligning moment for the opertor to keep the vehicle stle. In the following model we ssume, tht the wheels re controlled y n electromechnicl ctutor, which cn keep-up with the hnd wheel dynmics, disregrding the control effort prolem in this model. 3.1 Hptic feedck modeling The hptic feedck is relized with rushless DC motor nd teethed elt trnsmission. The hptic feedck contins inerti, viscous friction, rtio to hnd wheel nd rtio the steered wheels. The torques cting on the motor shft re: The generted ck electromgnetic force (BEMF) using the motor prmeters: The electricl differentil eqution with impednces for the rushless dc motor: 9 Copyright 11 y Lortory Soete

5 Sustinle Construction nd Design Imginry Axis Imginry Axis Rel Axis Rel Axis c Imginry Axis d Imginry Axis Rel Axis Rel Axis 1 e 8. incresing ground speed: loosing Imginry Axis Rel Axis Figure : System pole loctions with chnging model prmeters. stility t 5mps (positive rel prt of system mtrix eigenvlues). System poles t decresing rer wheel cornering stiffness: loosing stility c. decresing pneumtic tril, remining viscous friction d. decresing viscous friction, t 1 m/s () nd m/s () e. unstle Rer Wheel Steering poles t incresing speed Comining the mechnicl nd dynmic differentil equtions we get for the hptic feedck: 7 Copyright 11 y Lortory Soete

6 Sustinle Construction nd Design 11 The stte equtions for the hptic feedck device: Becuse of the limited dynmics of the whole system, in the simultion we ignore the inductive impednce. And therefore we cn reduce the numer of stte vriles to ngulr speed nd ngle position. The reduced stte equtions re: The input of the hptic feedck is the rmture voltge which is controlled y the stte feedck controller. 3. Explicit clcultion of feedck gin for emulted front wheel steering The control system is shown on Figure 3. There re severl methods for optiml design for the feedck gin, e.g. the concept of the liner qudrtic regultor (LQR). It will give optiml solution for full stte feedck t given trnsient nd stedy-stte constrins. D Hptic Feedck Device R Rer Wheel Steering Vehicle r v Stte Feedck Controller Figure 3: Stte feedck controller for rer wheel steered vehicle (without steering ctutor dynmics) sed on emulted front wheel ligning moment nd dded viscous friction We follow different method y explicit clculting the feedck gin, ecuse we would like to emulte steering system which hs front wheel steering. So the system my work suoptiml compred to the LQR design ut gives the opertor the feeling of n front wheel steered vehicle. The controller hs to clculte the necessry voltge to crete relistic steering torque: The emulted hnd wheel torque cn e clculted on the virtul ligning moment on the front wheels in cse of n front wheel steering plus the synthetic viscous friction in the system, which is used to modify system dynmics. 71 Copyright 11 y Lortory Soete

7 Sustinle Construction nd Design 11 Sustituting into the electric eqution we get for the voltge: After modifying the eqution ove we cn descrie the four feedck gins for ll four stte vriles: Some prmeters of the control system re given y vehicle geometry or electricl components(,, R, etc.) Stte vriles re directly or indirectly mesurle like yw rte, lterl ccelertion ngulr speed, ngle. Other prmeters like cornering stiffness must e estimted y online system identifiction lgorithms. The results of the simultion on unit hnd wheel torque is shown on figure 5. 3 Imginry Axis Rel Axis Figure : System poles of the single trck model with hptic feedck t incresing dmping t 1 mps() nd mps() CONCLUSIONS Off-rod vehicles with rer wheel steering hve cceptle hndling only t lower speeds. This ehvior cn e significntly improved y using ctive hptic feedck systems. The presented method of explicitly clculting the feedck gin to emulte front wheel steering feedck cn improve the stility of system. This is shown on Figure, wherey the closed loop poles of the system with incresing dmping t different ground speed re on the left hnd plne, If pproprite synthetic viscous friction hs een set. Further work is necessry to consider rod wheel ctutor with finite dynmics, nlyze the effect of the stte estimtion nd prmeter identifiction. The presented concept must e lso verified on rel vehicle. 7 Copyright 11 y Lortory Soete

8 Sustinle Construction nd Design tu D [Nm].. cc y [mps] et [rd] r [rd/sec] F SF [N].5 x F SR [N] 1 x delt R [rd] v [volt] Figure 5: Step response of the system to unit hnd wheel torque Copyright 11 y Lortory Soete

9 Sustinle Construction nd Design 11 5 NOMENCLATURE F SF,SR Lterl tire force N C F,R Cornering stiffness N/rd F,R Tire slip ngle rd F,R Steering ngle rd, cc to fig. 1 m r Yw rte rd/s Slip ngle rd v Ground speed m/s v Voltge V I Inerti kgm Hnd wheel ngle rd J S Steering inerti kgm Torque on hnd wheel Nm i S Steering rtio - Motor shft ngle rd J H HpticFeedck inerti kgm Current A K M Motor torque constnt Nm/A K F Viscous constnt Nms/rd K B BEMF constnt Vs/rd R Resistnce Ohm i H Hptic rtio - i M Force feedck rtio - REFERENCES [1] Jnosi, L., & Kis, J. (1.). Steer-y-Wire Technology: Steering wheel s new, intelligent Humn Mchine Interfce. VDI-MEG. Conference Agriculturl Engineering. (pp. 7.). Düsseldorf: VDI Verlg. [] Jzr, R. N. (8). Vehicle Dynmics: Theory nd Applictions. NY: Springer. [3] Kopetz, H. (1997). Rel-Time Systems: Design Principles for Distriuted Emedded Applictions. London: Kluwer Acdemic Pulishers. [] Odenthl, D. (). How to mke Steer-y-Wire Feel like Power Steering. 15th Triennil World Congress, Brcelon, Spin: Elsevier IFAC. [5] Switkes, J., Rossetter, E., & Gerdes, J. (). Hndwheel Force feedck for Lnekeeping Assistnce: Comined Dynmics nd Stility. Journl of Dynmic Systems Mesurement nd Control v.18, no. 3, [] Tpzdi, T., Kis, J., & Li, L. (1997). Does the Concept of the triler with propelled Axles Experince renissnce. VDI-MEG. Conference Agriculturl Engineering. (pp ). Düsseldorf.: VDI-Verlg. [7] Yih, P., & Gerdes, J. (5, oct. 5). Modifiction of vehicle hndling chrcteristics vi steer-y-wire. IEEE Trnsctions on Control Systems Technology, pp Copyright 11 y Lortory Soete