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Improvement of the Steering Feel of an Electric Power_图文

792 Journal of Mechanical Science and Technology {KSME Int. J), Vol 19, No. 3, pp 792-801, 200S

Improvement of the Steering Feel of an Electric Power Steering System by Torque Map Modification
M a n Hyung Lee* School of Mechanical Engineering, Pusan National University, Busan 609-735, Korea Seung Ki H a Department of Interdisciplinary Program in Mechatromcs, Pusan National University, Busan 609- 735, Korea Ju Yong Choi Department of Mechanical and Intelligent Systems Engineering, Pusan National University, Busan 609-735, Korea

Kang Sup Yoon
School of Automotive, Industrial and Mechanical Engineering, Daeku University, Gyeongsan 712-714, Korea

This papei discusses a dc motor equipped electric powei steering (EPS) system and demonstrates itb advantages over a typical hydraulic power steering (HPS) system The tire-road interaction torque at the steering tires is calculated using the 2 d o f bicycle model, in other vi/ords by using a smgle-track model, which was verified with the J-turn test of a real vehicle Because the detail parameters of a steering system are not easily acquired, a simple system is modeled here In previous EPS systems, the assisting torque for the measured driving torque is developed as a boost curve similar to that of the HPS system To improve steering stiffness and return-ability of the steering system, a third-oider polynomial as a torque map is introduced and modified within the preferred driving torques researched by BertoUini Using the torque map modification sufficiently improves the EPS system Key Words: Electric Power Steei ing, Assist Torque, Steering Feel, On-Center Handling, Return-Ability, Steering Stiffness

Nomenclature
a 7 S Side slip angle at C G (centei of gravity) [rad] Yaw rate [rad/s] Steering angle [rad] Steering wheel angle [rad] EPS motor angle [rad] EPS motor input current [A] Lateral acceleration at C G [m/s^]

V Side slip velocity at C G [m/s] u ' Longitudinal velocity [m/s]

1. Introduction
Recently the automotive industry has focused on improving vehicle peiformance, safety and convenience for drivers Steering assist systems play an important role in each area During lowspeed maneuvers, power-assisted steering systems reduce the amount of effort needed by the driver for steering However, it gives a hard feel to steering to drivers during high speed maneuvers The conventional hydraulic power steering (HPS) system, which is made up of an engine-

ay

* Corresponding Author, E-mail mahlec@pui,an ac kr TEL +82-51-510-2331, FAX -1-82-51-512-9835 School of Mechanical Engineering, Pusan Nationdl University, Busan 609-735, Korea (Manuscript Received August 2, 2004, Revised Janujiy 28, 2005)

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Improvement of the Steeimg Feel of an Electric Power Steering System by Torque Map Modification driven hydraulic pump and a hydraulic actuator, decreases engine efficiency but requires complex hydraulic components To cope with the deficiencies of HPS, an electric power steering (EPS) system has been vigorously researched Since the EPS system uses an engine-independent motoi without coinplex hydraulic units, the weight and volume of steering systems can be leduccd Thus, EPS systems achieve bettei fuel and space economy and maintains the fee! of the steering even duiing quick changes m driving conditions through softwaie Moieovei no hasm is done at the environment because no hydraulic Quid is used (Burton, 2003) Generally, there are three types of EPS Light vehicles have installed a column type where the assist motor connects to the steering column through spur gears and delivers assist torque to the coluinn, foi example Twmgo of Renault, MGh of Rover, ACTY of Honda, and ALTO/SERVO of Suzuki Foi heavy vehicles, the pinion type has been adopted, foi example MIRA/Hl-Jet of Daihatsu and MINICA of Mitsubishi The steer-by-wiie type gives the most efficient space, but countermeasure for malfunction should be researched Steering feel should be established for fine tunmg of steering systems Adams (1983) researched the feel of powei stcciing and Norman (1984) inttoduced center handhng performance Beitollini and Hogan (1999) drew up a preference cuive as a function of vehicle speed based on the steering effort by various drivers using VT] driving simulators Rakan and Wang (2001) used the boost curves of assist torque foi a given vehicle speed Based on these objective indices, Camuffo et ai (2002) tuned an EPS to have the same steering feel of an HPS Using a steer-bywire EPS, Tong Jm Paik et al (2002) controlled the front wheel motor by PID controller to minimize the erroi between steering angle and wheel angle With steeung wheel angle and torque sensors attached to a steeimg column. Button (2003) calculated assiiitimce torque by summing the high gam related to steering torque and the low gam related to steering position To improve leturn-abihty. Kurishige et al (2000) developed a control strategy based on an estimation of

793

alignment toique generated by tires and road surfaces without sensors Since steering torque assistance and return-ability are not active at the same tune, Kim and Song (2002) separated the two control algorithms where the reference steering toique v,'as determined by the torque map based on vehicle speed and steering wheel position In this paper, the 2 degiee of freedom (d o f) bicycle model will be used to calculate the tire road interaction torque Although the steering of a vehicle affects its tolling motion, a descnption of the rolling system is beyond the scope of this paper since an EPS does not control the active diivmg angle bin the assisting torque Since it is difficult to acquiie detailed parameters of the steering system, the steeimg system will be modeled similarly to the research of Kurishige et al (2000) In previous EPS systems (Chabaan and Wang, 2001), assisting toique foi the measured driving torque was making a chait as a boost curve like the HPS of Adams's research (1983) However, the boost curve map did not improve steeimg stiffness or return-ability To improve steeling stiffness and return-ability, wc will introduce and modify a third-order polynomial as a torque map The preferied driving toique lange developed by Beriollini and Hogan (1999) will be fitted as a linear polynomial function This proposed torque map will be verified for the 2 d o f vehicle model with a simple steering system To determine steering input, the relationship between 8 and a^ will be derived here In conclusion, the EPS system will be improved sufficiently on steering stiffness and retum-ability by the proposed toique map

2. Mathematical Models and Verifications
2.1 Vehicle model The classical single-track model (Choi et a l , 2002) IS obtained by lumping the two fiont wheels into one wheel m the centerline of the vehicle, the same is done with the two lear wheels as shown in big I By the vehicle kinematics, a lateial acceleration at C G is given by

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794

Man Hyiing Lee, Seung Ki Ha, Ju Yong Choi and Kang Sup Yoon

-^>r^

^
f)

A ^
t v

o c
to 0)

30-t
0-9

;0 G3

05 n

5

Q.6 S

Fig. 1 Coordinate of tlie single-track model ay=v + u-y (l)

i

10
Stterin^ .JRE!

0-3 0-0

^

Since tires can be modeled as linear within \ay\< 0.3 g, lateral force at the front tire is obtained as Fy=Cra And tjie side slip angle ibr d is presented by (2)

0

Time [sec] (a) Steering wheel angle 6 and steering angle S
04-

a^d-

v + a-y u

(3)

The vehicle model is described as 2(C/+Cr)
mil

l[aQ-bC, -umu l[a%+b'C,) Lu

la
m L
S (4)
1 2

l[aC,-bCr)

where a b I Cf/Cr m distance from C.G. (o front axle distance from C.G. to rear axle wheel base (i.e. 1 — a + b) front/rear lire cornering stiffnesses yaw moment of inertia of vehicle vehicle total mass

Time [sec] (bl Lateral acceleration Oy

From the IFAC benchmark example (Ackermann and Darenberg, 1990), the steering angle is limited to | 5 | < 4 0 deg and the steering angle rate is limited to deg/s. The relationship between S and 8. is assumed to be dominated by the first order delay and the multiplication of the gear ratio between the steering angle and the steering wheel angle. This formula is as follows : S{s)^ where n - gear ratio between d and 8 T - delay time between S and 6 Usually a J-turn test is fulfilled to verify the steering performance such as rollover or riding performance. In simulation, 0 is stepped up to

Time [sec] (cl Yaw rate y Fig. 2 J-turn test for the model verification

Ts + \

Sis)

(5)

34° within 0,2 sec with ; / = 2 2 m s. Figure 2 shows the J-turn results for the single-track model and the actual vehicle. Figure 2va shows the angle input of steering wheel and the delayed steering angle. The lateral acceleration and the yaw rate are settled to around 3.4 m , s ' and 8.3 deg/s as shown in Figs. K b ' and 'cl. The integrals of time multiplied bv the absolute magnitude of error ?IT.A.E for the lateral accelerati-

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Improvement of the Steering Feel of an Electric Power Steering System by Torque Map Modification on und the yaw rule are 0.29 m/s" and 0.42 deg/s, where ihe nonlinearity of the tire may be the main fac(or Tor the errors. The .single-track model has the characteristics nearly similar to the model of actual vehicle. 2,2 Steering system The masses, inertias, dampings, and stiffnesses of rack bar, tie rod, and tire had been entirely or partly considered in the previous researches by Park et al.(2002), Kurishige et al.{2000), Kim and Song (2002). In the researches by Bertollini and Hogan (1999) and Cymuffo et al.(2002). the tuning or design of the EPS controllers were depended on simulators. So the steering model was not described. As this system is modeled in detail, we can describe its responses more actually. However, to find out all of the parameters precisely is not a simple task. In this paper, a steering column is simply modeled with the mass moment of inertia, while damping and stiffness are ignored. The steering column is obtained as Jd^ta+Td-Vi where / Za Id T( It If '. inertia of steering column '. assist torque ! driving torque '. load torque (i.e. Ti — Ti + Vf) '? lire-road interaction torque '. friction torque (6) Slwritii'WJicc.1 Torque sensor—? Steering Column — ,— Tire U?

795

\

^—Tic rod *—Knuckle arm

Fig. 3 Constitution of steering system equipped an l?PS

=kTN- ia-\- Zd— zt — z/ The obtained steering system is shown in Fig. 3. To find the tire-road interaction torque, the kingpin torque, r*, (Gillespie, 2002) is obtained as
Zk=Zv+TL+ZA (9)

where ZA '? aligning torque TL ? lateral torque Zv '? vertical torque Because of the kingpin offset angle and a lateral inclination angle, the vertical force on the lire produces the vertical torque. When the kingpin offset angle and the lateral inclination angle are small, a torque generated by the vertical force can be approximated by zv = — FitdsmA-^mS where F^ '? vertical force d '? kingpin offset angle A '. lateral inclination angle Since the lateral force produces a torque through the longitudinal offset resulting from the caster angle, a torque generated by the lateral force is given by ZL=Fyri tan v where Fy'- lateral force acting at the tire center Tl '? tire radius (11) (10)

EPS motor generating Za can be modeled as a dc motor as follows :
J infy ml ijm (j m
I

Zm
?

7\J ^^

(7)
'

— KT'la

JIT Ta

where ]m '? inertia of EPS motor Bm- damping of EPS motor Zm '? EPS motor torque kT ? EPS motor constant A'^ '. gear ratio of EPS motor Thus, the steering system is obtained as

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796 V '? custer ;ingle

Man Hytiiig Lee, Seiing Ki Ha. Ju Yong Choi and Kang Sup Yoon torque in eq. iSl is defined as follows

The lateral Ibice is developed by a tire at a point behind (he tire cenLer. So the aligning torque is written as TA=piFy c o s / Z + l ? !12)

Lf^FySgnid''

\S'

where p is pneumatic trail distance. Considering the length From kingpin to rack-bar, the rack-bar force. FT, is written by Fr-rs

;/ocos(ft-,s)+/ocos((a+5)}

(13)

where k and da ure the length and the angle of tie-rod. The groiuid reactions, Ti. on the lire are described by Ti=Fr-ri, (141

where rp is the radius of pinion. The friction

where F/ is friction gain. More complex frictions in the steering system are ignored here. By the results of slalom test by INS \^ilh a GPS Multi-Antenna System (Hong et a!.. 2005 . the simple steering model is verified. Considering the driver safety, the vehicle speed and the steering wheel angle are limited. In the experimentation, 6 and Td are measured by encoder and torque sensor attached on steering column. Fy is calculated by the 2 d.o.f vehicle model. Figure 4 shows the plots of 9 versus id- As the \ehicle speed is increased, the side slip angle are increased. Therefore, higher speed needs more driving torque. The gap between experimentation and simulation is due lo modeling uncenainites or measuring errors.

3. E P S Control by Modification of Torque Map
Typical hydraulic power steering systems are controlled by the reference torque map. Many researchers including Adams 1.19831 have adopted a boost cur\e as the map. where the assisting level is related to Vd and u. Based on the previous models of a vehicle and a steering system. Fig. 5 shows the block diagram of the EPS control system, where is measured by a hole-sensor on transmission and the driving torque is measured by a torque sensor anached to the steering column between the steering wheel and assisting motor. The steering feel in vehicle handling has been characterized generally by "on center handling" (Norman, 1984). which is determined b> driving a vehicle on a normal highway under low lateral acceleration without wmd or road disturbances. The steering feel indices are defined by the relationships among 9, Td. and dy. These parameters are calculated or measured under H=100km h. where the steering wheel is a 0.2 Hz sinusoidal wave, The lateral acceleration of a vehicle is dorainantly related to the magnitude of the steering angle. When the lateral velocity and the yaw rate in eq. i4: have senled :i.e. i ' - = ; ' = 0 : .

-100

0

100

steering wheel angle |deg] (a) M = 8 m/s

E

-aoo

-100

0

100

2-

Steering wheel angle [deg] (b) tf = I4m/s i^'ig. 4 Steering wheel angle d vs. stL'cring V.\\K\ torqtie r,i

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linprovi^inenr of the Steering Feel of an Electric Power Steering System by Torque Map Modification

797

%
S^ 4-f V

Tire
Torque

j-*j^-

Friclioii ^^^ Torque

a
RefereiK* Torque map
Motor
(. n l i l t i l l l

^

Lateral motion oCVehicle

? y

Drivev
(I luniaii)

Fig. 5

EPS control syslem including an reference torque map

500'
CO

01

en
300 200

ai

100

O C 0)

a) C O
—I 1 1 1 1 1 1 1 I

0

50

10Q

150

200

250

-0.2

-0.1

00

0.1

Vehicle s p e e d [km/h] Fig, 6 Steering wheel tingles 6*10 be i7\'=0.2g Fig. 7 angle 0 the steering angle for (he given a, can be described as a function of vehicle speed u by

Lateral acceleration [g]
Lateral acceleration Uy v.s. steering wheel

-K[l-2)
where

-K-m

\ ay

(16J o

K-

aCf — bCr

0)

iCfCAa + b)
wheel

(17) angle for

Figure 6 shows the steering

G ^ = 0 . 2 g (acceleration of gravity) by eq. ( 1 6 ) . Figures 7 ~ 9 show the results of " o n center h a n d l i n g " without power assistance. T h e plot of d versus flj, as shown in Fig. 7 has three steering i n d i c e s : steering sensitivity at a . v ^ O . l g , T h e ratio of steering sensitivity at a.y^QA minig and 2.22.18 g / 1 0 0 deg ; the minimum steering sensitivity is 1.5825 g / l O O d e g ; and the steering hysteresis is I 1.3121 deg. T h e ratio of sensiti\ity is about 71.6% which is that of a compact front power Fig. 8 m u m steering sensiiivity, and steering hysteresis. minimum steering sensitivity shows the indtience of steering compliance and the hysteresis is relaied to the lag of yaw rate with steering In Fig. 7, the steering sensitivity input. at 0.1 g is
-0.1 0.0 0,1 0 2

Lateral acceleration [g] Lateral acceleration a.,, vs. steering wheel

torque Tj by the boost cnr\e map

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788

Man Hyiing Lee, Seiiug Ki Ha. Jii Vong Choi and Kang Sup

Yoon

o

5

-10

-5

0

5

10

15

Steering wheel angle [deg]
Fig. 9 Steering wheel angle ff vs. steering wheel torque td t>y the boost curve map Fig. 10

MEasured driver torque [Nm] Assisting torque torque Td la for measured driver

vehicle according to N o r m a n ' s research

(1984).

In the plot oF Td versus ay as shown in Fig. 8. steering indices such as lateral acceleration at 0 N m , steering wheel torques and steering v\'heel torque gradients at 0 g and 0.1 g are indicated. .A.t the point of releasing a steering wheel after step steering, td will be 0 Nin and lateral acceleration causes the steering wheel return to center. Thus, the lateral acceleration at O N m is an indication of return-ability. Steering wheel torque at 0 g is mainly dependent on C o u l o m b ' s friction in the steering system. T h e steering torque gradient at 0 g is influenced by the kingpin axis torque gradient and the overall steering ratio. T h e steering wheel t o r q u e at 0.1 g is a measure of steering effort. T h e steering t o r q u e gradient at 0.1 g is a measure of road feel just off straight ahead. With typical power steering systctns, both torque and torque gradient at 0.1 g are significantly reduced. T h e resu[t.s of a steering system by nature and an E P S by a boost curve shows (hat lateral acceleration at 0 N m a n d steering wheel t o r q u e at 0 g are similar, and steering wheel torque and steering wheel gradients at 0 g and 0.1 g are decreased. Drivers of an E P S equipped vehicle are able to reduce the steering effort and improve road feel, but return-ability is not improved by the boost curve alone. In the plot of td versus (9 as shown in Fig. 9, return-ability and steering stiffness are analyzed by steering wheel torque at 0 deg and steering t o r q u e gradient at 0 deg. These indices can't be improved by the boost curve at all.
Ta — ka' ~di Td i I p

Vehicle speed [km.'ti] Fig. 11 The preferred steermg torque rp by Bertollini

Therefore it is necessary to change the reference t o r q u e m a p from the typical boost c u r \ e . Since the assisting t o r q u e and the returning Torque are not simultaneously required, a cubic curve is introduced as a reference t o r q u e m a p as follows :
i

is

\i

where ka is the tuning gain considering the maximum torque of motor or steering feel and Tp is a preference t o r q u e depended on U- T h e cubic curve map as s h o w n in Fig. iO generates a returning torque when driving t o r q u e is smaller tlian Tti. Bertollini and H o g a n 1999 developed the preference torques as s h o ? n in Fig. 1 i using the VTI driving simulator. Here the preference torques are fitted as a rational polynomial curve as follows

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Impmveineiil

of ihe Steering Feel of an Electric Power Steering System by Torque Map Modification

799

1,

cr

E

///
-1^ ^fi^^^r^^--^:::^. Tr
^~'^^r^^---^^LL^TV

^

en

/A

7! i
-0.1 0.0 0.1 0,2

Hnldinu CW

crvv

Lateral accsleralion [g] Fig. 12 Latera accclcracion ay vs. steering wheel Fig. 14 torque Td by the preposed cubic curve map

Measured drivertorque [NmJ Assistiii" torque curves to improve the return-ability

i

1

.

J

^

1—

-.—-1

-i

1

1

the cubic curve is modiHed as shown in Fig. 14. W h e n the driving t o r q u e is increasing {i.e. frf>0) in spite of r d = 0 Nin, an E P S m o t o r generates the assisting t o r q u e up to Tr- This m a n n e r also applies to the reverse steering. As a result, the

0)

4-

cr 0-

?

l-y/^
L^s-*"^^^""''^

f

t

reference torque m a p by the modified cubic curve is defined by

c
05

-4-

B.
CO

CubiL LurvL- 1

{ r.=

h-rd{u-VTt){Td-Tp] kJj-Tr) {TA %)\zd-Tp),

, frf=0 (holding) r i > 0 (CW.) (20)

'
1

l i d L i s l <jiir\ t' 1
? r '

-15

? 1 0 - 5

0

5

10

15

I k^zA wliere

Tr) (T.+ TP) {u- Tp]. i,<0 (CCW)

Steering wheel angle [deg] Fig. 13 Steering wheel angle B vs. steering wheel torque Td by the proposed cubic curve map Tr is the tuning gain, which should be

further studied. In Figs, 15 and 16, lateral acceleration at 0 N m and steering wheel torque at 0 deg arc reduced, so return-ability is improved.

T,=

5.7SM + 131.5 w + 82.09

(19) (RMS) error of

Simultaneously

torque gradients are increased. in the T a b l e i.

All of results are summarized where the root mean square fitting is 0.0847 N m . Figures 12 and 13 show the results of ihe proposed cubic curve m a p . In F i g . 12, lateral acceleration at 0 N m is unchanged, steering wheel torques at 0 g and 0,1 g have increased slightly, and the steering wheel torque gradient at 0 g and 0.1 g have decreased. Because the steering wheel t o r q u e gradient at 0 deg is increased, ihe steering stiffness improves. But the return-ability deteriorates as shown in Fig 13. Therefore the cubic curve m a p should be modified to improve the return-ability. According to the states of the driving torque.

Indices in the plot of ^ v e r s u s Oy have no concern with p o w e r steering systems. Lateral accelerations at 0 N m related with r e t u r n - a b i l i t y are alike. By using power steering systems, steering effort and road feel are decreased. A l t h o u g h some indices in the plot of Td versus ay become a httle worse by the rnodified curve, the indices may be improved by fine tuning ka and Tr- T h e modification improves steering wheel torque and gradient at 0 deg reinarkably. The steering wheel torque Nmj {0.16S2 at 0 deg by the modified curve is smaller

than the half of torque (0.5027 N m l by the boost curve. T h e steering wheel torque gradient (0.6554 Nm/ijeg) at 0 deg is larger than 0.3590 N m / d e g .

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mo

Man Hrimg Lee. Seiiiig Ki Ha. Ju Yoiig Choi and Kang Sup Table 1 Steering indice-s Steering sensitivity at 0.1 g [g/lftOdeg] The results of steering Feel indices Meaning steering compliance steering compliance phase lag return-ability coulomb friction steering etTort steering ratio & kingpin road feel return-ability steering stilTness f 0.098! 2.7921 5.5509 No control Boost curve

Yoon

Proposed Modified curve \ cur%'e 2.223S 1.5825

ay

vs. d

Minimum steering sensitivity [g/lOQ deg] Steering hysteresis [deg] Lateral acceleration at 0 Nm [g] Steering wheel torque at 0 g [Nm]

11-3121 0.0982 1 2.6943 4.4141 0.0989 3.2754 4.6085 15.3623 ; 0.0839 3.1904 4.6734 17.4083 10.6909 0.1682 0.b554

ay

vs.

Steering wheel torque ai 0.1 g [Nm] Steering wheel torque gradient at Og [ N m / g ] Steering wheel torque gradient at 0,lg [ N m / g ]

27.8484 1 20.6239 26.9798 0.5006 0,3603 |

11.2782 1 9.9777 0.5027 0.3590 0.8281 0.5304

6
vs.

Steering wheel torque at 0° [Nm] Steering whee! torque gradient at 0° [Nm/deg]

4O

c
Mcsi.ned Lijr-.e CO -8 -0 = -0.1 0,0 0.1 0.2 -16 -10 -5 C = '-'-

J
'5

Lateral acceleration [g] Fig. 15 Lateral acceleration ay vs. steering wheel torque ta by the modincd cubic curve map Fig, 16

Steering wheel angle [deg] Steering wheel angle 8 vs- steering wheel torque Ta by the modified cubic curve map 8% lateral acceleration error and 5% yaw rate

4. Conclusions
T h i s paper discussed a dc motor equipped electric power steering (EPS) system. T h e tire-road interaction t o r q u e at the steering tires was calculated using a 3 d.o-f. bicycle model. The restilts of J-turti test for the model verification showed

error- A simple steeriitg system was modeled and tested for the sinusoidal steering inputs by uncertainties such as uncertain slalom test) - the simple steering model had errors caused parameters, friction, and backlash. Hence, the steering model and the 2 d.o.f bicycle model could replace with an actual \ehicle. T o improve sieerine stiflness

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Improvement of the Steeiing Feel of an Electric Power Steering System hv Torque Map Modification and retuin-ability of the bteenng system, a thirdoider polynomial as a torque map was mtroduced and modified within the preferred diivmg torques lesearched by BertoUmi and Hogan The prefeiied driving torque was fitted as a rational polynomial function hete The relationship between S and ay was derived m oidei to deteiminc steering input The proposed and modified torque maps were simulated using the 2 d o f vehicle model with a simple steering system By using the modified torque map, the steering wheel torque at 0 deg as the index of return-ability was 0 1682 Nm and the steering wheel toique gtadient at 0 deg as the index of steering stiffness was 0 6554 Nm/deg After all, the return-ability and steetmg stiffness of EPS system weie impioved sufficiently

801

Acknowledgments
This reseatch was financially suppoited by Korea Science and Engiuccimg Foundation ( K O S E F ) through the Engineering Research Center for Net Shape and Die Manufacturing at Pusdn National University and by Pusan National University Research Giant

References
Ackermann, J and Darcnbeig, W , 1990, "Automatic Tiack Control of a City Bus," IFAC Theoiv Report on Benchmark Problem for Control Systems Design Adams, F J , 1983, "Power Steermg Road Feel," SAE Paper 830998 Anthony W Buiton. 2003, '"Innovation Drivers for Electric Powei-Assisted Steeling," IEEE Control Systems Magazine, pp 30—39 Camuffo, I , Caviasso, G , Pascali, L , Pesce, M

and Alviano, E , 2002, '"Simulation Tools and Evaluation Criteria foi Steeling Wheel Feci Improvement ot an Electric Power Steering System," SAE Paper 2002-Q\-1593 Chabaan, R C and Wang, L Y , 2001, "Control of Electrical Power Assist Systems i/? Design, Torque Estimation and Structural Stability," JSAE Review 22, pp 435-444 Choi, J Y , Hong, S J , Paik, K. T , Yoo, W S and Lee, M H , 2002, "'Lateral Control of Autonomous Vehicle by Yaw Rate Feedback," KSME International Journal, Vol 16, No 3, pp 338-343 Gary P Bertollini, Robert M Hogan, 1999, '"Appiymg Driving Simulation to Quantify Steeling Effort Preference as a Function of Vehicle Speed," SAE Papei 1999-01-0394 Hong, S, Lee, M H , Rios, J A and Speyei, J L , 2002, "Observability Analysis of INS with a GPS Multi-Antenna System," KSME International Journal, VQ\ 16 No 11, pp 1367-1378 Kim, J H and Song, J B , 2002, "Control Logic foi an Electric Power Steeling System Using Assist Motor," Mechatromcs 12, pp 447 — 459 Kuiishige, M , Wada, S , Kifuku, T , Inoue, N , Nishiyama, R and Otagaki, S , 2000, "'A New EPS Contiol Strategy to Improve Steering Wheel letum-ability," SAE Paper 2000-01-0815 Noiman, K D, 1984, "Objective Evaluation of On-centei Handling Peiformance," SAE Paper 840069 Thomas D Gillespie, 1992, fundamentals of Vehicle Dynamics, SAE Inc , pp 284—291 Tong Jm Park, Se Wook Oh, Jae Ho Jang and Chang Soo Han, 2002, "'The Design of a Controller for the Steer-by-Wire System Using the Hardwaie-In-the-Loop-Simulation System," SAE Paper 2002-01-1596

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controlmethodofSBWsystemwasa producethe steeringroadfeel almostthewas that...本文选取某国产样车,将样车中原有的电动助 力转向(electricpower 2.1方向盘...
Power steering_图文.pdf
In other power steering systems, electric motors provide the assistance ...Francis W. Davis, an engineer of the truck division of Pierce Arrow began...
基于Isight的电动助力转向系统集成优化.pdf
InordertotakeaccountsteeringSimulink ofthe vehiclesteeringstabilityandtheconveniencean ofoptimization on theelectricpower system(EPS)parameters,itrn础esplatform.It ...
文献翻译-汽车电动助力转向系统发展综述.doc
of an electric power steering(EPS) system in an automobile is explicated....cost;The drawback to motor torque ripple effects of driver feel bigger 。...
...Response of Electric Power Steering(EPS)_图文.pdf
Steering Response of Electric Power Steering(EPS)_...But the advent of EPS made steering system an ...characterize the on center feel of the vehicle. ...
...液压动力转向系统的发展___外文翻译中英文全_图文.doc
Yamamoto Within a frame of development of ecological power steering systems, we have completed the development of an electric motor-driven pump type ...
四轮驱动汽车电动助力转向控制策略研究_论文.pdf
In order to resolve the contradiction between steering portability and road feel of four-wheel drive vehicle, an electric power steering control strategy base...
Electric Power Steering (ESP)_图文.pdf
you feel is wrong, unclear or missing at all?...power steering with an electric motor-driven ...for a massive improvement of overall system safety...
Electric power assisted steering (EPAS)_图文.pdf
Electric power assisted steering (EPAS)_交通运输_...The lack of driver ‘feel’ at high speeds can...Figure 3. shows an implementation of an EPAS ...
英语长难句分析.ppt
an excellent chance of surviving for tens, if ...? Shippers who feel they are being overcharged ...suggest its grip on the steering wheel is ...
...泵控制的液压动力转向系统的发展外文翻译中英文全_图文.doc
Yamamoto Within a frame of development of ecological power steering systems, we have completed the development of an electric motor-driven pump type ...
steering_图文.pdf
where a minute turn of the steering cockpit of an Ariel Atom sports car ...Electric power steering (EPS) is more efficient than the hydraulic power ...
Electric power steering(EPS)电动助力转向机.pdf
generates the power required for steering assistance through an electric motor...This fact is the reason why any modification of the steering feel (i.e....
门座起重机四连杆组合臂架变幅系统优化方法(1)_图文.pdf
In addition, it proposes the improvement of initial point of four-link 〔...Xi’ an Jiaotong 〔Abstract〕 Electric power steering system is the power ...
汽车英语_steering_system_图文.ppt
Review 1: What’s the function of Steering ...steering response and good road feel for the ...(EHPS)液压电动转向系统 Electric Power Assisted ...
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