(1) (2) (3) (4) x& r. ( θ. Fig.1. Schematic diagram of an EPS system. Steering shaft and column(jsc, Bsc,θsc) Reduction gear(n)

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1 Develoent of Active Steeing Angle Contol based on Electic Powe Steeing Systes JinYan Hsu, ChihJung Yeh, TsungHsien Hu, TsungHua Hsu, and FuHsien Sun Autootive Reseach and Testing Cente(ARTC) Abstact The nube of electic owe steeing(eps) alications continues to gow aidly. EPS systes utilize electic otos to ovide steeing assistance when coneing. Because of the contollability of the EPS oto, it ovides oe and oe ossibility to hel the dive in diving ocess actively. An autoatic aking syste(aps), one of the Advanced Dive Assist Syste(ADAS), is a tyical alication by contolling the EPS oto to assist dives in aking vehicle autoatically. In this ae, two aoaches ae oosed fo active steeing angle contol based on EPS systes and the syste dynaics was analysed to iove the angle contol efoance in APS. Futheoe, the active angle contol algoith was ealized with an ebeddeddsp and validated in a ototye vehicle. I. INTRODUCTION An electical owe steeing syste utilizes an electic oto as an actuato to ovide a suitable assist toque when the dive tuns the steeing wheel. Coaed with the conventional owe steeing syste, it is an ondeand syste that oeates only when the steeing wheel is tuned. Besides, because of its electoechanical stuctue, it has ossibility of steeing vehicle actively. By integating the EPS syste with othe vehicle systes, advanced steeing functions can be fulfilled. The ost oinent exale is the autoatic aking syste (APS)[1]. The APS takes advantage of the EPS syste to hel dives autoatically ak in constained envionents whee needs uch attention and exeience is equied. The APS geneates a stea of values fo the steeing angle when the vehicle evesing into a aking sot. These values ae tansfoed into the oto toque coands at the steeing angle contol level by the EPS syste. In ecent yeas, the eseach of the APS is a oula toic. Because of APS, aking is not a toublesoe action. Many studies have been done on aking stategies. Fo instance Hsu et al.[1] ovided the ath lanning and the ath tacking stategy fo the APS. Lin et al.[2] used ultasonic sensos, caea vision and develoed algoith to decease aking sace fo aallel aking. Besides, the coecial oduct of the APS has been fist intoduced by Toyota Moto Cooation in Toyota Pius/Lexus LS odels. Howeve, little attention has been aid to steeing angle contol efoance. The otational otion of the steeing wheel ay ake the dive feel dangeous and even oe influence his/he confidence in the APS. The uose of this ae is to oose the steeing angle contol algoith which is suitable fo the EPS syste and caable of bette efoance fo the APS. The ath tajectoy of the vehicle fo the APS [1] is lanned in advance and tansfoed into the steeing angle coands. The esonse of the steeing wheel will be diussed. II. ELECTRIC POWER STEERING The basic contol of an EPS syste is achieved by oto cuent contol. The faewok of an EPS syste includes an electic oto and steeing echaniss. An EPS atheatic odel is consideed as below, and the heatic diaga of the EPS syste is showed in Fig.1. The odel is used to deibe the syste dynaics and to veify the accuacy and eliability of the steeing toque contol logic. T K ( θ θ ) B & θ = J & θ (1) h tb θ x K tb ( θ θ ) K ( θ ) T f k ( θ ) B & θ = J & θ n (2) k x (θ ) F b x& = && x (3) 1 θ T K ( θ ) B & θ = J & θ n n (4) whee Th is the toque that dive act on the steeing wheel; Ktb is the stiffness of the tosion ba; J and B ae the inetia and the daing constant of the steeing shaft and colun esectively; θ and θ ae the inion shaft otational angle and the steeing colun angle esectively; θ is the echanical oto osition of the oto; n is the eduction gea atio; K is the stiffness between the oto and eduction gea; Tf is the fiction toque on the steeing colun and shaft; k is the stiffness between the ack and inion; x is the dislaceent of the ack; is the stoke atio; F is the alignent foce on the ack fo the oad wheel; and b ae the ass and the daing constant of the ack; T is the electoagnetic dive toque. Reduction gea(n) Fig.1. Scheatic diaga of an EPS syste Rack & Pinion(F,,b,k,x, ) Steeing shaft and colun(j, B,θ) Tosion ba(ktb) Pinion shaft(j, B, θ)

2 DC Bus Cuent(A) cuentco and feedback cuent Fig.2. the exeiental esult of cuent contol The oto used fo the EPS syste in this study is a theehase eanent agnet synchonous achine (PMSM). Hee use the dq fae though the otation efeence fae tansfoation to odel the PMSM fo achieving toque contol by cuent contol. The intenal odel contol (IMC) ethod is alied to design the cuent contol loo of the PMSM[3]. The contolle was ileented by an ebedded icoocesso. Fig.2 is the exeiental esult of the cuent esonse which was veified by a dyno. III. AUTOMATIC PARKING SYSTEM The APS is an auxiliay syste which hels dives having oe convenience in aking. The ajo techniques of the APS syste ae aking tajectoy lanning and tacking. The APS faewok is showed as Fig.3. Afte the APS detects o the dive decides the aking sace, the tajectoy of the aking ocess is calculated, and the vehicle will follow it with the active steeing contol. The aveage font wheel angle will be fist obtained by using the cuvatue of the ath and the Ackean steeing equation showed as equation(5) whee L is the wheelbase, Ri is the cuvatue of the atial ath tajectoy, δi and δsw is the steeing angle of font wheel and the steeing wheel angle at evey cuvatue esectively, and k is the steeing atio. The sketch Tajectoy tacking EPS Cuent Moto Contol Steeing Angle Contol Path Tajectoy Planning Tacking Contol Coodinate Tansfo Fig.3. The APS faewok Vehicle Position Estiato R 1 Ca B Ca A δ 1 Ca B A Ca B α δ 2 R 2 Ca C Fig.4. the sketch a of the APS ath tajectoy a is deicted as Fig.4, it is a two tun odel fo exale, and oint A is the evese oint of the steeing wheel angle. δ = k δ = k L / R ) (5) sw i ( i While the font wheel steeing angle is known, the steeing angle contol can be efoed to achieve APS function. Because of the chaacteistics of the steeing and susension echanis, the steeing atio is not a constant. In ode to have ecision steeing angle of the font wheel, the elationshi between font wheel steeing angle and the steeing wheel angle ust be consideed. The steeing atio of the exeiental vehicle is showed as Fig.5. Duing the autoatic aking ocedues, the steeing wheel angle will vay with the vehicle osition which can be obtained based on the accuulation as the equation(6) and (7). x = x l cos( ψ ) (6) y = y l sin( ) (7) ψ whee x and y ae the cuent ositions, x and y ae the foe ositions, l is the distance tavelled in the tie inteval, and ψ is the yaw angle which is calculated fo the wheel seed signals of the two sides. The calculating equation is showed as equation(8) whee Lw is the tead diension, l is the diffeential tavelling distance between the left ea wheel Steeing atio Font left wheel Font ight wheel Steeing Wheel angle(degee) Fig.5. the steeing atio

3 ψ 6 Coand Feedback l ψ L w Steeing angle(degee) Fig.6. the geoetic elationshi of the yaw angle and ight ea wheel, V l and V ae the wheel seed of the left ea wheel and the ight ea wheel esectively. The geoetic elationshi is showed as Fig w [( V dt V dt) L ] ψ = tan ( Δl L ) = tan (8) In ode to get the evese tiing of the steeing wheel, the distance fo the cente of the ea axle of the vehicle to the evese oint of the steeing wheel is necessay to onito. The global coodinate is tansfoed to vehicle coodinate fo the tajectoy tacking algoith of the evese osition woks oely. The tansfoed equations ae showed as bellow. Whee xg and yg ae the evese oint of the evesing of the steeing wheel in global coodinate, xgv and ygv ae the goal oint in vehicle coodinate. x gv = ( xg x )cos( ψ ) ( y g y )sin( ψ ) l cos(2ψ ) (9) y = x x )cos( ψ ) ( y y )sin( ) l (1) gv ( g g ψ IV. STEERING ANGLE CONTROL STRATEGY The objective of the ae is to develo steeing angle contol stategies based on the cuent contol loo to achieve the function of the aking tajectoy tacking. In this section, the bief steeing angle contol algoith (naed as tye1) will be diussed fist, and a colete contol algoith (naed as tye2) will be oosed. The tye1 contol algoith is showed as Fig.7. It is sile to achieve the steeing angle contol with PI contol stategy (Ca) which doesn t conside the vaiation of the steeing angle ate. The contolle decides the oto cuent coand accoding to the diffeence between the steeing angle coand and steeing angle feedback. θ Angle T L Plant contolle θ i ω θ 1/n C a K t 1/(J sb ) 1/s n T l w θ Fig.8.the steeing angle tacking efoance on ashalt oad(tye1) C a = K K I / s (11) Afte the contolle designed, the contol algoith was ileented in the EPS syste to achieve the active steeing angle contol. The steeing angle tacking efoance is showed as Fig.8. It has good tacking efoance at the lage angle vaiation, but bad at the slight vaiation. If it has good efoance at the slight vaying inteval, it will tack badly at the lage vaying inteval. The tye1 contol algoith can t have the sae tacking efoance at the diffeent angula degee vaying inteval. Based on tye1 contol algoith, the tye2 contol algoith adds the steeing angula velocity contol into the loo. The tye2 algoith is showed as Fig.9. It is a colete steeing angle contol loo, which includes the steeing angula velocity contol loo and cuent contol loo inside. Ca and Cav ae the contolle fo steeing angle contol and steeing angula seed contol esectively. Sat is the satuation of the steeing angula seed coand to estain the axiu steeing angula seed. C a = K K I / s (12) C av = K v K Iv / s (13) The PI contol stategy is also be utilized to design the contolle as showed in equation (12) and (13). The efoance is showed as below. θ θ e sw e 1/n C a Sat C av K t Plant ω θ Angle contolle ω 1 ω Angula seed contolle n 1/s 1/(J sb ) Fig.9. tye2 steeing angle contol algoith e ω i T L T Fig.7. tye1 steeing angle contol algoith

4 Steeing angle(degee) Coan feedback Fig.1. the steeing angle tacking efoance on ashalt oad(tye2) Fig. 1 shows that the tye2 contol algoith had good efoance at diffeent steeing angle vaiation. V. EXPERIMENTAL RESULT The oosed steeing contol stategies wee achieved on the exeiental vehicle showed in Fig.11 equied with Pinion EPS to coae the efoance of those steeing angle contol algoiths which wee alied to APS function. The twotun odel[1] was used fo tajectoy lanning of aallel aking. The aaetes of the exeiental vehicle ae showed as table1. Taking the aaetes of the vehicle into consideation, the ath tajectoy was lanned as Fig.12. The diffeent active steeing stategies wee utilized to achieve APS function with the tajectoy, and the esults of ath tacking and soe vehicle chaacteistics wee coaed as bellow. Y osition(c) X osition(c) Fig.12. the ath tajectoy of the APS The exeiental vehicle efoed autoatic aking on the oad sufaces with diffeent fiction which included the ashalt, ceent and ix fiction oad. Fig.13 deonstates that, the tye1 contol algoith has bad tacking efoance on the diffeent fiction of the oad sufaces with the sae contolle gain. The contolle gain used in the ashalt oad could get good efoance, but when the oad tye is diffeent, thee wee obvious tacking eo at the end of the tajectoy. If the tacking eo wants to be eliinated, the contolle gain needs to be etuned, o a colex contol stategy needs to be used which has the function of self etune, like the adative contol. On the othe hand, the tye2 contol algoith using the sae contolle gain has the sae efoance on the oad sufaces with diffeent fiction, showed as Fig.14. Without etuning the contolle gain, the tacking efoance is siila. Y osition(c) The lanning ath tajectoy Ashalt oad Ceent oad Mix fiction oad 5 Fig.11. the exeiental vehicle TABLE I The aaetes of the exeiental vehicle Ites value unit Length 49 Width 157 Height 195 Weight 126 kg Wheelbase 261 Tead(ea) 1395 Tie size 165R13 The esolution of the wheel seed senso 1 ulses/cycle The steeing angle of the steeing wheel 58~58 degee The eduction gea atio of inion EPS 15 Y osition(c) X osition(c) Fig.13. tye1 contol on diffeent tyes of the oad The lanning ath tajectoy Ashalt oad Cceent oad Mix fiction oad X osition(c) Fig.14. tye2 contol on diffeent tyes of the oad

5 Toque(N) Toque(N) Toque(N) The toque vay on the steeing wheel(ashalt oad) The toque vay on the steeing wheel(ceent oad) The toque vay on the steeing wheel(mix fiction oad) Tye1 contol Tye2 contol Tye1 contol Tye2 contol Tye1 contol Tye2 contol Fig.15. the toque vaies acts at the steeing wheel on diffeent oad tyes The esults show that the tye1 algoith can not handle the load vaiation. Theefoe, the efoance of the APS will be inconsistent in diffeent envionents. Beside of the efoance of the ath tacking, the vehicle dynaic chaacteistics ae also diussed. The chaacteistics include the toque vaying on the steeing wheel and the vaiations of the steeing angle and steeing angula velocity. Fig.15 shows the steeing toque detected by the EPS toque senso duing the exeients. The tye2 contol algoith has the salle toque vaiation on the steeing wheel which is about half of the toque vaiation of the tye1 contol algoith. The salle toque vaiation on the steeing wheel is bette, because the toque vaiation eesents the iact and the inetia effect acts on the steeing echanis and the tosion ba. The bigge toque vaiation ay cause the vibation and even the daage of the steeing echanis. As fa as the steeing angle ate is concened. Fig. 16 shows the tye1 contol algoith has sha vaiation at the steeing angle ate. The sha vaiation also caused bigge toque vaiation on the steeing wheel. And the level of the vaiation is not contollable on diffeent oad tye. The tye2 contol algoith take the steeing angle ate contol into account. As a esult, the vaiation of the steeing angle ate is not so sha, and has the sooth chaacteistic at the oint of the steeing angula velocity etuning to zeo. It is like the daing effect, and the situation doesn t cause any oveshoot o oillation at steeing angle contol on any tye of oad. Steeing angle ate(degee/sec) Tye1 contol Tye2 contol Fig.16. the steeing angle ate between diffeent contol algoiths Both two tyes of contol algoiths ae tuned on the ashalt oad. Thee ae no oillation at steeing angle tacking, showed as Fig.8 and Fig.1, but when the vehicle efoed APS function acts on the diffeent oad, like the ceent oad, of which fiction is salle than the fiction on the ashalt oad. Soe diffeence haened. The esults showed in Fig. 17 and Fig. 18 eveal that although tye1 has faste esonse tie than tye2, oillation aeaed befoe the steady state. In fact, the APS is enabled at low seed, noally less than 1 k/h; theefoe, the diffeence caused by esonse tie is not significant. The othe issue is that the steeing wheel otates too fast would ake the dive feel aed, so the suitable steeing angula seed of the steeing wheel is needed to be consideed. The tajectoy tacking is oe iotant if the ultitun odel is used in steeing contol of the APS function in the futue. The good tacking ability will achieve good efoance in ultitun odel. Steeing angle(degee) Coand Feedback Fig.17. the angle tacking of the tye1 contol on ceent oad Steeing angle(degee) Coand Feedback Fig.18. the angle tacking of the tye2 contol on ceent oad

6 VI. CONCLUSIONS This ae has coaed two tyes of steeing angle contol algoith. The stategy which includes steeing ate contol has bette efoance of the APS in vaing envionent. It also has the advantage of coact code size which is cucial fo ebedded systes. In addition, contollable steeing wheel angula velocity will be easie to satisfy dives feeling, which can let the APS becoe oe fiendly. ACKNOWLEDGMENT This wok was funded by the Deatent of Industial Technology of MOEA (Ministy of Econoic Affais), Taiwan, R.O.C unde Contact No.1EC17A4283. REFERENCES [1] TsungHua Hsu, JingFu Liu, PenNing Yu, WangShuan Lee and JiaSing Hsu, Develoent of an Autoatic Paking Syste fo Vehiclel,"IEEE Vehicle Powe and Poulsion Confeence (VPPC), Setebe 35, 28. [2] Chia Feng Lin, Chan Wei Hsu, Mink Kuan Ko, Chi Chun Yao and Kuang Jen Chang, A Multile Tun Achieveent of Advanced Paking Guidance Syste in Paallel Paking via Senso Fusion, 1 th Intenational Syosiu on Advanced Vehicle Contol (AVEC 1) August 2226, 21. [3] TsungHsien Hu, and ChihJung Yeh, Hadwae Ileentation of the Cuent Contol Using the Intenal Model Method in the Electic Powe Steeing Alication, IEEE Vehicle Powe and Poulsion Confeence (VPPC), Setebe 711, 29. [4] Thoas D. Gillesie, Fundaentals of Vehicle Dynaics, 2 nd Edition, Society of Autootive Enginees, Inc., USA, 1992.