Research Article Development of Estimation Force Feedback...

Research ArticleDevelopment of Estimation Force FeedbackTorque Control Algorithm for Driver Steering Feel in VehicleSteer by Wire System Hardware in the Loop

Sheikh Muhammad Hafiz Fahami1 Hairi Zamzuri2 and Saiful Amri Mazlan2

1UTM-Razak School of Engineering and Advanced Technology Universiti Teknologi Malaysia Jalan Semarak54100 Kuala Lumpur Malaysia2Vehicle System Engineering I-Kohza North Wing MJIIT Universiti Teknologi Malaysia Jalan Semarak54100 Kuala Lumpur Malaysia

Correspondence should be addressed to Hairi Zamzuri hairiklutmmy

Received 11 November 2014 Revised 10 April 2015 Accepted 30 April 2015

Academic Editor C S Shankar Ram

Copyright copy 2015 Sheikh Muhammad Hafiz Fahami et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

In conventional steering system a feedback torque is produced from the contact between tire and road surface and its flows throughmechanical column shaft directly to driverThis allows the driver to sense the steering feel during driving However in steer by wire(SBW) system the elimination of the mechanical column shaft requires the system to generate the feedback torque which shouldproduce similar performance with conventional steering system Therefore this paper proposes a control algorithm to create theforce feedback torque for SBW system The direct current measurement approach is used to estimate torque at the steering wheeland front axle motor as elements to the feedback torque while adding the compensation torque for a realistic feedback torqueThegain scheduling with a linear quadratic regulator controller is used to control the feedback torque and to vary a steering feel gainTo investigate the effectiveness of the proposed algorithm a real-time hardware in the loop (HIL) methodology is developed usingMatlab XPC target toolbox The results show that the proposed algorithm is able to generate the feedback torque similar to EPSsteering system Furthermore the compensation torque is able to improve the steering feel and stabilize the system

1 Introduction

The latest generation of integrated steering system is steer bywire (SBW) systemwhich is also known as independent steer-ing system It eliminates the need of mechanical column shaftbetween the steering wheel and the front axle system and wasreplaced with sensor actuators and electronic controller unit(ECU) as shown in Figure 1 The SBW system offers numer-ous advantages such as large space in cabin [1ndash3] While forvehicle manufacturers the absence of mechanical columnshaft gives maximum freedom interior design and ergonom-ics thus making it more comfortable for the driver [4 5]Moreover it reduces the driver impact force from the frontalaccident The SBW system is also potential to enhance thevehicle performance such asmaneuverability and stability [1]

There are several characteristics of SBW system [1] Oneof the characteristics of a SBW system is feedback torquefor driver steering feel whereby it is the most challengingissue in SBW system [6 7] The function of feedback torqueis for driver steering feel and steering wheel returnabilitywhen drivers release their hand from the steering wheel [8]Previous researchers have done several studies on how tocreate the feedback torque Based on control parameter ofvehicle speed and steeringwheel angleOh et al [9] developeda torque map to generate the feedback torque The generatedtorque quantity is small at low speed and increased at highspeed Authors proposed to control a gain for each controlparameter in order to vary the feedback torque Authors alsoclaimed that the torque map could give engineers freedomto tune for a real driver steering feel Kim et al proposed that

Hindawi Publishing CorporationInternational Journal of Vehicular TechnologyVolume 2015 Article ID 314597 17 pageshttpdxdoiorg1011552015314597

2 International Journal of Vehicular Technology

Steering wheel system

Steering wheel

DC motor

Positionsensorencoder

ECU

Electronic controller unit Wiring

Front axle system

DC motorPositionsensorencoder

Rack and pinion Tire

Steer by wire (SBW) system

Steering wheel

CouplingMechanical column shaft

Conventional steering system

Figure 1 Difference between SBW system and conventional steering system

improvement to the torquemap has beenmade by adding thedamping torque to create more realistic driver steering feeland to improve steering wheel returnability [10] MeanwhileAmberkare et al [6] used the steering wheel angle and fed tomodel transfer function to create a feedback torque By usingthe appropriate transfer function it is possible to changethe desired steering feel by varying a proper gain of thetransfer function The approach of the disturbance observeris introduced by Asai et al [11] The position and current ofthe front axle motor are used to generate the feedback torqueFurthermore a reference model that consists of the inertiaand damping factor of steering wheel motor is proposed byPark et al [12] to generate the feedback torque The modelmatching technique which combines the mechanical andelectrical parts has been introduced by Odenhtal et al [13]to generate the feedback torque while the series of vehiclecornering control algorithm is taken into consideration tooptimize the feedback torque as proposed by Na et al [14]

The main objective of this paper is to proposes a controlalgorithm to generate the force feedback torque for driversteering feel in the vehicle SBW system The subsystem ofSBW system which is steering wheel and front axle system ismodelled and the control algorithm is explained To verify theeffectiveness of the proposed algorithm the hardware in theloop (HIL) is presented and interfaced using a Matlab XPCtarget toolbox The result was then is compared with electricpower steering (EPS) system [15]

2 The Modelling of Steer byWire (SBW) System

The SBW system is divided into two subsystems that consistof steering wheel and front axle system The system diagramof subsystem is shown in Figure 2

Table 1 Steering wheel system parameter

Parameter Description Value Unit1198771 Motor resistance 564 ohm1198711 Motor inductance 0017 henry119870119904119898

Motor constant 0024 Nm1198691198981 Motor inertia 00036 kgm2

1198871198981 Motor damping 00068 Nm(rads)1198961199041 Lumped torque stiffness 0025 Nm

1198811199041 Voltage source mdash Volt

21 Steering Wheel Model The main purpose of steeringwheel motor is to generate the steering feedback torque fordriver steering feel Figure 2(a) shows the system diagramfor the steering wheel system The input to the system is thetotal feedback torque (120591total feedback) and the output is the ratechange of steering wheel motor angular displacement ( 120575

1198981)the motor angular displacement (120575

1198981) and the current ofsteering wheel motor (119894

1198861) The parameters of the steeringwheel system are illustrated in Table 1

The mathematical equations of the steering wheel systemare written as follows

The steering motor angular displacement is

1205751198981 = minus

11988711989811198691198981

1205751198981 +

1198961199041

1198691198981

1198941198861 (1)

and the steering motor current is

1198941198861 = minus

11987711198711

1198941198861 +

119896119904119898

1198711

1205751198981 +

1198811199041

1198711 (2)

International Journal of Vehicular Technology 3

120591totalfeedback

ks1

120575sw

bm1

120575m1

Jm1

L1

R1

Vs1

ia1

(a)

Vs2

L2

R2

ia2

bm2

120575m2

Jm2

ks2

brackf

Mrackf

yrackfklf klfBkpf Bkpf

Jm2 Jm2

(b)

Figure 2 System diagram (a) steering wheel and (b) front axle system [15]

Consequently the state equation of steering wheel system isgiven as

119904119898

= 119860119904119898

119909119904119898

+119861119904119898

119906119904119898

119910119904119898

= 119862119904119898

119909119904119898

119909119904119898

= [ 1205751198981 1205751198981 1198941198861]

(3)

And 119906119904119898

is considered the input of the steering wheel motorand the parameter states are

119860119904119898

=

[[[[[[

[

minus(11988711989811198691198981

) 01198961199041

1198691198981

1 0 0

minus(119896119904119898

1198711) 0 minus(

11987711198711

)

]]]]]]

]

119861119904119898

=

[[[[

[

0

0

11198711

]]]]

]

119906119904119898

= 120591total feedback = 1198811199041

(4)

22 Front Wheel System The function of the front axle sys-tem is to ensure the front tire angle follows the steering wheelangle command according to the steering ratio [17]The frontaxle is composed of a front axle DC motor rack and pinionand tire model The system diagram of the front axle systemand the subsystem block diagram are shown in Figures 2(b)and 3 respectively The input to the system is the steeringwheel angle (120575

119904119908) while the front tire angle (120575

119891) is considered

the output The parameters of the front axle system areapproximated assumption that are illustrated in Table 2

Table 2 Front axle system parameter [15]




119861rack Rack damping coefficient 0015 henry119872rack Rack lumped mass 0032 Nm119896119897119891

Rack linkage stiffness 000062 kgm2

119903119871

Offset of king pin axis 000036 m119903119901

Pinion gear radius 0025 m119861119896119901

King pin damping coefficient 000062 kgm2

119868119891

Lumped front wheel inertia 000036 kgm2

1198961199042 Lumped torque stiffness 0025 Nm

120575sw 120575m2 120575fyrack

Front axle system

Front axleDC motor

Rack andpinionsystem

Front tiredynamics

Figure 3 Block diagram of front axle subsystem

The mathematical equation of the front axle DC motor iswritten as follows

The front axle motor angular displacement is

1205751198982 = minus

11988711989821198691198982

1205751198982 +

1198961199042

1198691198982

1198941198862 (5)


and the front axle motor current is

1198941198862 = minus

11987721198712

1198941198862 +

119896119891119898

1198712

1205751198982 +

1198811199042

1198712 (6)

Consequently the state equations of the front axle motor aregiven as

119891119898

= 119860119891119898

119909119891119898

+119861119891119898

119906119891119898

119910119891119898

= 119862119891119898

119909119891119898

119909119891119898

= [ 1205751198982 1205751198982 1198941198862]

(7)

And 119906119891119898

is the input to the front axle motor while outputis the rate change of front axle motor angular displacement( 1205751198982) the front axle motor angular displacement (120575

1198982) andthe current of front axle motor (119894

1198862)The parameter states are written as follows

119860119891119898

=

[[[[[[[

[

minus(11988711989821198691198982

) 01198961199042

1198691198982

1 0 0

minus(

119896119891119898

1198712) 0 minus(

11987721198712

)

]]]]]]]

]

119861119891119898

=

[[[[

[

0

0

11198712

]]]]

]

119906119891119898

= 120575119904119908

= 1198811199042

(8)

The rack and pinion system is

119910rack =1

119872rack[(minus

2119896119897119891119910rack

1199032119871

)minus(1198961199042119910rack1199032119901

)

minus119861rack119891 119910rack +(11989611990421205751198982119903119901

)]

(9)

And 119906119910rack is considered the input of the rack and pinion

system and the output is the rack displacement (119910rack) andthe parameter states are as follows

119860119910rack

=[[[

[

0 1

minus[(

2119896119897119891

119872rack1199032119871

) + (1198961199042

119872rack1199032119901

)] minus(119861rack119872rack

)

]]]

]

119861119910rack =

[[

[

0

(1198961199042

119872rack119903119901)

]]

]

119906119910rack = 120575

1198982

(10)

Fyr

lr lf

r

120572r

120573

Fyf120572f

120575f

Figure 4 Single track-linear vehicle model

and the front tire dynamic is

120575119891=

1119868119891

[(minus119896119897119891120575119891+(

119896119897119891119910rack

119903119871

)minus119861119896119901

120575119891)] (11)

and 119906tire is considered the input of the front tire dynamicTheoutput is the front tire angle (120575

119891) and the parameter state is

119860 tire =[[

[

0 1

minus(

119896119897119891

119868119891

) minus(

119861119896119901

119868119891

)

]]

]

119861tire =[[

[

0

(

119896119897119891

119868119891119903119871

)

]]

]

119906tire = 119910rack

(12)

23 Single Track-Linear Vehicle Model The stability charac-teristics of a steer-by-wire vehicle are affected by the influenceof front tires via the feedback of the vehicle dynamic responseThus it is necessary to develop a single track-linear vehiclemodel as mentioned by author [16 18ndash21] in simulation andexperimental validationThe single track linear vehiclemodelis shown in Figure 4 In this paper the aim is to model thelinear vehicle in order to generate the estimation of self align-ing torque (120591

119886) This acts as the disturbance input to the front

axle system and assures the road contact with front tire Thedynamics of single track-linear vehicle model is representedby bicycle model where the states contain yaw rate (119903) andvehicle body slip angle (120573)

The following assumptions are considered for normaldriving maneuverer These assumptions could simplify thevehicle model [18]

(i) friction force in the 119909-direction is negligible

(ii) vehicle speed is constant

(iii) angle for right and left tire is approximately the same


With the aforementioned assumptions the derived equationsof the motion of yaw rate (119903) and vehicle body slip angle (120573)are shown in (13) as follows

119903 = [

[

(1198972119891119862119891+ 119897

2119903119862119903)

119868119904119881

]

]

119903+[

[

(1198972119903119862119903minus 119897

2119891119862119891)

119868119904

]

]

120573

+[

(119897119891119862119891)

119868119904

]120575119891

120573 = [1+(119897119903119862119903minus 119897119891119862119891)

1198981198812 ] 119903 minus[

(119862119891+ 119862119903)

119898119881]120573

+[

119862119891

119898119881]120575119891

(13)

In the linear tire region lateral force at the front and rear isrelated to slip angle by cornering stiffness of the front and reartires written as follows

119865119910119891

= minus119862119891120572119891

119865119910119903

= minus119862119903120572119903

(14)

At a larger slip angle the relation between lateral force andslip angle becomes nonlinear By assuming a smaller slipangle approximation the slip angle is written in terms ofvehicle body slip angle and yaw rate that are considefed asfollows

120572119891= (120573+

119897119891

119881119903minus 120575119891)

120572119903= (120573+

119897119903

119881119903minus 120575119903)

(15)

Rewriting (13) into state space form we haveV119898 = 119860V119898119909V119898 +119861V119898119906V119898

119910V119898 = 119862V119898119909V119898

119909V119898 = [119903 120573]

(16)

And 119906V119898 is considered the input to the linear vehicle modelwhile the yaw rate (119903) and vehicle body slip angle (120573) arethe output of the linear vehicle model The parameter stateis written as follows119860V119898

=

[[[[[[

[

(

(1198712119891119862119891+ 119871

2119903119862119903)

119868119904119881

) minus

(119871119903119862119903minus 119871119891119862119891)

119868119904

1 + (

(119871119903119862119903minus 119871119891119862119891)

1198981198812 ) minus

(119862119891+ 119862119903)

119898119881

]]]]]]

]

119861V119898 =[[[

[

119871119891119862119891

119868119904

119862119891

119898119881

]]]

]

119906V119898 = 120575119891

(17)

The parameter of a linear vehicle model directly can bemeasured but some parameters need to be estimated Thereare several methods to estimate themodel parameter [22 23]A method based on Sahoo et al [22] is used to estimate themodel parameters with assumption that the vehicle mass isdistributed to front and rear of each tire The total of vehiclemass (119898) that is based on the front (119898

119891) and rear (119898

119903) tire

masses is written as follows

119898 = 119898119891+119898119903

(18)

when

119898119891= 119898119891119897+119898119891119903

119898119903= 119898119903119897+119898119903119903

(19)

where 119898119891119897 119898119891119903 119898119903119897 and 119898

119903119903are the masses of the vehicle

at front left front right rear left and rear right respectivelyThe parameter length of wheel base (119897) which is sum of lengthfrom a center of front tire 119897

119891and rear tire 119897

119903to COG of vehicle

body is written as follows

119897 = 119897119891+ 119897119903 (20)

while the inertia of vehicle 119868119904that is approximated by assum-

ing the vehicle as two point masses joined with mass-lessroad [22] is written as follows

119868119904= 1198981198911198972119891+1198981199031198972119903 (21)

The front cornering stiffness 119862119891and rear cornering stiffness

119862119903parameters are written in (22) by assuming that the type

of radial tire is used and cornering stiffness per degree of slipangle is approximately 16-17 of the load on the tire [22]Consider

119862119891= 119898119891lowast 119892 lowast 0165 (Ndeg)


(22)

The parameters of the linear vehicle model are illustrated inTable 3

3 Force Feedback Torque EstimationControl Algorithm

It has been known that the force feedback torque for driversteering feel should be created artificially due to the elimina-tion of mechanical column shaft in SBW system

Moreover the proportion of the steering feel obtainedshould be similar to conventional steering system For thisreason the steering wheel in SBW system that is equippedwith the motor actuator is used to generate the steeringfeel by controlling the total feedback torque (120591total feedback)A schematic block diagram of the proposed force feedbacktorque control is shown in Figure 5

Based on Figure 5 the total force feedback torque consistsof the torque of front axle motor (120591

119891119898) torque on steering

wheel motor (120591119904119898) and compensation torque which is the

inertia (120591inertia) and damping torque (120591damp) Meanwhile the


+

+

+

minus

minus

Wheel synchronization

120575sw

120575sw

120591a

Frontaxle

system

LQRcontroller

LQRcontroller

120575m2

120575m2

120575f

ia2

120573

r

Linearvehiclemodel

Force feedback torque

120591map

120591fm

120591sm

120591damp

120591inertia

VGain

scheduling

kfm

kfeelsum

120591total feedback Steeringwheelsystem


Steeringwheel

120575m1

120575m1

ia1

ksm

Estimation selfaligning torque

Torque(RMS)

Figure 5 Overview of force feedback torque control algorithm for SBW system

Table 3 Linear vehicle model [16]

Parameter Description Value Unit119862119891 Front cornering stiffness 40000 Nrad

119862119903 Rear cornering stiffness 35000 Nrad

119897119891

Length from center frontwheel to (COG) vehicle 14 m

119897119903

Length from center rearwheel to COG vehicle 1 m

119898 Mass of the vehicle 1535 kg119868119904 Inertia of vehicle 2149 kgm2

119881 Speed of vehicle mdash kmh119865119910119891 Front tire lateral force mdash Nm

119865119910119903 Rear tire lateral force mdash Nm

120572119891 Front tire slip angle mdash Nm

120572119903 Rear tire slip angle mdash Nm

torque map is based on the function of the steering wheelangle and vehicle speed is added to the total feedback torqueMoreover a steering feel gain (119896feel) is adapted based on thefunction of steering wheel angle and vehicle speed to varythe feedback torque In order to control the feedback torquethe gain scheduling with LQR controller is used To showthe influence of the tire on the road surface the self aligningtorque (120591

119886) acts as input disturbance to the front axle system

as follows

120591119886= minus119862

119891(119905119901+ 119905119898) [120573+

119897119891119903

119881minus 120575119891]120583 (23)

where 120583 is coefficient for road dry condition pneumatic trail(119905119901) and mechanical trail (119905

119898)

On the other hand any change of the road surface couldchange the feedback torque magnitude of the front axlemotor Furthermore the LQR controller of the front axle sys-tem is used to synchronize the front tire angle (120575

119891) with driver

input steering wheel angle (120575119904119908) by controlling the angle of

the front axle motor (1205751198982) in accordance with the steering

ratioThus based on the proposed control algorithm the total

force feedback torque to the steering wheel system is writtenas follows

120591total feedback = ([(radicmean (120591119904119898

+ 120591119891119898

+ 120591map))]

+ 120591inertia + 120591damp) 119896feel

(24)

Author [9 10] has generated and discussed the force feed-back torque using the torque map conceptThe torque map isbased on the function of the steering wheel angle and vehiclespeed parameter The feedback torque is determined by twocontrol parameters (119896

120573) for the vehicle speed and (119896

120572) for the

steering wheel angle functionThe torque based on the function of vehicle speed is given

as follows [9]

1205911 = 1198961205731199092(13119909minus

12119881max)+119879in (25)


0 2 4 6 8 10minus40

minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

torq

ue (N

m)

70kmh75kmh

50kmh40kmh30kmh20kmh10kmh

80kmh

60kmh

Figure 6 Steering torque based on torque map at different speed

where (119909) is initial velocity and (119881max) is maximum velocitywhile the torque based on a function of steering wheel angleis written as follows [9]

1205912 = 119896120572radic1003816100381610038161003816120575119904119908

1003816100381610038161003816 sgn 120575119904119908 (26)

Based on the torque map concept the results of steeringtorque at different vehicle speed are shown in Figure 6 whenthe input steering wheel angle is a double lane changemanoeuvreThe torque increased at high speed anddecreasedat low speed [9 24] By varying the two control parametersthe steering reactive torque changes at different torque mag-nitude However the feedback torque based on the torquemap concept did not create the artificial steering feel dueto the fact that no element of road contact such as vehicledynamic responses are feedback to the torque map modelThus driver not sense realistic driver steering feel

Thus for this reason the front axle motor torque andsteering wheel motor torque are added to the torque mapThese ensure that the driver senses the feedback torque fromroad contact The front axle motor torque is chosen due toits proportion to the road surface The reaction torque of theroad surface gives the effect to the rack and pinion systemand it connects to the front axle DC motor Thus the frontaxle motor torque would always be proportional to the roadsurface Any changes in road surface will influence the frontaxle motor torque In order to measure the torque at the frontaxle motor the direct currentmeasurement technique is usedto estimate the torque

The direct relationship between torque and current of amotor can be defined [25]Thus then front axlemotor torque(120591119891119898

) that consists of the front axle motor constant (119896119891119898

) andthe motor current (119894

1198862) is written as follows

120591119891119898

= 1198941198862119896119891119898 (27)

and the corresponding steeringwheelmotor torque (120591119904119898) that

consists of the steering wheel motor constant (119896119904119898) and the

motor current (1198941198861) is written as follows

120591119904119898

= 1198941198861119896119904119898 (28)

0 2 4 6 8 10Time (s)

Mot

or to

rque

(Nm

)

Front axle motor torque

Steering wheel motor torque6

4

2

0

minus2

minus4

minus6

Figure 7 Steering wheel and front axle motor torque at 80 kmh

Figure 7 shows the front axle motor and steering wheelmotor torque response when the input is a double lanechangemanoeuvreThe results show that the front axlemotorgives a high torque This is due to the fact that the inputdisturbance torque between the tire and road surface which isthe self aligning torque has an effect on the front axle motorIncreasing the vehicle speedwill increase the front axlemotortorque On the other hand the magnitude of steering wheelmotor torque is decreased due to the elimination of mechan-ical column shaft and is not affected by the self aligningtorque

The phase compensation torque consists of the inertiatorque and damping torque potential to recreate the artificialsteering feel of the conventional steering system Moreoverit is intended to adjust the steering feel reduce the vibrationand stabilize the system Due to this fact the element of com-pensation torque is taken in order to improve the feedbacktorque for a driver steering feel and to stabilize the system

The damping torque (120591damp) which is the rate change ofthe steering wheel motor angle ( 120575

1198981) and the damping gain(119896damp) is written as follows

120591damp = 1205751198981119896damp (29)

The inertia torque (120591inertia) that is the acceleration of thesteering wheel motor angle ( 120575

1198981) and the inertia gain (119896inertia)is written as follows

120591inertia = 1205751198981119896inertia (30)

The inertia and damping torque responses are shown inFigure 8 when the input steering wheel angle is a double lanechange manoeuvre It is obtained that the damping torquegives a smooth signal and reduces the vibration Meanwhilethe inertia torque gives high magnitude Thus the combina-tion between the inertia torque and damping torque not onlyprovides an average of steering feel but is also able to stabilizethe system at the same time Figure 9 shows the feedback


0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Torq

ue (N

m)

Inertia torque Damping torque

Figure 8 Inertia and damping torque

0 2 4 6 8 10Time (s)

Forc

e fee

dbac

k to

rque

(Nm

)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

10kmh

50kmh100 kmh120 kmh

135kmh

Figure 9 Proposed force feedback torque response at differentvehicle speed

torque response based on (24) The torque is increasedaccording to the vehicle speed The higher vehicle speed willincrease the feedback torque and vice versa due to the samefact that is proposed by torque map

31 Linear Quadratic Regulator (LQR) Controller The LQRcontroller provides the best possible performance to controland stabilize the system by changing the location of the polesof the system to the optimal location for a time responseovershoot and steady stateThis is done by designing the statefeedback control119870 thatminimized cost function 119869 to stabilizethe system In this paper the LQR controller is used firstlyto control the front axle motor angle for the wheel synchro-nization and secondly to control the steering wheel motorfor a feedback torque

The wheel synchronization or directional control is abasic characteristic for steering function where a front tire

+

minus

sum

k1

k2

k3

x1

x2

x3

Plantr(t)

LQR controller

Figure 10 Basic control block diagram of LQR controller

angle should follow driver input steering wheel angle accord-ing to the steering ratio This is done by controlling theangle of the front axle motor In the LQR control schemesa feedback gain matrix is designed to achieve some compro-mise between the use of control effort the magnitude andthe speed of response that will guarantee a stable systemFigure 10 shows the control block diagram of the LQRcontroller

The optimal LQRproblem is often definedmore generallyand consists of finding controller transfer matrix that mini-mizes the cost function 119869 that is written as follows

119869 = int

prop

0(119909119879

119876119909+119906119879

119877119906) 119889119905 (31)

where 119909119879 and119880119879 respectively represent the transpose of the

state and input vector The 119876 and 119877 are positive definite (orpositive-semi definite) real symmetric matrix The 119876 and 119877

are usually chosen to be diagonal matrix written as follows

119876119894119894=

1maximum acceptable value of 1199092

119894

119877119895119895

=1

maximum acceptable value of 1199062119895

(32)

where

119894 = 120576 1 2 ℓ

119895 = 120576 1 2 119895 (33)

In essence Brysonrsquos rule scales the variables that appear in 119869 sothat the maximum acceptable value for each term is oneThisis especially important when the units used for the differentcomponents of 119906 and 119909 make the values for these variablesnumerically very different from each other

Assume that the steering ratio is 15 1 and the gains ofthe LQR controller are [01 098 0008] Figure 11 shows aresponse of the front axle system when the input steeringwheel angle is a step function as shown in Figure 11(a)

The results show that the angle of the front axle motorhas a fast response compared to the EPS steering system


0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Stee

ring

whe

el an

gle (

deg)

(a) Steering wheel angle

0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Mot

orc

olum

n an

gle (

deg)

EPS steeringmdashcolumn shaft angle

SBW systemmdashmotor angle

(b) Front axle motor angle

0 2 4 6 8 10

Rack

disp

lace

men

t (m

)

SBW system

EPS steering

Time (s)

18

16

14

12

10

8

6

4

2

0

times10minus3

(c) Rack displacement

0 2 4 6 8 100

02

04

06

08

1

12

14Fr

ont t

ire an

gle (

deg)

SBW system

EPS steering

Time (s)

(d) Front tire angle

Figure 11 Front axle system response for wheel synchronization

Moreover the LQR controller is able to reduce the delaycaused by the self aligning torque created from the contactbetween the tire and road surfaces This not only improvedthe vehicle stability but also ensured that the driver has amore confident level during manoeuvre Compared to theEPS steering system the delay caused by mechanical columnshaft connected to the steering wheel system Furthermore itcan be seen that the front tire angle is at almost fairly close to1∘ as shown in Figure 11(d) However it has small chatteringdue to the self aligning torque However with wide rangeadjustment gains of the LQR controller the steering responsecould be improved

32 Gain Scheduling (GS) with LQR Controller In certainsituations the dynamic behaviour of the process changed inaccordance with the conditions of the process This situation

could affect the stability of the system if not to control prop-erly Thus it is possible to change the gains of the controllerby monitoring the operating conditions of the process tohave a stable system The gain scheduling (GS) techniqueis used to change the gain of the LQR controller in order tocontrol the feedback torque and the steering feel gain (119896feel)is used to increase and decrease the torque It is important toincrease the feedback torque at high speed for steering stabil-ity and to decrease it in low speed especially during parkingto improve vehicle manoeuvre [9] This is based on the steer-ingwheel angle and vehicle speed function in order to achievethe feedback torque for the real driver steering feel

The relationship between a gain scheduling with LQRcontroller is shown in Table 4 The vehicle speed is dividedinto 3 categories at low speed (0ndash30 kmh) medium speed(31ndash100 kmh) and high speed (101ndash120 kmh) The maxi-mum vehicle speed is limited to 120 kmhThe steering wheel


0 2 4 6 8 10minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

Time (s)

Stee

ring

whe

el an

gle (

deg)

(a) Input steering wheel angle

0 1 2 3 4 5 6 7 8 9 10minus15

minus10

minus5

0

5

10

Time (s)

Stee

ring

torq

ue (N

m) LQR

LQR + GS

Reference

(b) 120583 = 1

0 1 2 3 4 5 6 7 8 9 10

minus15

minus10

minus5

0

5

10

15

Stee

ring

torq

ue (N

m) LQR

Reference

Time (s)

LQR + GS

(c) 120583 = 14

0 1 2 3 4 5 6 7 8 9 10minus20

minus15

minus10

minus5

0

5

10

15

20

Stee

ring

torq

ue (N

m) LQR LQR + GS

Reference

Time (s)

(d) 120583 = 17

Figure 12 Comparison of torque response of LQR and LQR + GS controller at different 120583

Table 4 The gains of LQR controller and steering feel

119881 (kmh) 120575119904119908

(degree) 1198961 1198962 1198963 119896feel

(0ndash30) (plusmn180∘ lt 120575119904119908

lt plusmn405∘) 003 065 0001 014(31ndash100) (plusmn46∘ lt 120575

119904119908lt plusmn179∘) 003 084 0001 060

(101ndash120) 120575119904119908

le +45∘ or 120575119904119908

le minus45∘ 005 095 0001 095

angle is also divided into 3 categories according to vehiclespeed condition The notation ldquo+rdquo means that the driverturned the steering wheel clockwise and notation ldquominusrdquo is usedfor counter clockwise in which the maximum steering wheelturn is plusmn405∘

The gains of the LQR controller are defined using Brysonrsquosrule method and the steering feel gain is defined usingintuitive and has a range from 01 to 1 This range has beendefined for various speeds 10 kmh 80 kmh and 120 kmhafter comparing with EPS steering system [15] For exampleif the driver turns a steering wheel between (plusmn180∘ lt 120575

119904119908lt

plusmn405∘) and vehicle speed is 10 kmh the total feedback torque

is multiplied by steering feel gain 119896feel = 014 Thus thefeedback torque is decreased which results in making thedriver feel it easier turning the steering wheel and improvesvehicle manoeuvre The feedback torque is regulated by LQRcontroller when the gains are 1198961 = 003 1198962 = 065 and1198963 = 0001 The gains are the optimum that has been assuredby providing a better torque control based on vehicle speedand steering wheel angle function

Comparing torque response between LQR and LQR +GScontroller for different coefficient (120583) is shown in Figure 12when the input steering wheel angle is a double lane changemanoeuvre as shown in Figure 12(a) The vehicle speed isset to be 80 kmh Based on results obtained the LQR + GStechnique offers an improvement 90 and the curve trend isalmost similar to reference torque compared to the LQR con-troller This is because the gains of LQR controller changedbased on the steering wheel angle and vehicle speed param-eter which is able to reject the uncertainty torque of a roadcondition Meanwhile with the fixed gains of the LQR con-troller it has an excessive torque that can cause the system tobe unstable The RMS torque values are illustrated in Table 5


Table 5 Comparison of RMS torque values of LQR and LQR + GScontroller

Reference LQR LQR + GS120583 = 1 56361 50795 55450120583 = 14 61218 68339 57243120583 = 17 66184 72888 62080

minus50 0 50minus15

minus10

minus5

0

5

10

15

Steering angle (deg)

Stee

ring

torq

ue (N

m) Feel gain = 5

Feel gain = 01Feel gain = 05

Feel gain = 1

(a) Different steering feel gain at 80 kmh

minus50 minus40 minus30 minus20 minus10 0 10 20 30 40 50

minus15

minus10

minus5

0

5

10

15

Steering wheel angle (deg)

Stee

ring

torq

ue (N

m)

80kmh kfeel = 060

120 kmh kfeel = 095

10kmh kfeel = 014

(b) Different steering feel gain at various speed

Figure 13 Steering feel gains response at various vehicle speed

Figure 13(a) shows the steering torque with respect tosteering wheel angle when different steering feel gain is usedat various vehicle speeds It is observed that when the steeringfeel gain is increased at maximum range which is 1 thesteering torque will increase and driver will sense stiffer onthe steering wheel at high speed manoeuvre Meanwhilewhen decreasing the steering feel gain this will result inreducing the steering torqueThus the driver will sense softer

Target monitor

Host PC

Cross over cableConnector block

PCI 6221

Power supplyCurrent sensor

DC motor driver

Figure 14 Steering wheel system hardware overview

during turning the steering wheel at the low speed manoeu-vre However when the steering feel gain is 5 which exceedsits maximum limit the steering torque becomes unstableFigure 13(b) shows the steering feel gains at various speedsAt high speed of 120 kmh the steering feel gain is increasedand this will increase the steering torque for steering stabilityMeanwhile at low speed the steering feel gain is decreasedwhich will help improve vehicle manoeuvre especially duringparking Based on the proposed gain scheduling with theLQR controller not only does it provide better control on thesteering torque but also it is optional for a designer to have awide range adjustment to vary the steering torque for a betterdriver steering feel and to improve vehicle manoeuvre

4 Hardware in the Loop (HIL) and Result

For hardware in the loop (HIL) setup the front axle systemand linear vehicle model are simulated on the host computerThe steering wheel system is replaced by HIL mechanismThe position of the steering wheel motor is measured usinga rotary encoder with 500 pulses per revolution To measurethe steering wheel torque the current sensor is connectedin series with the DC motor driver The steering wheel DCmotor has a torque 129Nm with 100 rpm The single tracklinear vehicle model is used to generate the estimation selfaligning torque as element to the feedback torque and distur-bance to the front axle system The HIL system is executedunder 1ms sampling time and interfaced using Matlab-XPCtarget toolbox configuration as shown in Figures 14 and 15

The assumptions through the experiment are listed asfollows

(i) the vehicle cruises at constant speed(ii) the condition of dry asphalt road (120583 = 085)

The experiments are done under high medium and lowspeed manoeuvre [26] The same input steering wheel anglebetween simulation and experiment is given Therefore theresult obtained from real time control is compared with theelectronic power steering (EPS) system [15]

41 Motor Model Validation for Steering Wheel SystemAlthough the model of steering wheel system has been


Stee

ring

whe

el sy

stem

DC motor

Current

Encoder

16 bit card PCI 6221

Analogoutput

Analoginput

Counterchannel

TargetPC

Monitortarget

PC

Crossover cable

Host PC

Front axle systemand

linear vehicle model

Hardware part Simulation part

Figure 15 Block diagram of the steering wheel-XPC target interfaced

Steering wheel model

120575m1

120575m1

ia1

r(t)

Figure 16 Block diagrammotormodel validation for steeringwheelsystem

derived the model validation is necessary to ensure thesystem is fairly able to adequate for real time applicationThis section describes the motor model validation of steeringwheel system The block diagram is shown in Figure 16

The input signal is 119903(119905) and the output is rate change ofmotor ( 120575

1198981) motor position (1205751198981) and the motor current

( 1198941198981) The measured output response is then used and com-

pared with simulation to estimate the parameter of the steer-ing wheel model using the Matlab tool software The mea-sured output data are taken based on the open loop systemwhen the input to the system is sinusoidal signal withamplitude of plusmn45∘ for 10 sec The Gaussian method is usedto estimate the parameters of the steering wheel motorThe comparison between simulation and measured outputis shown in Figure 17 It is obtained that the output of thesimulation is almost identical to the measured output How-ever small difference errors occur due to the small parametricuncertainties that have not been modelled The parameterestimation value is illustrated in Table 6

42 Noise Filtering Both analog and digital devices have atrait of noise or unwanted features that have effect on thesystem performance such as electromagnetic interferenceThe noise could be either random or white noise Attenuationof this noise is often as a primary goal in control systemapplication and in particular when controlling the processsystem The average value of noise typically is zero whichwill give misreading information to the process and it wouldnot be possible to control the process In order to reduce thenoise inference filtering technique is used A filter is used toremove unwanted noise It removes some noise frequenciesto suppress interfacing signal and reduce background noise

Table 6 Parameter estimation for DCmotor steering wheel system

Parameter Value Estimation value Unit1198771 4405 564 ohm1198711 0010 0017 henry119870119904119898

1459 0024 Nm1198691198981 0002 00036 (kgm2)1198871198981 0004 00068 Nm(rads)1198961199041 165 0025 Nm

There are many types of filtering techniques such as low passfilter that has been used in this study The low pass filter isused to filter out the interference noise from the output of thecurrent sensor

Figure 18 shows the comparison of the output responsefor a current sensor with and without using filters Withouta filter the current sensor has high amplitude interferencenoise However with low pass filter under the frequency of5Hz the interference noise is reduced and the fluctuations areremoved Thus this provides a smoother output response

43 Effect on Compensation Torque A steering torque com-parison without and with compensation torque is shown inFigure 19The results for without compensation torque showsthat the steering torque response curve is far away fromEPS steering system with different amplitude as shown inFigure 19(a) This happens due to less of derivative reactiontorque from the steering wheel motor Figure 19(b) showssteering torque response with compensation torque

It is observed that by adding the additional compensationtorque the steering torque response curve trends fairly closeto EPS steering system Thus it helps to improve the driversteering feel during manoeuvre and stabilize the systemHowever with the wide range adjustment gains of the com-pensation torque it could improve the steering torqueresponse

44 Medium Speed Manoeuvre The experimental steeringtorque results at medium speed manoeuvre are shown inFigure 20(b) when the steering wheel angle is plusmn100∘ as shown


0 2 4 6 8 10minus50

0

50

Time (s)

Rate

chan

ge m

otor

pos

ition

(deg

s)

MeasurementSimulation

(a) Rate change of motor position

0 2 4 6 8 100

10

20

30

40

50

60

Time (s)

Mot

or p

ositi

on (d

eg)

Measurement

Simulation

(b) Position of the motor

0 2 4 6 8 10minus01

minus005

0

005

01

015

Mot

or cu

rren

t (A

)


Time (s)

(c) Current of the motor

Figure 17 Motor model validation comparison between simulation and measurement

With filter Without filter

Time (s)

Curr

ent (

A)

008

006

004

002

0

minus002

minus004

minus006

minus0081 15 2 25 3 35 4 45 5 55

Figure 18 Noise filtering using low pass filter

in Figure 20(a) From the results the experimental steeringtorque response is almost identical to the EPS steering systemHowever it has small different torque amplitudes These

occur due to the fact that mechanism or friction from themechanical gearbox motor is not modelled in proposedcontrol algorithm


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10

(a) Without compensation torque

Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10

(b) With compensation torque

Figure 19 Steering torque influence on compensation torque

minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10

(a) Steering wheel angle at 80 kmh

Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10

(b) Steering torque estimation at 80 kmh

Figure 20 Steering torque estimation and steering wheel angle response at 80 kmh

45 High Speed Manoeuvre At high speed manoeuvre theinput steering wheel angle that is more than plusmn45∘ is very dan-gerous [12] Therefore in this experiment the input steeringwheel angle is less than plusmn45∘ as shown in Figure 21(a) Basedon the results shown in Figures 21(b) and 21(c) the experi-mental steering torque is obtained fairly similar to the EPSsteering system Although the steering wheel angle is at smallangles the influence of vehicle speed cause the steering torqueis increased Moreover at higher speed the vehicle has moreunder steer propensity [9] This increased the self aligningtorque in proportional high torque at front axle motorThusthe driver will sense stiffer on the steering wheel duringmanoeuvre

In general the centering of the steering wheel perfor-mance or steering wheel returnability is better when thesteering torque gradient is large and the hysteresis is small [9]Based on this fact the result is shown in Figure 21(c) whereby

the hysteresis of the steering wheel returnability based onexperimental result is smaller compared to EPS steeringsystem In addition the steering torque gradient is larger thanEPS steering torque Therefore it is considered that the pro-posed feedback torque algorithmnot only achieved a steeringfeel but also improved the steering wheel returnability

46 Lower Speed Manoeuvre The steering torque results atlow speed manoeuvre are shown in Figures 22(b) and 22(c)when the input steering wheel is as shown in Figure 22(a)The vehicle cruised at constant speed of 10 kmh

The experimental steering torque is almost comparableto EPS torque but the amplitude is decreases The torque isdecreased due to the fact that the vehicle speed is reducedwhich is effect on reducing the demand to the total feedbacktorque Moreover the large turning of the steering wheelincreases the backlash of the motor which then contributes


2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)

EPS steeringSimulationExperiment

10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering

SimulationExperiment10

15

5

0

minus5

minus10

minus15minus20 minus10 0 10 20 30 40


(c) Steering torque estimation against steering wheel angle at 120 kmh

Figure 21 Steering torque estimation response at 120 kmh

to the decrease of the motor torque Thus driver will sensesofter during steering the wheel during maneuver Howeverit has small different torque against EPS steering Wide rangeadjustment of gains in proposed control algorithm may helpimprove the steering torque response

3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering

SimulationExperiment

10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150



5 Conclusion and Future Work

The proposed force feedback torque estimation and controlalgorithm have been described The proposed control algo-rithm is considered as an effort to generate the feedback


torque for driver steering feel in the vehicle SBW systemThe mathematical model of SBW subsystem consists ofsteering wheel and front axle systems that are modelledThe effectiveness of the control algorithm is verified throughthe experimental hardware in the loop (HIL) interfacedwith Matlab XPC target toolbox software According to theexperimental results the proposed control algorithm is ableto generate the feedback torque and the driver is able to sensesteering feel similar to that obtained in EPS steering systemThe LQR controller with gain scheduling based on steeringwheel angle and vehicle speed function provides better torquecontrol that allows rejection of the uncertainty torque froma road condition Furthermore the steering feel gain is ableto increase and lower the steering torque with improvedsteering stability at high speed and it improved the vehiclemanoeuvre at low speed It is also found that compensationtorque is able to improve the feedback torque and to stabilizethe system However it has small different torque magnitudethat occurs due to the backlash of steering wheel motor anduncertainty disturbance of mechanical properties Howeverwith a wide range adjustment of the gains on the proposedcontrol algorithm it may improve and provide realisticsteering torque for better driver steering feel

In future work the proposed control algorithm will betested in real vehicle in order to have more realistic steeringtorque for further investigation and analysis

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is fully supported by the Ministry of Higher Edu-cation Malaysia and University Technology Malaysia underFRGS (vote 4F370) and Research University Grant (vote00G64) This work is also supported by Proton HoldingBerhad

References

[1] Y Yao ldquoVehicle steer-by-wire system controlrdquo SAE TechnicalPaper 2006-01-1175 2006

[2] E A Kumar D Dinesh and N Kamble ldquoAn overview of activefront steering systemrdquo International Journal of Scientific ampEngineering Research vol 3 no 6 2012

[3] S M H Fahami H Zamzuri S A Mazlan and N B Zulkar-nain ldquoThe design of vehicle active front steering based on steerby wire systemrdquo Advanced Science Letters vol 19 no 1 pp 61ndash65 2013

[4] S M H Fahami H Zamzuri S A Mazlan and S A SaruchildquoThe variable steering ratio for vehicle steer by wire systemusing hyperbolic tangent methodrdquo Applied Mechanics andMaterials vol 575 pp 781ndash784 2014

[5] T Kaufmann S Milsap B Murray and J Petrowski ldquoDevelop-ment experience with steer by wirerdquo in Proceedings of the SAEInternational Congress and Exhibition SAE 2001-01-2479 2001

[6] S Amberkare F Bolourchi J Demerly and S Millsap ldquoAcontrol system methodology for steer by wire systemsrdquo SAETechnical Paper 2004-01-1106 2004

[7] A Baviskar J R Wagner D M Dawson D Braganza andP Setlur ldquoAn adjustable steer-by-wire haptic-interface trackingcontroller for ground vehiclesrdquo IEEE Transactions on VehicularTechnology vol 58 no 2 pp 546ndash554 2009

[8] M Segawa S Kimura T Kada and S Nakona ldquoA study of reac-tive torque control for steer bywire systemrdquo inProceedings of theInternational Symposium on Advanced Vehicle Control (AVECrsquo02) pp 653ndash658 Hiroshima Japan September 2002

[9] S W Oh H C Chae S C Yun and C S Han ldquoThe design ofa controller for the steer-by-wire systemrdquo JSME InternationalJournal Series C Mechanical Systems Machine Elements andManufacturing vol 47 no 3 pp 896ndash907 2004

[10] C J Kim J H Jang S K Oh J Y Lee and J K HedrickldquoDevelopment of a control algorithm for a rack-actuating steer-by-wire system using road information feedbackrdquo Proceedingsof the Institution of Mechanical Engineers Part D Journal ofAutomobile Engineering vol 222 no 9 pp 1559ndash1571 2008

[11] S Asai H Kuroyanagi and S Takeuchi ldquoDevelopment of asteer-by-wire system with force feedback using a disturbanceobserverrdquo inProceedings of the SAEWorldCongressampExhibitionon Steering amp Suspension Technology Detroit Mich USA 2004

[12] T J Park C S Han and S H Lee ldquoDevelopment of the elec-tronic control unit for the rack-actuating steer-by-wire usingthe hardware-in-the-loop simulation systemrdquo Mechatronicsvol 15 no 8 pp 899ndash918 2005

[13] D Odenhtal T Bunte H D Heitzer and C Eicker ldquoHow tomake steer-by-wire feel like power steeringrdquo in Proceedings ofthe 15th IFACWorld Congress Barcelona Spain July 2000

[14] H Na C Zong and D Hu ldquoInvestigations on corneringcontrol algorithm design and road feeling optimization for asteer-by-wire vehiclerdquo in Proceedings of the IEEE InternationalConference on Mechatronics and Automation (ICMA rsquo09) pp3246ndash3251 Changchun China August 2009

[15] S Ancha A Baviskar J RWagner andDMDawson ldquoGroundvehicle steering systems modelling control and analysis ofhydraulic electric and steer-by-wire configurationsrdquo Interna-tional Journal of Vehicle Design vol 44 no 1-2 pp 188ndash2082007

[16] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[17] S M H Fahami H Zamzuri S A Mazlan and M A ZakarialdquoModeling and simulation of vehicle steer by wire systemrdquoin Proceedings of the IEEE Symposium on Humanities Scienceand Engineering Research (SHUSER rsquo12) pp 765ndash770 KualaLumpur Malaysia June 2012

[18] S Anwar and L Chen ldquoAn analytical redundancy-based faultdetection and isolation algorithm for a road-wheel controlsubsystem in a steer-by-wire systemrdquo IEEE Transactions onVehicular Technology vol 56 no 5 pp 2859ndash2869 2007

[19] M T Do Z Man C Zhang H Wang and F S Tay ldquoRobustsliding mode-based learning control for steer-by-wire systemsin modern vehiclesrdquo IEEE Transactions on Vehicular Technol-ogy vol 63 no 2 pp 580ndash590 2014

[20] J Duan R Wang and Y Yu ldquoResearch on control strategies ofsteer-by-wire systemrdquo in Proceedings of the International Con-ference on Intelligent Computation Technology and Automation(ICICTA rsquo10) vol 2 pp 1122ndash1125 May 2010


[21] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[22] S Sahoo S C Subramanian and S Srivastava ldquoDesign andimplementation of a controller for navigating an autonomousground vehiclerdquo in Proceedings of the 2nd International Confer-ence on Power Control and Embedded Systems (ICPCES rsquo12) pp1ndash6 IEEE Allahabad India December 2012

[23] T D Gillespie Fundamentals of Vehicle Dynamics Society ofAutomotive Engineers 1992

[24] M H Lee S K Ha J Y Choi and K S Yoon ldquoImprovement ofthe steering feel of an electric power steering system by torquemap modificationrdquo Journal of Mechanical Science and Technol-ogy vol 19 no 3 pp 792ndash801 2005

[25] R Pastorino M A Naya J A Perez and J Cuadrado ldquoGearedPM coreless motor modelling for driverrsquos force feedback insteer-by-wire systemsrdquo Mechatronics vol 21 no 6 pp 1043ndash1054 2011

[26] P Koehn andM Eckrich ldquoActive steeringmdashthe BMWapproachtowards modern steering technologyrdquo SAE Technical PaperSeries 2004-01-1105 SAE International 2004

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Hindawi Publishing Corporation httpwwwhindawicom

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Submit your manuscripts athttpwwwhindawicom

VLSI Design



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Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks




Steering wheel

DC motor

Positionsensorencoder

ECU

Electronic controller unit Wiring

Front axle system

DC motorPositionsensorencoder

Rack and pinion Tire

Steer by wire (SBW) system

Steering wheel

CouplingMechanical column shaft

Conventional steering system

Figure 1 Difference between SBW system and conventional steering system

improvement to the torquemap has beenmade by adding thedamping torque to create more realistic driver steering feeland to improve steering wheel returnability [10] MeanwhileAmberkare et al [6] used the steering wheel angle and fed tomodel transfer function to create a feedback torque By usingthe appropriate transfer function it is possible to changethe desired steering feel by varying a proper gain of thetransfer function The approach of the disturbance observeris introduced by Asai et al [11] The position and current ofthe front axle motor are used to generate the feedback torqueFurthermore a reference model that consists of the inertiaand damping factor of steering wheel motor is proposed byPark et al [12] to generate the feedback torque The modelmatching technique which combines the mechanical andelectrical parts has been introduced by Odenhtal et al [13]to generate the feedback torque while the series of vehiclecornering control algorithm is taken into consideration tooptimize the feedback torque as proposed by Na et al [14]

The main objective of this paper is to proposes a controlalgorithm to generate the force feedback torque for driversteering feel in the vehicle SBW system The subsystem ofSBW system which is steering wheel and front axle system ismodelled and the control algorithm is explained To verify theeffectiveness of the proposed algorithm the hardware in theloop (HIL) is presented and interfaced using a Matlab XPCtarget toolbox The result was then is compared with electricpower steering (EPS) system [15]

2 The Modelling of Steer byWire (SBW) System

The SBW system is divided into two subsystems that consistof steering wheel and front axle system The system diagramof subsystem is shown in Figure 2

Table 1 Steering wheel system parameter




1198811199041 Voltage source mdash Volt

21 Steering Wheel Model The main purpose of steeringwheel motor is to generate the steering feedback torque fordriver steering feel Figure 2(a) shows the system diagramfor the steering wheel system The input to the system is thetotal feedback torque (120591total feedback) and the output is the ratechange of steering wheel motor angular displacement ( 120575

1198981)the motor angular displacement (120575

1198981) and the current ofsteering wheel motor (119894

1198861) The parameters of the steeringwheel system are illustrated in Table 1

The mathematical equations of the steering wheel systemare written as follows

The steering motor angular displacement is

1205751198981 = minus

11988711989811198691198981

1205751198981 +

1198961199041

1198691198981

1198941198861 (1)

and the steering motor current is

1198941198861 = minus

11987711198711

1198941198861 +

119896119904119898

1198711

1205751198981 +

1198811199041

1198711 (2)


120591totalfeedback

ks1

120575sw

bm1

120575m1

Jm1

L1

R1

Vs1

ia1

(a)

Vs2

L2

R2

ia2

bm2

120575m2

Jm2

ks2

brackf

Mrackf


Jm2 Jm2

(b)



119904119898

= 119860119904119898

119909119904119898

+119861119904119898

119906119904119898

119910119904119898

= 119862119904119898

119909119904119898

119909119904119898

= [ 1205751198981 1205751198981 1198941198861]

(3)

And 119906119904119898


119860119904119898

=

[[[[[[

[

minus(11988711989811198691198981

) 01198961199041

1198691198981

1 0 0

minus(119896119904119898

1198711) 0 minus(

11987711198711

)

]]]]]]

]

119861119904119898

=

[[[[

[

0

0

11198711

]]]]

]

119906119904119898

= 120591total feedback = 1198811199041

(4)











119903119871




119868119891



120575sw 120575m2 120575fyrack

Front axle system

Front axleDC motor


Front tiredynamics




1205751198982 = minus

11988711989821198691198982

1205751198982 +

1198961199042

1198691198982

1198941198862 (5)



1198941198862 = minus

11987721198712

1198941198862 +

119896119891119898

1198712

1205751198982 +

1198811199042

1198712 (6)


119891119898

= 119860119891119898

119909119891119898

+119861119891119898

119906119891119898

119910119891119898

= 119862119891119898

119909119891119898

119909119891119898

= [ 1205751198982 1205751198982 1198941198862]

(7)

And 119906119891119898




119860119891119898

=

[[[[[[[

[

minus(11988711989821198691198982

) 01198961199042

1198691198982

1 0 0

minus(

119896119891119898

1198712) 0 minus(

11987721198712

)

]]]]]]]

]

119861119891119898

=

[[[[

[

0

0

11198712

]]]]

]

119906119891119898

= 120575119904119908

= 1198811199042

(8)


119910rack =1

119872rack[(minus

2119896119897119891119910rack

1199032119871

)minus(1198961199042119910rack1199032119901

)

minus119861rack119891 119910rack +(11989611990421205751198982119903119901

)]

(9)



119860119910rack

=[[[

[

0 1

minus[(

2119896119897119891

119872rack1199032119871

) + (1198961199042

119872rack1199032119901


)

]]]

]

119861119910rack =

[[

[

0

(1198961199042

119872rack119903119901)

]]

]

119906119910rack = 120575

1198982

(10)

Fyr

lr lf

r

120572r

120573

Fyf120572f

120575f



120575119891=

1119868119891

[(minus119896119897119891120575119891+(

119896119897119891119910rack

119903119871

)minus119861119896119901

120575119891)] (11)



119860 tire =[[

[

0 1

minus(

119896119897119891

119868119891

) minus(

119861119896119901

119868119891

)

]]

]

119861tire =[[

[

0

(

119896119897119891

119868119891119903119871

)

]]

]

119906tire = 119910rack

(12)










119903 = [

[

(1198972119891119862119891+ 119897

2119903119862119903)

119868119904119881

]

]

119903+[

[

(1198972119903119862119903minus 119897

2119891119862119891)

119868119904

]

]

120573

+[

(119897119891119862119891)

119868119904

]120575119891

120573 = [1+(119897119903119862119903minus 119897119891119862119891)

1198981198812 ] 119903 minus[

(119862119891+ 119862119903)

119898119881]120573

+[

119862119891

119898119881]120575119891

(13)


119865119910119891

= minus119862119891120572119891

119865119910119903

= minus119862119903120572119903

(14)


120572119891= (120573+

119897119891

119881119903minus 120575119891)

120572119903= (120573+

119897119903

119881119903minus 120575119903)

(15)


119910V119898 = 119862V119898119909V119898

119909V119898 = [119903 120573]

(16)


=

[[[[[[

[

(

(1198712119891119862119891+ 119871

2119903119862119903)

119868119904119881

) minus

(119871119903119862119903minus 119871119891119862119891)

119868119904

1 + (

(119871119903119862119903minus 119871119891119862119891)

1198981198812 ) minus

(119862119891+ 119862119903)

119898119881

]]]]]]

]

119861V119898 =[[[

[

119871119891119862119891

119868119904

119862119891

119898119881

]]]

]

119906V119898 = 120575119891

(17)


119891) and rear (119898

119903) tire


119898 = 119898119891+119898119903

(18)

when

119898119891= 119898119891119897+119898119891119903

119898119903= 119898119903119897+119898119903119903

(19)

where 119898119891119897 119898119891119903 119898119903119897 and 119898






119897 = 119897119891+ 119897119903 (20)



119868119904= 1198981198911198972119891+1198981199031198972119903 (21)






(22)










+

+

+

minus

minus


120575sw

120575sw

120591a

Frontaxle

system

LQRcontroller

LQRcontroller

120575m2

120575m2

120575f

ia2

120573

r

Linearvehiclemodel


120591map

120591fm

120591sm

120591damp

120591inertia

VGain

scheduling

kfm

kfeelsum



Steeringwheel

120575m1

120575m1

ia1

ksm


Torque(RMS)





119897119891


119897119903









as follows

120591119886= minus119862

119891(119905119901+ 119905119898) [120573+

119897119891119903

119881minus 120575119891]120583 (23)


119898)


119891) with driver






+ 120591119891119898

+ 120591map))]


(24)



120572) for the


as follows [9]

1205911 = 1198961205731199092(13119909minus

12119881max)+119879in (25)


0 2 4 6 8 10minus40

minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

torq

ue (N

m)

70kmh75kmh


80kmh

60kmh



1205912 = 119896120572radic1003816100381610038161003816120575119904119908

1003816100381610038161003816 sgn 120575119904119908 (26)







120591119891119898

= 1198941198862119896119891119898 (27)




120591119904119898

= 1198941198861119896119904119898 (28)

0 2 4 6 8 10Time (s)

Mot

or to

rque

(Nm

)



4

2

0

minus2

minus4

minus6






120591damp = 1205751198981119896damp (29)



120591inertia = 1205751198981119896inertia (30)



0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Torq

ue (N

m)



0 2 4 6 8 10Time (s)

Forc

e fee

dbac

k to

rque

(Nm

)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

10kmh

50kmh100 kmh120 kmh

135kmh





+

minus

sum

k1

k2

k3

x1

x2

x3

Plantr(t)

LQR controller




119869 = int

prop

0(119909119879

119876119909+119906119879

119877119906) 119889119905 (31)




119876119894119894=


119894

119877119895119895

=1


(32)

where

119894 = 120576 1 2 ℓ

119895 = 120576 1 2 119895 (33)





0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Mot

orc

olum

n an

gle (

deg)




0 2 4 6 8 10

Rack

disp

lace

men

t (m

)

SBW system

EPS steering

Time (s)

18

16

14

12

10

8

6

4

2

0

times10minus3


0 2 4 6 8 100

02

04

06

08

1

12

14Fr

ont t

ire an

gle (

deg)

SBW system

EPS steering

Time (s)








0 2 4 6 8 10minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 1 2 3 4 5 6 7 8 9 10minus15

minus10

minus5

0

5

10

Time (s)

Stee

ring

torq

ue (N

m) LQR

LQR + GS

Reference

(b) 120583 = 1

0 1 2 3 4 5 6 7 8 9 10

minus15

minus10

minus5

0

5

10

15

Stee

ring

torq

ue (N

m) LQR

Reference

Time (s)

LQR + GS

(c) 120583 = 14

0 1 2 3 4 5 6 7 8 9 10minus20

minus15

minus10

minus5

0

5

10

15

20

Stee

ring

torq

ue (N

m) LQR LQR + GS

Reference

Time (s)

(d) 120583 = 17



119881 (kmh) 120575119904119908

(degree) 1198961 1198962 1198963 119896feel

(0ndash30) (plusmn180∘ lt 120575119904119908


119904119908lt plusmn179∘) 003 084 0001 060

(101ndash120) 120575119904119908

le +45∘ or 120575119904119908

le minus45∘ 005 095 0001 095



119904119908lt







minus50 0 50minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m) Feel gain = 5


Feel gain = 1



minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m)

80kmh kfeel = 060

120 kmh kfeel = 095

10kmh kfeel = 014




Target monitor

Host PC


PCI 6221


DC motor driver










Stee

ring

whe

el sy

stem

DC motor

Current

Encoder


Analogoutput

Analoginput

Counterchannel

TargetPC

Monitortarget

PC

Crossover cable

Host PC






120575m1

120575m1

ia1

r(t)










1459 0024 Nm1198691198981 0002 00036 (kgm2)1198871198981 0004 00068 Nm(rads)1198961199041 165 0025 Nm







0 2 4 6 8 10minus50

0

50

Time (s)

Rate

chan

ge m

otor

pos

ition

(deg

s)



0 2 4 6 8 100

10

20

30

40

50

60

Time (s)

Mot

or p

ositi

on (d

eg)

Measurement

Simulation


0 2 4 6 8 10minus01

minus005

0

005

01

015

Mot

or cu

rren

t (A

)


Time (s)




Time (s)

Curr

ent (

A)

008

006

004

002

0

minus002

minus004

minus006

minus0081 15 2 25 3 35 4 45 5 55





Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10



minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10









2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










120591totalfeedback

ks1

120575sw

bm1

120575m1

Jm1

L1

R1

Vs1

ia1

(a)

Vs2

L2

R2

ia2

bm2

120575m2

Jm2

ks2

brackf

Mrackf


Jm2 Jm2

(b)



119904119898

= 119860119904119898

119909119904119898

+119861119904119898

119906119904119898

119910119904119898

= 119862119904119898

119909119904119898

119909119904119898

= [ 1205751198981 1205751198981 1198941198861]

(3)

And 119906119904119898


119860119904119898

=

[[[[[[

[

minus(11988711989811198691198981

) 01198961199041

1198691198981

1 0 0

minus(119896119904119898

1198711) 0 minus(

11987711198711

)

]]]]]]

]

119861119904119898

=

[[[[

[

0

0

11198711

]]]]

]

119906119904119898

= 120591total feedback = 1198811199041

(4)











119903119871




119868119891



120575sw 120575m2 120575fyrack

Front axle system

Front axleDC motor


Front tiredynamics




1205751198982 = minus

11988711989821198691198982

1205751198982 +

1198961199042

1198691198982

1198941198862 (5)



1198941198862 = minus

11987721198712

1198941198862 +

119896119891119898

1198712

1205751198982 +

1198811199042

1198712 (6)


119891119898

= 119860119891119898

119909119891119898

+119861119891119898

119906119891119898

119910119891119898

= 119862119891119898

119909119891119898

119909119891119898

= [ 1205751198982 1205751198982 1198941198862]

(7)

And 119906119891119898




119860119891119898

=

[[[[[[[

[

minus(11988711989821198691198982

) 01198961199042

1198691198982

1 0 0

minus(

119896119891119898

1198712) 0 minus(

11987721198712

)

]]]]]]]

]

119861119891119898

=

[[[[

[

0

0

11198712

]]]]

]

119906119891119898

= 120575119904119908

= 1198811199042

(8)


119910rack =1

119872rack[(minus

2119896119897119891119910rack

1199032119871

)minus(1198961199042119910rack1199032119901

)

minus119861rack119891 119910rack +(11989611990421205751198982119903119901

)]

(9)



119860119910rack

=[[[

[

0 1

minus[(

2119896119897119891

119872rack1199032119871

) + (1198961199042

119872rack1199032119901


)

]]]

]

119861119910rack =

[[

[

0

(1198961199042

119872rack119903119901)

]]

]

119906119910rack = 120575

1198982

(10)

Fyr

lr lf

r

120572r

120573

Fyf120572f

120575f



120575119891=

1119868119891

[(minus119896119897119891120575119891+(

119896119897119891119910rack

119903119871

)minus119861119896119901

120575119891)] (11)



119860 tire =[[

[

0 1

minus(

119896119897119891

119868119891

) minus(

119861119896119901

119868119891

)

]]

]

119861tire =[[

[

0

(

119896119897119891

119868119891119903119871

)

]]

]

119906tire = 119910rack

(12)










119903 = [

[

(1198972119891119862119891+ 119897

2119903119862119903)

119868119904119881

]

]

119903+[

[

(1198972119903119862119903minus 119897

2119891119862119891)

119868119904

]

]

120573

+[

(119897119891119862119891)

119868119904

]120575119891

120573 = [1+(119897119903119862119903minus 119897119891119862119891)

1198981198812 ] 119903 minus[

(119862119891+ 119862119903)

119898119881]120573

+[

119862119891

119898119881]120575119891

(13)


119865119910119891

= minus119862119891120572119891

119865119910119903

= minus119862119903120572119903

(14)


120572119891= (120573+

119897119891

119881119903minus 120575119891)

120572119903= (120573+

119897119903

119881119903minus 120575119903)

(15)


119910V119898 = 119862V119898119909V119898

119909V119898 = [119903 120573]

(16)


=

[[[[[[

[

(

(1198712119891119862119891+ 119871

2119903119862119903)

119868119904119881

) minus

(119871119903119862119903minus 119871119891119862119891)

119868119904

1 + (

(119871119903119862119903minus 119871119891119862119891)

1198981198812 ) minus

(119862119891+ 119862119903)

119898119881

]]]]]]

]

119861V119898 =[[[

[

119871119891119862119891

119868119904

119862119891

119898119881

]]]

]

119906V119898 = 120575119891

(17)


119891) and rear (119898

119903) tire


119898 = 119898119891+119898119903

(18)

when

119898119891= 119898119891119897+119898119891119903

119898119903= 119898119903119897+119898119903119903

(19)

where 119898119891119897 119898119891119903 119898119903119897 and 119898






119897 = 119897119891+ 119897119903 (20)



119868119904= 1198981198911198972119891+1198981199031198972119903 (21)






(22)










+

+

+

minus

minus


120575sw

120575sw

120591a

Frontaxle

system

LQRcontroller

LQRcontroller

120575m2

120575m2

120575f

ia2

120573

r

Linearvehiclemodel


120591map

120591fm

120591sm

120591damp

120591inertia

VGain

scheduling

kfm

kfeelsum



Steeringwheel

120575m1

120575m1

ia1

ksm


Torque(RMS)





119897119891


119897119903









as follows

120591119886= minus119862

119891(119905119901+ 119905119898) [120573+

119897119891119903

119881minus 120575119891]120583 (23)


119898)


119891) with driver






+ 120591119891119898

+ 120591map))]


(24)



120572) for the


as follows [9]

1205911 = 1198961205731199092(13119909minus

12119881max)+119879in (25)


0 2 4 6 8 10minus40

minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

torq

ue (N

m)

70kmh75kmh


80kmh

60kmh



1205912 = 119896120572radic1003816100381610038161003816120575119904119908

1003816100381610038161003816 sgn 120575119904119908 (26)







120591119891119898

= 1198941198862119896119891119898 (27)




120591119904119898

= 1198941198861119896119904119898 (28)

0 2 4 6 8 10Time (s)

Mot

or to

rque

(Nm

)



4

2

0

minus2

minus4

minus6






120591damp = 1205751198981119896damp (29)



120591inertia = 1205751198981119896inertia (30)



0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Torq

ue (N

m)



0 2 4 6 8 10Time (s)

Forc

e fee

dbac

k to

rque

(Nm

)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

10kmh

50kmh100 kmh120 kmh

135kmh





+

minus

sum

k1

k2

k3

x1

x2

x3

Plantr(t)

LQR controller




119869 = int

prop

0(119909119879

119876119909+119906119879

119877119906) 119889119905 (31)




119876119894119894=


119894

119877119895119895

=1


(32)

where

119894 = 120576 1 2 ℓ

119895 = 120576 1 2 119895 (33)





0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Mot

orc

olum

n an

gle (

deg)




0 2 4 6 8 10

Rack

disp

lace

men

t (m

)

SBW system

EPS steering

Time (s)

18

16

14

12

10

8

6

4

2

0

times10minus3


0 2 4 6 8 100

02

04

06

08

1

12

14Fr

ont t

ire an

gle (

deg)

SBW system

EPS steering

Time (s)








0 2 4 6 8 10minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 1 2 3 4 5 6 7 8 9 10minus15

minus10

minus5

0

5

10

Time (s)

Stee

ring

torq

ue (N

m) LQR

LQR + GS

Reference

(b) 120583 = 1

0 1 2 3 4 5 6 7 8 9 10

minus15

minus10

minus5

0

5

10

15

Stee

ring

torq

ue (N

m) LQR

Reference

Time (s)

LQR + GS

(c) 120583 = 14

0 1 2 3 4 5 6 7 8 9 10minus20

minus15

minus10

minus5

0

5

10

15

20

Stee

ring

torq

ue (N

m) LQR LQR + GS

Reference

Time (s)

(d) 120583 = 17



119881 (kmh) 120575119904119908

(degree) 1198961 1198962 1198963 119896feel

(0ndash30) (plusmn180∘ lt 120575119904119908


119904119908lt plusmn179∘) 003 084 0001 060

(101ndash120) 120575119904119908

le +45∘ or 120575119904119908

le minus45∘ 005 095 0001 095



119904119908lt







minus50 0 50minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m) Feel gain = 5


Feel gain = 1



minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m)

80kmh kfeel = 060

120 kmh kfeel = 095

10kmh kfeel = 014




Target monitor

Host PC


PCI 6221


DC motor driver










Stee

ring

whe

el sy

stem

DC motor

Current

Encoder


Analogoutput

Analoginput

Counterchannel

TargetPC

Monitortarget

PC

Crossover cable

Host PC






120575m1

120575m1

ia1

r(t)










1459 0024 Nm1198691198981 0002 00036 (kgm2)1198871198981 0004 00068 Nm(rads)1198961199041 165 0025 Nm







0 2 4 6 8 10minus50

0

50

Time (s)

Rate

chan

ge m

otor

pos

ition

(deg

s)



0 2 4 6 8 100

10

20

30

40

50

60

Time (s)

Mot

or p

ositi

on (d

eg)

Measurement

Simulation


0 2 4 6 8 10minus01

minus005

0

005

01

015

Mot

or cu

rren

t (A

)


Time (s)




Time (s)

Curr

ent (

A)

008

006

004

002

0

minus002

minus004

minus006

minus0081 15 2 25 3 35 4 45 5 55





Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10



minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10









2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1198941198862 = minus

11987721198712

1198941198862 +

119896119891119898

1198712

1205751198982 +

1198811199042

1198712 (6)


119891119898

= 119860119891119898

119909119891119898

+119861119891119898

119906119891119898

119910119891119898

= 119862119891119898

119909119891119898

119909119891119898

= [ 1205751198982 1205751198982 1198941198862]

(7)

And 119906119891119898




119860119891119898

=

[[[[[[[

[

minus(11988711989821198691198982

) 01198961199042

1198691198982

1 0 0

minus(

119896119891119898

1198712) 0 minus(

11987721198712

)

]]]]]]]

]

119861119891119898

=

[[[[

[

0

0

11198712

]]]]

]

119906119891119898

= 120575119904119908

= 1198811199042

(8)


119910rack =1

119872rack[(minus

2119896119897119891119910rack

1199032119871

)minus(1198961199042119910rack1199032119901

)

minus119861rack119891 119910rack +(11989611990421205751198982119903119901

)]

(9)



119860119910rack

=[[[

[

0 1

minus[(

2119896119897119891

119872rack1199032119871

) + (1198961199042

119872rack1199032119901


)

]]]

]

119861119910rack =

[[

[

0

(1198961199042

119872rack119903119901)

]]

]

119906119910rack = 120575

1198982

(10)

Fyr

lr lf

r

120572r

120573

Fyf120572f

120575f



120575119891=

1119868119891

[(minus119896119897119891120575119891+(

119896119897119891119910rack

119903119871

)minus119861119896119901

120575119891)] (11)



119860 tire =[[

[

0 1

minus(

119896119897119891

119868119891

) minus(

119861119896119901

119868119891

)

]]

]

119861tire =[[

[

0

(

119896119897119891

119868119891119903119871

)

]]

]

119906tire = 119910rack

(12)










119903 = [

[

(1198972119891119862119891+ 119897

2119903119862119903)

119868119904119881

]

]

119903+[

[

(1198972119903119862119903minus 119897

2119891119862119891)

119868119904

]

]

120573

+[

(119897119891119862119891)

119868119904

]120575119891

120573 = [1+(119897119903119862119903minus 119897119891119862119891)

1198981198812 ] 119903 minus[

(119862119891+ 119862119903)

119898119881]120573

+[

119862119891

119898119881]120575119891

(13)


119865119910119891

= minus119862119891120572119891

119865119910119903

= minus119862119903120572119903

(14)


120572119891= (120573+

119897119891

119881119903minus 120575119891)

120572119903= (120573+

119897119903

119881119903minus 120575119903)

(15)


119910V119898 = 119862V119898119909V119898

119909V119898 = [119903 120573]

(16)


=

[[[[[[

[

(

(1198712119891119862119891+ 119871

2119903119862119903)

119868119904119881

) minus

(119871119903119862119903minus 119871119891119862119891)

119868119904

1 + (

(119871119903119862119903minus 119871119891119862119891)

1198981198812 ) minus

(119862119891+ 119862119903)

119898119881

]]]]]]

]

119861V119898 =[[[

[

119871119891119862119891

119868119904

119862119891

119898119881

]]]

]

119906V119898 = 120575119891

(17)


119891) and rear (119898

119903) tire


119898 = 119898119891+119898119903

(18)

when

119898119891= 119898119891119897+119898119891119903

119898119903= 119898119903119897+119898119903119903

(19)

where 119898119891119897 119898119891119903 119898119903119897 and 119898






119897 = 119897119891+ 119897119903 (20)



119868119904= 1198981198911198972119891+1198981199031198972119903 (21)






(22)










+

+

+

minus

minus


120575sw

120575sw

120591a

Frontaxle

system

LQRcontroller

LQRcontroller

120575m2

120575m2

120575f

ia2

120573

r

Linearvehiclemodel


120591map

120591fm

120591sm

120591damp

120591inertia

VGain

scheduling

kfm

kfeelsum



Steeringwheel

120575m1

120575m1

ia1

ksm


Torque(RMS)





119897119891


119897119903









as follows

120591119886= minus119862

119891(119905119901+ 119905119898) [120573+

119897119891119903

119881minus 120575119891]120583 (23)


119898)


119891) with driver






+ 120591119891119898

+ 120591map))]


(24)



120572) for the


as follows [9]

1205911 = 1198961205731199092(13119909minus

12119881max)+119879in (25)


0 2 4 6 8 10minus40

minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

torq

ue (N

m)

70kmh75kmh


80kmh

60kmh



1205912 = 119896120572radic1003816100381610038161003816120575119904119908

1003816100381610038161003816 sgn 120575119904119908 (26)







120591119891119898

= 1198941198862119896119891119898 (27)




120591119904119898

= 1198941198861119896119904119898 (28)

0 2 4 6 8 10Time (s)

Mot

or to

rque

(Nm

)



4

2

0

minus2

minus4

minus6






120591damp = 1205751198981119896damp (29)



120591inertia = 1205751198981119896inertia (30)



0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Torq

ue (N

m)



0 2 4 6 8 10Time (s)

Forc

e fee

dbac

k to

rque

(Nm

)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

10kmh

50kmh100 kmh120 kmh

135kmh





+

minus

sum

k1

k2

k3

x1

x2

x3

Plantr(t)

LQR controller




119869 = int

prop

0(119909119879

119876119909+119906119879

119877119906) 119889119905 (31)




119876119894119894=


119894

119877119895119895

=1


(32)

where

119894 = 120576 1 2 ℓ

119895 = 120576 1 2 119895 (33)





0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Mot

orc

olum

n an

gle (

deg)




0 2 4 6 8 10

Rack

disp

lace

men

t (m

)

SBW system

EPS steering

Time (s)

18

16

14

12

10

8

6

4

2

0

times10minus3


0 2 4 6 8 100

02

04

06

08

1

12

14Fr

ont t

ire an

gle (

deg)

SBW system

EPS steering

Time (s)








0 2 4 6 8 10minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 1 2 3 4 5 6 7 8 9 10minus15

minus10

minus5

0

5

10

Time (s)

Stee

ring

torq

ue (N

m) LQR

LQR + GS

Reference

(b) 120583 = 1

0 1 2 3 4 5 6 7 8 9 10

minus15

minus10

minus5

0

5

10

15

Stee

ring

torq

ue (N

m) LQR

Reference

Time (s)

LQR + GS

(c) 120583 = 14

0 1 2 3 4 5 6 7 8 9 10minus20

minus15

minus10

minus5

0

5

10

15

20

Stee

ring

torq

ue (N

m) LQR LQR + GS

Reference

Time (s)

(d) 120583 = 17



119881 (kmh) 120575119904119908

(degree) 1198961 1198962 1198963 119896feel

(0ndash30) (plusmn180∘ lt 120575119904119908


119904119908lt plusmn179∘) 003 084 0001 060

(101ndash120) 120575119904119908

le +45∘ or 120575119904119908

le minus45∘ 005 095 0001 095



119904119908lt







minus50 0 50minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m) Feel gain = 5


Feel gain = 1



minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m)

80kmh kfeel = 060

120 kmh kfeel = 095

10kmh kfeel = 014




Target monitor

Host PC


PCI 6221


DC motor driver










Stee

ring

whe

el sy

stem

DC motor

Current

Encoder


Analogoutput

Analoginput

Counterchannel

TargetPC

Monitortarget

PC

Crossover cable

Host PC






120575m1

120575m1

ia1

r(t)










1459 0024 Nm1198691198981 0002 00036 (kgm2)1198871198981 0004 00068 Nm(rads)1198961199041 165 0025 Nm







0 2 4 6 8 10minus50

0

50

Time (s)

Rate

chan

ge m

otor

pos

ition

(deg

s)



0 2 4 6 8 100

10

20

30

40

50

60

Time (s)

Mot

or p

ositi

on (d

eg)

Measurement

Simulation


0 2 4 6 8 10minus01

minus005

0

005

01

015

Mot

or cu

rren

t (A

)


Time (s)




Time (s)

Curr

ent (

A)

008

006

004

002

0

minus002

minus004

minus006

minus0081 15 2 25 3 35 4 45 5 55





Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10



minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10









2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119903 = [

[

(1198972119891119862119891+ 119897

2119903119862119903)

119868119904119881

]

]

119903+[

[

(1198972119903119862119903minus 119897

2119891119862119891)

119868119904

]

]

120573

+[

(119897119891119862119891)

119868119904

]120575119891

120573 = [1+(119897119903119862119903minus 119897119891119862119891)

1198981198812 ] 119903 minus[

(119862119891+ 119862119903)

119898119881]120573

+[

119862119891

119898119881]120575119891

(13)


119865119910119891

= minus119862119891120572119891

119865119910119903

= minus119862119903120572119903

(14)


120572119891= (120573+

119897119891

119881119903minus 120575119891)

120572119903= (120573+

119897119903

119881119903minus 120575119903)

(15)


119910V119898 = 119862V119898119909V119898

119909V119898 = [119903 120573]

(16)


=

[[[[[[

[

(

(1198712119891119862119891+ 119871

2119903119862119903)

119868119904119881

) minus

(119871119903119862119903minus 119871119891119862119891)

119868119904

1 + (

(119871119903119862119903minus 119871119891119862119891)

1198981198812 ) minus

(119862119891+ 119862119903)

119898119881

]]]]]]

]

119861V119898 =[[[

[

119871119891119862119891

119868119904

119862119891

119898119881

]]]

]

119906V119898 = 120575119891

(17)


119891) and rear (119898

119903) tire


119898 = 119898119891+119898119903

(18)

when

119898119891= 119898119891119897+119898119891119903

119898119903= 119898119903119897+119898119903119903

(19)

where 119898119891119897 119898119891119903 119898119903119897 and 119898






119897 = 119897119891+ 119897119903 (20)



119868119904= 1198981198911198972119891+1198981199031198972119903 (21)






(22)










+

+

+

minus

minus


120575sw

120575sw

120591a

Frontaxle

system

LQRcontroller

LQRcontroller

120575m2

120575m2

120575f

ia2

120573

r

Linearvehiclemodel


120591map

120591fm

120591sm

120591damp

120591inertia

VGain

scheduling

kfm

kfeelsum



Steeringwheel

120575m1

120575m1

ia1

ksm


Torque(RMS)





119897119891


119897119903









as follows

120591119886= minus119862

119891(119905119901+ 119905119898) [120573+

119897119891119903

119881minus 120575119891]120583 (23)


119898)


119891) with driver






+ 120591119891119898

+ 120591map))]


(24)



120572) for the


as follows [9]

1205911 = 1198961205731199092(13119909minus

12119881max)+119879in (25)


0 2 4 6 8 10minus40

minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

torq

ue (N

m)

70kmh75kmh


80kmh

60kmh



1205912 = 119896120572radic1003816100381610038161003816120575119904119908

1003816100381610038161003816 sgn 120575119904119908 (26)







120591119891119898

= 1198941198862119896119891119898 (27)




120591119904119898

= 1198941198861119896119904119898 (28)

0 2 4 6 8 10Time (s)

Mot

or to

rque

(Nm

)



4

2

0

minus2

minus4

minus6






120591damp = 1205751198981119896damp (29)



120591inertia = 1205751198981119896inertia (30)



0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Torq

ue (N

m)



0 2 4 6 8 10Time (s)

Forc

e fee

dbac

k to

rque

(Nm

)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

10kmh

50kmh100 kmh120 kmh

135kmh





+

minus

sum

k1

k2

k3

x1

x2

x3

Plantr(t)

LQR controller




119869 = int

prop

0(119909119879

119876119909+119906119879

119877119906) 119889119905 (31)




119876119894119894=


119894

119877119895119895

=1


(32)

where

119894 = 120576 1 2 ℓ

119895 = 120576 1 2 119895 (33)





0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Mot

orc

olum

n an

gle (

deg)




0 2 4 6 8 10

Rack

disp

lace

men

t (m

)

SBW system

EPS steering

Time (s)

18

16

14

12

10

8

6

4

2

0

times10minus3


0 2 4 6 8 100

02

04

06

08

1

12

14Fr

ont t

ire an

gle (

deg)

SBW system

EPS steering

Time (s)








0 2 4 6 8 10minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 1 2 3 4 5 6 7 8 9 10minus15

minus10

minus5

0

5

10

Time (s)

Stee

ring

torq

ue (N

m) LQR

LQR + GS

Reference

(b) 120583 = 1

0 1 2 3 4 5 6 7 8 9 10

minus15

minus10

minus5

0

5

10

15

Stee

ring

torq

ue (N

m) LQR

Reference

Time (s)

LQR + GS

(c) 120583 = 14

0 1 2 3 4 5 6 7 8 9 10minus20

minus15

minus10

minus5

0

5

10

15

20

Stee

ring

torq

ue (N

m) LQR LQR + GS

Reference

Time (s)

(d) 120583 = 17



119881 (kmh) 120575119904119908

(degree) 1198961 1198962 1198963 119896feel

(0ndash30) (plusmn180∘ lt 120575119904119908


119904119908lt plusmn179∘) 003 084 0001 060

(101ndash120) 120575119904119908

le +45∘ or 120575119904119908

le minus45∘ 005 095 0001 095



119904119908lt







minus50 0 50minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m) Feel gain = 5


Feel gain = 1



minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m)

80kmh kfeel = 060

120 kmh kfeel = 095

10kmh kfeel = 014




Target monitor

Host PC


PCI 6221


DC motor driver










Stee

ring

whe

el sy

stem

DC motor

Current

Encoder


Analogoutput

Analoginput

Counterchannel

TargetPC

Monitortarget

PC

Crossover cable

Host PC






120575m1

120575m1

ia1

r(t)










1459 0024 Nm1198691198981 0002 00036 (kgm2)1198871198981 0004 00068 Nm(rads)1198961199041 165 0025 Nm







0 2 4 6 8 10minus50

0

50

Time (s)

Rate

chan

ge m

otor

pos

ition

(deg

s)



0 2 4 6 8 100

10

20

30

40

50

60

Time (s)

Mot

or p

ositi

on (d

eg)

Measurement

Simulation


0 2 4 6 8 10minus01

minus005

0

005

01

015

Mot

or cu

rren

t (A

)


Time (s)




Time (s)

Curr

ent (

A)

008

006

004

002

0

minus002

minus004

minus006

minus0081 15 2 25 3 35 4 45 5 55





Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10



minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10









2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










+

+

+

minus

minus


120575sw

120575sw

120591a

Frontaxle

system

LQRcontroller

LQRcontroller

120575m2

120575m2

120575f

ia2

120573

r

Linearvehiclemodel


120591map

120591fm

120591sm

120591damp

120591inertia

VGain

scheduling

kfm

kfeelsum



Steeringwheel

120575m1

120575m1

ia1

ksm


Torque(RMS)





119897119891


119897119903









as follows

120591119886= minus119862

119891(119905119901+ 119905119898) [120573+

119897119891119903

119881minus 120575119891]120583 (23)


119898)


119891) with driver






+ 120591119891119898

+ 120591map))]


(24)



120572) for the


as follows [9]

1205911 = 1198961205731199092(13119909minus

12119881max)+119879in (25)


0 2 4 6 8 10minus40

minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

torq

ue (N

m)

70kmh75kmh


80kmh

60kmh



1205912 = 119896120572radic1003816100381610038161003816120575119904119908

1003816100381610038161003816 sgn 120575119904119908 (26)







120591119891119898

= 1198941198862119896119891119898 (27)




120591119904119898

= 1198941198861119896119904119898 (28)

0 2 4 6 8 10Time (s)

Mot

or to

rque

(Nm

)



4

2

0

minus2

minus4

minus6






120591damp = 1205751198981119896damp (29)



120591inertia = 1205751198981119896inertia (30)



0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Torq

ue (N

m)



0 2 4 6 8 10Time (s)

Forc

e fee

dbac

k to

rque

(Nm

)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

10kmh

50kmh100 kmh120 kmh

135kmh





+

minus

sum

k1

k2

k3

x1

x2

x3

Plantr(t)

LQR controller




119869 = int

prop

0(119909119879

119876119909+119906119879

119877119906) 119889119905 (31)




119876119894119894=


119894

119877119895119895

=1


(32)

where

119894 = 120576 1 2 ℓ

119895 = 120576 1 2 119895 (33)





0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Mot

orc

olum

n an

gle (

deg)




0 2 4 6 8 10

Rack

disp

lace

men

t (m

)

SBW system

EPS steering

Time (s)

18

16

14

12

10

8

6

4

2

0

times10minus3


0 2 4 6 8 100

02

04

06

08

1

12

14Fr

ont t

ire an

gle (

deg)

SBW system

EPS steering

Time (s)








0 2 4 6 8 10minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 1 2 3 4 5 6 7 8 9 10minus15

minus10

minus5

0

5

10

Time (s)

Stee

ring

torq

ue (N

m) LQR

LQR + GS

Reference

(b) 120583 = 1

0 1 2 3 4 5 6 7 8 9 10

minus15

minus10

minus5

0

5

10

15

Stee

ring

torq

ue (N

m) LQR

Reference

Time (s)

LQR + GS

(c) 120583 = 14

0 1 2 3 4 5 6 7 8 9 10minus20

minus15

minus10

minus5

0

5

10

15

20

Stee

ring

torq

ue (N

m) LQR LQR + GS

Reference

Time (s)

(d) 120583 = 17



119881 (kmh) 120575119904119908

(degree) 1198961 1198962 1198963 119896feel

(0ndash30) (plusmn180∘ lt 120575119904119908


119904119908lt plusmn179∘) 003 084 0001 060

(101ndash120) 120575119904119908

le +45∘ or 120575119904119908

le minus45∘ 005 095 0001 095



119904119908lt







minus50 0 50minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m) Feel gain = 5


Feel gain = 1



minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m)

80kmh kfeel = 060

120 kmh kfeel = 095

10kmh kfeel = 014




Target monitor

Host PC


PCI 6221


DC motor driver










Stee

ring

whe

el sy

stem

DC motor

Current

Encoder


Analogoutput

Analoginput

Counterchannel

TargetPC

Monitortarget

PC

Crossover cable

Host PC






120575m1

120575m1

ia1

r(t)










1459 0024 Nm1198691198981 0002 00036 (kgm2)1198871198981 0004 00068 Nm(rads)1198961199041 165 0025 Nm







0 2 4 6 8 10minus50

0

50

Time (s)

Rate

chan

ge m

otor

pos

ition

(deg

s)



0 2 4 6 8 100

10

20

30

40

50

60

Time (s)

Mot

or p

ositi

on (d

eg)

Measurement

Simulation


0 2 4 6 8 10minus01

minus005

0

005

01

015

Mot

or cu

rren

t (A

)


Time (s)




Time (s)

Curr

ent (

A)

008

006

004

002

0

minus002

minus004

minus006

minus0081 15 2 25 3 35 4 45 5 55





Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10



minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10









2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 10minus40

minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

torq

ue (N

m)

70kmh75kmh


80kmh

60kmh



1205912 = 119896120572radic1003816100381610038161003816120575119904119908

1003816100381610038161003816 sgn 120575119904119908 (26)







120591119891119898

= 1198941198862119896119891119898 (27)




120591119904119898

= 1198941198861119896119904119898 (28)

0 2 4 6 8 10Time (s)

Mot

or to

rque

(Nm

)



4

2

0

minus2

minus4

minus6






120591damp = 1205751198981119896damp (29)



120591inertia = 1205751198981119896inertia (30)



0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Torq

ue (N

m)



0 2 4 6 8 10Time (s)

Forc

e fee

dbac

k to

rque

(Nm

)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

10kmh

50kmh100 kmh120 kmh

135kmh





+

minus

sum

k1

k2

k3

x1

x2

x3

Plantr(t)

LQR controller




119869 = int

prop

0(119909119879

119876119909+119906119879

119877119906) 119889119905 (31)




119876119894119894=


119894

119877119895119895

=1


(32)

where

119894 = 120576 1 2 ℓ

119895 = 120576 1 2 119895 (33)





0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Mot

orc

olum

n an

gle (

deg)




0 2 4 6 8 10

Rack

disp

lace

men

t (m

)

SBW system

EPS steering

Time (s)

18

16

14

12

10

8

6

4

2

0

times10minus3


0 2 4 6 8 100

02

04

06

08

1

12

14Fr

ont t

ire an

gle (

deg)

SBW system

EPS steering

Time (s)








0 2 4 6 8 10minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 1 2 3 4 5 6 7 8 9 10minus15

minus10

minus5

0

5

10

Time (s)

Stee

ring

torq

ue (N

m) LQR

LQR + GS

Reference

(b) 120583 = 1

0 1 2 3 4 5 6 7 8 9 10

minus15

minus10

minus5

0

5

10

15

Stee

ring

torq

ue (N

m) LQR

Reference

Time (s)

LQR + GS

(c) 120583 = 14

0 1 2 3 4 5 6 7 8 9 10minus20

minus15

minus10

minus5

0

5

10

15

20

Stee

ring

torq

ue (N

m) LQR LQR + GS

Reference

Time (s)

(d) 120583 = 17



119881 (kmh) 120575119904119908

(degree) 1198961 1198962 1198963 119896feel

(0ndash30) (plusmn180∘ lt 120575119904119908


119904119908lt plusmn179∘) 003 084 0001 060

(101ndash120) 120575119904119908

le +45∘ or 120575119904119908

le minus45∘ 005 095 0001 095



119904119908lt







minus50 0 50minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m) Feel gain = 5


Feel gain = 1



minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m)

80kmh kfeel = 060

120 kmh kfeel = 095

10kmh kfeel = 014




Target monitor

Host PC


PCI 6221


DC motor driver










Stee

ring

whe

el sy

stem

DC motor

Current

Encoder


Analogoutput

Analoginput

Counterchannel

TargetPC

Monitortarget

PC

Crossover cable

Host PC






120575m1

120575m1

ia1

r(t)










1459 0024 Nm1198691198981 0002 00036 (kgm2)1198871198981 0004 00068 Nm(rads)1198961199041 165 0025 Nm







0 2 4 6 8 10minus50

0

50

Time (s)

Rate

chan

ge m

otor

pos

ition

(deg

s)



0 2 4 6 8 100

10

20

30

40

50

60

Time (s)

Mot

or p

ositi

on (d

eg)

Measurement

Simulation


0 2 4 6 8 10minus01

minus005

0

005

01

015

Mot

or cu

rren

t (A

)


Time (s)




Time (s)

Curr

ent (

A)

008

006

004

002

0

minus002

minus004

minus006

minus0081 15 2 25 3 35 4 45 5 55





Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10



minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10









2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Torq

ue (N

m)



0 2 4 6 8 10Time (s)

Forc

e fee

dbac

k to

rque

(Nm

)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

10kmh

50kmh100 kmh120 kmh

135kmh





+

minus

sum

k1

k2

k3

x1

x2

x3

Plantr(t)

LQR controller




119869 = int

prop

0(119909119879

119876119909+119906119879

119877119906) 119889119905 (31)




119876119894119894=


119894

119877119895119895

=1


(32)

where

119894 = 120576 1 2 ℓ

119895 = 120576 1 2 119895 (33)





0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Mot

orc

olum

n an

gle (

deg)




0 2 4 6 8 10

Rack

disp

lace

men

t (m

)

SBW system

EPS steering

Time (s)

18

16

14

12

10

8

6

4

2

0

times10minus3


0 2 4 6 8 100

02

04

06

08

1

12

14Fr

ont t

ire an

gle (

deg)

SBW system

EPS steering

Time (s)








0 2 4 6 8 10minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 1 2 3 4 5 6 7 8 9 10minus15

minus10

minus5

0

5

10

Time (s)

Stee

ring

torq

ue (N

m) LQR

LQR + GS

Reference

(b) 120583 = 1

0 1 2 3 4 5 6 7 8 9 10

minus15

minus10

minus5

0

5

10

15

Stee

ring

torq

ue (N

m) LQR

Reference

Time (s)

LQR + GS

(c) 120583 = 14

0 1 2 3 4 5 6 7 8 9 10minus20

minus15

minus10

minus5

0

5

10

15

20

Stee

ring

torq

ue (N

m) LQR LQR + GS

Reference

Time (s)

(d) 120583 = 17



119881 (kmh) 120575119904119908

(degree) 1198961 1198962 1198963 119896feel

(0ndash30) (plusmn180∘ lt 120575119904119908


119904119908lt plusmn179∘) 003 084 0001 060

(101ndash120) 120575119904119908

le +45∘ or 120575119904119908

le minus45∘ 005 095 0001 095



119904119908lt







minus50 0 50minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m) Feel gain = 5


Feel gain = 1



minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m)

80kmh kfeel = 060

120 kmh kfeel = 095

10kmh kfeel = 014




Target monitor

Host PC


PCI 6221


DC motor driver










Stee

ring

whe

el sy

stem

DC motor

Current

Encoder


Analogoutput

Analoginput

Counterchannel

TargetPC

Monitortarget

PC

Crossover cable

Host PC






120575m1

120575m1

ia1

r(t)










1459 0024 Nm1198691198981 0002 00036 (kgm2)1198871198981 0004 00068 Nm(rads)1198961199041 165 0025 Nm







0 2 4 6 8 10minus50

0

50

Time (s)

Rate

chan

ge m

otor

pos

ition

(deg

s)



0 2 4 6 8 100

10

20

30

40

50

60

Time (s)

Mot

or p

ositi

on (d

eg)

Measurement

Simulation


0 2 4 6 8 10minus01

minus005

0

005

01

015

Mot

or cu

rren

t (A

)


Time (s)




Time (s)

Curr

ent (

A)

008

006

004

002

0

minus002

minus004

minus006

minus0081 15 2 25 3 35 4 45 5 55





Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10



minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10









2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Mot

orc

olum

n an

gle (

deg)




0 2 4 6 8 10

Rack

disp

lace

men

t (m

)

SBW system

EPS steering

Time (s)

18

16

14

12

10

8

6

4

2

0

times10minus3


0 2 4 6 8 100

02

04

06

08

1

12

14Fr

ont t

ire an

gle (

deg)

SBW system

EPS steering

Time (s)








0 2 4 6 8 10minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 1 2 3 4 5 6 7 8 9 10minus15

minus10

minus5

0

5

10

Time (s)

Stee

ring

torq

ue (N

m) LQR

LQR + GS

Reference

(b) 120583 = 1

0 1 2 3 4 5 6 7 8 9 10

minus15

minus10

minus5

0

5

10

15

Stee

ring

torq

ue (N

m) LQR

Reference

Time (s)

LQR + GS

(c) 120583 = 14

0 1 2 3 4 5 6 7 8 9 10minus20

minus15

minus10

minus5

0

5

10

15

20

Stee

ring

torq

ue (N

m) LQR LQR + GS

Reference

Time (s)

(d) 120583 = 17



119881 (kmh) 120575119904119908

(degree) 1198961 1198962 1198963 119896feel

(0ndash30) (plusmn180∘ lt 120575119904119908


119904119908lt plusmn179∘) 003 084 0001 060

(101ndash120) 120575119904119908

le +45∘ or 120575119904119908

le minus45∘ 005 095 0001 095



119904119908lt







minus50 0 50minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m) Feel gain = 5


Feel gain = 1



minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m)

80kmh kfeel = 060

120 kmh kfeel = 095

10kmh kfeel = 014




Target monitor

Host PC


PCI 6221


DC motor driver










Stee

ring

whe

el sy

stem

DC motor

Current

Encoder


Analogoutput

Analoginput

Counterchannel

TargetPC

Monitortarget

PC

Crossover cable

Host PC






120575m1

120575m1

ia1

r(t)










1459 0024 Nm1198691198981 0002 00036 (kgm2)1198871198981 0004 00068 Nm(rads)1198961199041 165 0025 Nm







0 2 4 6 8 10minus50

0

50

Time (s)

Rate

chan

ge m

otor

pos

ition

(deg

s)



0 2 4 6 8 100

10

20

30

40

50

60

Time (s)

Mot

or p

ositi

on (d

eg)

Measurement

Simulation


0 2 4 6 8 10minus01

minus005

0

005

01

015

Mot

or cu

rren

t (A

)


Time (s)




Time (s)

Curr

ent (

A)

008

006

004

002

0

minus002

minus004

minus006

minus0081 15 2 25 3 35 4 45 5 55





Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10



minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10









2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 10minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

Time (s)

Stee

ring

whe

el an

gle (

deg)


0 1 2 3 4 5 6 7 8 9 10minus15

minus10

minus5

0

5

10

Time (s)

Stee

ring

torq

ue (N

m) LQR

LQR + GS

Reference

(b) 120583 = 1

0 1 2 3 4 5 6 7 8 9 10

minus15

minus10

minus5

0

5

10

15

Stee

ring

torq

ue (N

m) LQR

Reference

Time (s)

LQR + GS

(c) 120583 = 14

0 1 2 3 4 5 6 7 8 9 10minus20

minus15

minus10

minus5

0

5

10

15

20

Stee

ring

torq

ue (N

m) LQR LQR + GS

Reference

Time (s)

(d) 120583 = 17



119881 (kmh) 120575119904119908

(degree) 1198961 1198962 1198963 119896feel

(0ndash30) (plusmn180∘ lt 120575119904119908


119904119908lt plusmn179∘) 003 084 0001 060

(101ndash120) 120575119904119908

le +45∘ or 120575119904119908

le minus45∘ 005 095 0001 095



119904119908lt







minus50 0 50minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m) Feel gain = 5


Feel gain = 1



minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m)

80kmh kfeel = 060

120 kmh kfeel = 095

10kmh kfeel = 014




Target monitor

Host PC


PCI 6221


DC motor driver










Stee

ring

whe

el sy

stem

DC motor

Current

Encoder


Analogoutput

Analoginput

Counterchannel

TargetPC

Monitortarget

PC

Crossover cable

Host PC






120575m1

120575m1

ia1

r(t)










1459 0024 Nm1198691198981 0002 00036 (kgm2)1198871198981 0004 00068 Nm(rads)1198961199041 165 0025 Nm







0 2 4 6 8 10minus50

0

50

Time (s)

Rate

chan

ge m

otor

pos

ition

(deg

s)



0 2 4 6 8 100

10

20

30

40

50

60

Time (s)

Mot

or p

ositi

on (d

eg)

Measurement

Simulation


0 2 4 6 8 10minus01

minus005

0

005

01

015

Mot

or cu

rren

t (A

)


Time (s)




Time (s)

Curr

ent (

A)

008

006

004

002

0

minus002

minus004

minus006

minus0081 15 2 25 3 35 4 45 5 55





Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10



minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10









2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












minus50 0 50minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m) Feel gain = 5


Feel gain = 1



minus15

minus10

minus5

0

5

10

15


Stee

ring

torq

ue (N

m)

80kmh kfeel = 060

120 kmh kfeel = 095

10kmh kfeel = 014




Target monitor

Host PC


PCI 6221


DC motor driver










Stee

ring

whe

el sy

stem

DC motor

Current

Encoder


Analogoutput

Analoginput

Counterchannel

TargetPC

Monitortarget

PC

Crossover cable

Host PC






120575m1

120575m1

ia1

r(t)










1459 0024 Nm1198691198981 0002 00036 (kgm2)1198871198981 0004 00068 Nm(rads)1198961199041 165 0025 Nm







0 2 4 6 8 10minus50

0

50

Time (s)

Rate

chan

ge m

otor

pos

ition

(deg

s)



0 2 4 6 8 100

10

20

30

40

50

60

Time (s)

Mot

or p

ositi

on (d

eg)

Measurement

Simulation


0 2 4 6 8 10minus01

minus005

0

005

01

015

Mot

or cu

rren

t (A

)


Time (s)




Time (s)

Curr

ent (

A)

008

006

004

002

0

minus002

minus004

minus006

minus0081 15 2 25 3 35 4 45 5 55





Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10



minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10









2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Stee

ring

whe

el sy

stem

DC motor

Current

Encoder


Analogoutput

Analoginput

Counterchannel

TargetPC

Monitortarget

PC

Crossover cable

Host PC






120575m1

120575m1

ia1

r(t)










1459 0024 Nm1198691198981 0002 00036 (kgm2)1198871198981 0004 00068 Nm(rads)1198961199041 165 0025 Nm







0 2 4 6 8 10minus50

0

50

Time (s)

Rate

chan

ge m

otor

pos

ition

(deg

s)



0 2 4 6 8 100

10

20

30

40

50

60

Time (s)

Mot

or p

ositi

on (d

eg)

Measurement

Simulation


0 2 4 6 8 10minus01

minus005

0

005

01

015

Mot

or cu

rren

t (A

)


Time (s)




Time (s)

Curr

ent (

A)

008

006

004

002

0

minus002

minus004

minus006

minus0081 15 2 25 3 35 4 45 5 55





Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10



minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10









2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 10minus50

0

50

Time (s)

Rate

chan

ge m

otor

pos

ition

(deg

s)



0 2 4 6 8 100

10

20

30

40

50

60

Time (s)

Mot

or p

ositi

on (d

eg)

Measurement

Simulation


0 2 4 6 8 10minus01

minus005

0

005

01

015

Mot

or cu

rren

t (A

)


Time (s)




Time (s)

Curr

ent (

A)

008

006

004

002

0

minus002

minus004

minus006

minus0081 15 2 25 3 35 4 45 5 55





Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10



minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10









2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

minus152 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

5

0

minus5

minus10

21 3 4 5 6 7 8 9 10



minus80

minus60

minus40

minus20

0

20

40

60

80

100

Stee

ring

whe

el an

gle (

deg)

Time (s)3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

Time (s)

EPS steering

Simulation

Experiment

10

15

20

5

0

minus5

minus10

minus15

minus203 4 5 6 7 8 9 10









2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2 3 4 5 6 7 8 9 10minus30

minus20

minus10

0

10

20

30

40

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

Time (s)


10

5

0

minus5

minus10

3 4 5 6 7 8 9


Stee

ring

torq

ue (N

m)

EPS steering


15

5

0

minus5

minus10






3 4 5 6 7 8 9 10minus150

minus100

minus50

0

50

100

150

200

Time (s)

Stee

ring

whe

el an

gle (

deg)


Stee

ring

torq

ue (N

m)

EPS steering


10

15

5

0

minus5

minus10

minus15

Time (s)2 3 4 5 6 7 8 9 10


Stee

ring

torq

ue (N

m)

EPS steering



10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

minus100 minus50 0 50 100 150










Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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