A study of dynamics performance improvement by rear right and left independent drive system

A study of dynamics performance improvement by rear right and left independent drive system Takashi Sugano, Hitoshi Fukuba and Takamasa Suetomi Mazda Motor Corporation 3-1, Shinch

A study of dynamics performance improvement

by rear right and left independent drive system

Takashi Sugano, Hitoshi Fukuba and Takamasa Suetomi

Mazda Motor Corporation

3-1, Shinchi, Fuchu-cho, Aki-gun, Hiroshima, 730-8670, JAPAN

Phone: +81 82 252 5011 Fax: +81 82 252 5342 E-mail: sugano.t@mazda.co.jp

In this paper, a motion control of a rear right and left independent electric motor drive vehicle was

researched There is making to instability when acceleration turns as a problem considered in a

rear wheel drive vehicle In this research, a control method that especially dealt with this problem

was examined, and the performance of independent drive system was evaluated by a simulation

Moreover, the effects for driver were confirmed with a driving simulator The effectiveness of the

system was confirmed from these results

Topics / Direct Yaw-moment, electrical vehicle, driving simulator

1 INTRODUCTION

Cars will be driven by electric motor from the

lower-fuel consumption in the near future In electric

drive systems, decentralized arrangement of the drive

unit is possible Herewith, a driving force distribution

system, which needs a complex mechanism, now, will

be realized with comparative ease so far In addition, a

Direct Yaw moment Control (DYC) with a fast response

and accurate driving torque by the motor will be

possible and expected to enlarge vehicle dynamics

performance The research that uses the tire force to its

maximum has been done by the combination of the

driving/braking torque and the independent steer, and

the improvement of the limit performance is

suggested[1][2] Moreover, the research to which the

dynamics performance is improved by the thing

combined with DYC and other systems, for instance,

Active Front Steer (AFS) and Active Rear Steer (ARS)

is done[3] In this paper, a study of the improvement of

driving operation and the dynamics performance by a

simple rear right-left independent driving vehicle is

conducted The precondition is to think about more

realizable system by avoiding the complication of a

mechanism

On rear drive system, there is a possibility that the

vehicle characteristic becomes unstable due to the slip

angle – lateral force gradient decrease when the vehicle

has accelerated The gradient is named ‘local Cp’ in this

paper And, it is not evaluated enough how the DYC

effects on driver’s maneuver Furthermore, It is

proposed to keep the stability of the DYC vehicle by

limiting yaw rate from acceleration/deceleration and

friction between tire and road[4] But, the local Cp

reduction is not minded in the paper For conventional

vehicle, research that a driver operation and vehicle

motion on cornering with acceleration was conducted and it was proposed that the combination of driving/braking and steering was important to effectively uses tire force[5]

First of all, stabilization logic on acceleration in turn situations is designed and the improvement of the vehicle dynamics by DYC is validated by the simulation for a certain vehicle Next, the influence on the driver is evaluated with a driving simulator As a result, it is confirmed that driver's unnecessary steering decreased since the stability of the vehicle is increased

2 CONFIGURE OF VEHICLE

In this report, a vehicle system that equipped right and left independent motor on rear axle was considered The configure of vehicle system is shown in fig.1 On this configuration, yaw moment caused by difference

of driving force between right and left tires affects vehicle turning motion in addition to driving force to move forward motion Hence, this yaw moment control expected to improve a cornering stability and a steering response

Center of Gravity

l f

V

M

l r

Electric Motors

V Velocity

Slip Angle Yaw Rate

l f Length from C.G to front tire

l r Length from C.G to rear tire

l t

l t Tread

M Yaw Moment

F XL Driving force on left side

F XR Driving force on right side

f Steering Angle

Fig 1 Target vehicle model

3 CONTROL SYSTEM DESIGN

3.1 Requirement for Controller

The characteristics of vehicle dynamics are possible

to become unstable when turning motion with high

driving force is generated on Rear Wheel Drive (RWD)

vehicle It is thought that the cause of this problem is

decreasing local Cp The phenomenon is shown in fig 2

The C f is the sum of local Cp of the front tires and the

C r is same for rear tires

B Unstable

A Stable

Slip Angle

C f

C r on A

C r on B

The rear wheels don't put out lateral force to correspond to force where the front wheels are generated

Fig 2 Degradation of local Cp caused by Driving Force

If rear local Cp is excessive decreasing, rear tires

can not generate anti yaw moment that corresponds to

an increase of yaw moment that the front tires generate

when the slip angle increases As a result, yaw moment

that increases slip angle will remain, and yaw moment

will be increased in the self-excitation Therefore, there

is a possibility of making the vehicle unstable even if

there is margin in the tire availability Because the

problem is the balance of front and rear local Cp A

system that improves stability on acceleration in turn

was constructed by controlling this phenomenon The

over-view of control system is shown in fig 3

Vehicle

K FB

f

&Driver

Yaw rate

Target Model

Velocity

Tire Load Slip Angle

Steering

Angle

Throttle

Pedal

DYC Moment

FB Controller

FF

Controller K FF

Driving Force

on stability limit

Direct Yaw Moment Controller

Acceleration Force Limitation Logic

Traction Control Min

Cp Limit Estimator Maximum Driving

Force Estimator Target

Rear Cp

Driving

Force

Cp Limit Estimator

Acceleration Controller

Traction Control

Target

Yaw rate

Tire force Tire load

Fig 3 Overview of Control System

3.2 Direct Yaw Moment Control

A target model following feedforward and feedback

controllers are designed Same type of control system

has researched well heretofore The target model is a

first order delay that assumes steering wheel angle to be

input And the yaw gain was changed depending on the

velocity It is set based on base vehicle Therefore,

target yaw rate is increasing on acceleration in turn even

if steering wheel angle is fixed The feedback controller

is a simple proportional and integral (PI) controller The control gain is designed based on theoretical 2-DOF vehicle model and motor systems The motor system is assumed as a first order delay model that includes characteristics of transfer of driving torque

3.3 Acceleration Control

The high accuracy of acceleration control will be designed using advantage of motor drive[7][8] But, a simple feed forward logic, the driving force is calculated proportional to acceleration pedal, and wheel inertia compensator is implemented in this research

3.4 Traction Control (TRC)

Traction control logic is implemented and it is used with DYC In this logic, driving force is limited as

equation (1) Note that F X_CMD is target driving force; F Z

is tire load; F Y lateral force; and is friction coefficient

The ‘*’ means each wheel The inputs, F Z , F Y and , should be estimation value But in this paper, the true values are used

2

* 2

*

*

In addition, even if driving torque for one side is limited, the DYC moment is fulfilled by reducing the other hand

3.5 Driving Force Limitation Logic (DFL)

The rear local Cp deceleration on acceleration in turn is prevented by this logic One of a direct solution

in this problem is to deaden driving force However, it is necessary to maintain the turn ability by making the best use of DYC in the viewpoint of safety Consequently, as shown in fig.4, the control method is that driving force

of both tires is similarly decreased to keep the difference of driving force

Fx

Slip Angle

Fig 4 Strategy to compensate stability

[Stability of turning motion]

There is a well known 2-DOF model to study vehicle turning motion on steady velocity analytically It

is shown as equation (2) and (3) Note that m is vehicle

mass and the other symbols are same as fig.1 and fig.2

f f

r r f f r

f

C

C l C l V C

C mV

2

2 1 2

&

(2)

f f f

r r f f r

r f f Z

C l

C l C l V C l C l I

2

2

&

(3) The condition of stability of this model is obtained

as equation (4) by evaluating the characteristic equation

by Routh stability criterion, etc[8] It leads to assuring

stability by enlarging C r more than a value of right hand

of equation (4) The C r calculated by equation (4) is

used as reference Cp in this logic

r f

r

f

f f r

l mV l

l

C

C l mV

2

[Tire Force and Local Cp]

In this paper, Brush Model, that is a well known

physical tire model[9], is applied to estimate driving

force on the Cp of stability limit The equations of tire

force on driving side are shown as follows:

For s > 0 :

3 2 2

3

1 2

1 6

1 cos

s

s

X K s F

3 2 2

3

1 2

1 6

1 sin

6

tan 1

s s Z

s Y

F

s

K

F

(6)

Note that F X is longitudinal force; F Y is lateral

force; F Z is tire load; K s is driving stiffness; K is

cornering stiffness; s is length of adhesion area of

ground plane; is slipping direction of ground plane

The s is represented as equation (7), (8) and cos and

sin are approximated as equation (9), (10)

z

s

s

F

K

3

2 2 2 2

tan

1 s

K

K

s

s

(8)

s

K

K

s

(9),(10) The expression of local Cp is obtained from equation

(6) by partial differential in the slip angle It is shown

as follows:

s z

s s p

F

s K s

K

9 cos

Note that C p is local Cp of certain tire Using

described above, target yaw moment and target local Cp

that is combined two tires are expressed as follows:

) , ( ) , (

2 X ZL, L L X ZR, R R

t

REF l F F s F F s

) , ( ) ,

p

REF

r C F s C F s

Note that M REF is the target yaw moment that is

defined by DYC and it is generated by difference of

driving force; C rREF is the target rear local Cp to satisfy

a stability condition It is calculated by equation (4) with

some additional margin Equations (12) are expressions

to relate yaw moment to cornering force But, they are

functions of slip ratio, not of driving force Furthermore,

it is difficult to resolve analytically So, at first, a target

slip ratio is solved by numerical approach And then, a

driving force is calculated with equation (5)

And now, an example of figure of equation (11) is

shown as the right hand of fig.5 In this figure, the

direction of slip ratio to increase local Cp is changed

with slip angle A larger slip ratio is required to

decrease local Cp when large slip angle It is mismatch sensuously And, it is unsuitable for convergence calculation because of having local solution So, the equation (11) is approximated as equation (11)’ An example of figure is shown in the left hand of fig.5 It is shown that the local Cp is increasing on very large slip angle In this logic, it is assumed as 0 Because such a large angle is all skid area even if slip ratio equal to zero And this approximated local Cp is calculated smaller than original local Cp So, it is considered safe side error

2 2

2

2

3 3

1 3

1 1

tan 3

1 cos

s F

K s

F

K s

F

K K

C

z s z

s z p

(11)’

Fig 5 An example of local Cp and approximated it

[Limitation of Driving Force]

Now, it thinks about the following expression

concerning yaw moment Note that W M is proper value

of weight value; M is yaw moment at a certain s L and s R

2

) , ( L R

REF M

M W M M s s

The example of plotting this equation is shown in

fig.6 L M becomes 0 when target yaw moment is filled,

and it is identified as a line in s L -s R space

Same as L M , L CP is thought as equation (15) As

same as L M , L CP becomes 0 when the target is filled

2

) , ( L R

r REF r CP

CP W C C s s

Note that C r is combined local Cp at a certain s L and

s R In these expressions, s L and s R that wants to be

obtained where L CP should be minimized on the

condition of L M equal to zero In other word, there is

possibility that L CP doesn't become zero in the restraint

condition of L M equal to zero.In this logic, find a proper yaw moment is more important rather than finding minimum

For looking the figure of L M carefully, a direction to

minimize L M becomes vertical to the line of L M equal to

0 as it approaches the line And the shape is expected simple like fig 6 So, moving direction on convergence

calculation is considered to separate L M from L CP

At first, a direction to minimize L M value (vector A)

is calculated on a certain pair of s L and s R Next, a

direction for L CP (vector B) is calculated Then, the vector C is defined as the vector B restricted the vertical direction of the vector A The moving direction on convergence calculation is defined to use the vector A and the vector C as shown in fig 7 But in the case of

not becoming L CP equal to zero in L M equal to 0, s L and

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

4

slip angle(deg)

0.1 0.08 0.04 0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

4

slip angle(deg)

0.1 0.08 0.04 0

Slip ratio

To increase Local Cp, Slip ratio

is increased in this area

Direction of slip ratio increasing

Opposite direction to increase Local Cp, unlike the left area

Direction of slip ratio increasing

Slip ratio

Local Cp is assumed as 0 Because, ratio equal to zero

Direction where slip ratio increases

s R will be calculated as excessive large value To begin

with, the purpose of this logic is to limit a driving force

on safe value, not to find out the optimal value So, the

limited slip ratio is searched in only adhesion area that

means that  s is greater than 0

By the way, the slip angle , tire load F Z and

tire-road friction parameter are required in this logic

And, cornering stiffness K and driving stiffness K s are

required, too Heretofore, the research to estimate these

parameters has been done [10][11][12] In this paper,

the controller uses true values of these parameters

-0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

sR

sL

Direction of Slope

a vector A

Fig 6 Example of LM

s L

s R

Line of L M = 0

Line of L CP = 0

vector A

direction of vector A

vector B vector C

The direction to find

the convergence point

The convergence point

Fig 7 Schematic of direction to find the optimized point

4 VERIFICATION AND EVALUATION

4.1 Target Vehicle

The main parameters of the target vehicle system

are shown in table 1.The speed torque diagram of the

motor is shown in fig.8 The ability of the motor is

limited under this line An example of the vehicle

performance is shown in fig.9 A capability of yaw rate

change is in this range when the vehicle is turning on

0.3g of lateral acceleration The reason why the

capability decreases in high-speed area is not only the

motor ability but also aerodynamics drag However, the

figure shows that the vehicle has sufficient ability from

low to middle speed

Table 1 Vehicle System Parameters

0 200 400 600 800 1000 1200 1400

Velocity(km/h)

Fig 8 Vehicle Speed to Tire Torque

-15 -10 -5 0 5 10 15 20 25 30 35

Velocity(km/h)

Motor ability limit

Nominal Yaw Rate

Capability of Yaw Rate change

Stability limit

Motor ability limit Stability limit

Fig 9 Example of Capability of yaw rate change by DYC (Nominal vehicle is turning on 0.3(g).)

4.2 Methodology

The control logic is evaluated by a computer simulation The simulation was conducted using veDYNA that is a product of TESIS Corporation And the benefit for driver by DYC system is checked using a motion-base driving simulator

[Cases for computer simulation]

We conducted several case including follows But,

a result of following (1) is described in this paper (1) Turn in Acceleration

In this case, driving force limitation logic is checked in this case

(2) Disturbance reduction performance

A simple DYC logic that follows a yaw rate target

is checked in this case And, an influence of drive shaft elasticity to control performance is checked

[Cases for Driving Simulator]

We conducted several case including follows using

a driving simulator shown in Fig 10[13] The driving simulator has a single-seat cabin, which can move 3 meters in lateral direction with 0.8 g, 160 degrees in

yaw rotation and 40 degrees in roll and pitch rotations

by electrical motors to provide motion sensation to the

driver and gives him/her a frontal view, an engine sound,

and a steering control feel

(3) Straight -ahead driving in crosswind disturbance

How the disturbance reduction control performance

worked effectively was confirmed

(4) Lane change feeling

The influence on driver's operation by the target

yaw rate following

In this paper, the result of (3) above is described

Fig.10 Driving Simulator

4.3 Simulation Result

Simulations that steering wheel angle was held as

constant and vehicle turned in acceleration were

conducted The case of that steering wheel angle is 40

degree and road friction factor is 0.5 are shown in fig

11 to 13 In this case, acceleration pedal was opened

20% at first, and then, it was opened 40%

-20

0

20

40

60

80

100

120

140

0.9[deg]

0.6[deg]

0.2[deg]

0.0[deg]

-0.2[deg]

-0.5[deg]

-0.7[deg]

-0.9[deg]

-1.1[deg]

-1.3[deg]

-1.5[deg]

-1.7[deg]

-2.0[deg]

-2.2[deg]

-2.6[deg]

-3.0[deg]

-3.6[deg]

-4.5[deg]

0.9[deg]

0.6[deg]

0.4[deg]

0.1[deg]

-0.3[deg]

-0.6[deg]

-1.0[deg]

-1.5[deg]

-2.1[deg]

-2.9[deg]

-4.1[deg]

-5.6[deg]

-7.1[deg]

-8.4[deg]

-9.1[deg]

-9.1[deg]

-8.1[deg]

-6.2[deg]

0.9[deg]

0.6[deg]

0.4[deg]

0.1[deg]

-0.3[deg]

-0.6[deg]

-1.0[deg]

-1.5[deg]

-2.1[deg]

-2.7[deg]

-2.6[deg]

-2.5[deg]

-2.6[deg]

-2.5[deg]

-2.6[deg]

-2.5[deg]

-2.6[deg]

-2.6[deg]

X[m]

DYC, TRC and DFL

DYC Only DYC and TRC

Inner wheel is spinning out and slip angle is increasing

The stable state is maintained

Slip angle is being settled But maximum slip angle is large (9.1deg)

Acceleration pedal is opened from 20% to 40% at this point

* The represented angle values are slip angle in the moment

Fig 11 vehicle trajectories on acceleration in turn

Vehicle trajectories are shown in fig.11 It is

represented the result of 20 sec The DYC only vehicle

is turning inner line and slow, because the inner wheel

is spinning out soon after acceleration force changed So,

only driving force of outer side is remained It cause

less driving force and generates uncontrolled yaw

moment And then, the yaw moment will make

instability since slip angle continues to increase The vehicle of DYC and TRC is turning outer line And the maximum slip angle is a little large The vehicle of DYC, TRC and DFL is turning center line It is looks like stable since slip angle is only 2.6 degree

0 5 10 15 20

DYC DYC+TRC DYC+TRC+DFL Reference

0 1 2 3 4 5 6

2 )

DYC DYC+TRC DYC+TRC+DFL

0 10 20 30 40 50 60 70

Time(s)

DYC DYC+TRC DYC+TRC+DFL

D

A

B

C

Fig 12 Result of vehicle state

-500 0 500 1000 1500 2000 2500

DYC+TRC+DFL Limit

-500 0 500 1000 1500 2000 2500

DYC+TRC DYC+TRC+DFL Limit

0 1 2 3 4

5x 10 4

Time(s)

F

DYC+TRC+DFL (Vehicle Output) Force Limit(Controller)

DYC+TRC (Vehicle Output)

Long Forces are limited by TRC

E

Long Forces are limiting by DFL after this time

Front (DYC+TRC+AFL)

Rear Limit

Rear (DYC+TRC+AFL) Rear (DYC+TRC)

Fig 13 Longitudinal force and Estimated local Cp The yaw rate, lateral acceleration and vehicle speed are shown in fig 12 The inner wheel of DYC only vehicle is spinning out after point A So, driving force is

not able to be generated enough, and the slope of

velocity is moderate incline The DYC, TRC and DFL

vehicle is able to be following the reference yaw rate

well as shown at pointed as B The DYC and TRC

vehicle is following, too But on the peak region of yaw

rate and lateral acceleration, pointed as area C, it looks

like unstable It is considered that DYC system isn’t

able to generate enough additional force and the vehicle

characteristics become unstable Therefore, the vehicle

motion is unstable-ish and it is not able to keep the

speed as pointed on D

The longitudinal force of rear axle and estimated

local Cp is shown in fig.13 DYC and TRC vehicle and

DYC, TRC and DFL vehicle are generating the same

forces at first But, after the time pointed on D, the

driving force is restricted on DYC, TRC and DFL

vehicle The result by this control, local Cp becomes

lower than stable limit on DYC and TRC vehicle But,

local Cp of DYC, TRC and DFL vehicle doesn’t

become lower than the limit as pointed on F

4.4 Driving Simulator Result

A bias and random disturbance of crosswind was

occurred when a vehicle moving straight-ahead The

result of this test is shown as fig.14 It shows steering

wheel angle on the frequency domain Even when the

vehicle is driven straight, the driver is always steering a

low frequency of about 0.1Hz The DYC compensation

was not effective for this frequency But, reducing large

operation angle of steering wheel was confirmed on

frequency of 0.8 to 1.1Hz The, the total angle of

steering wheel is reduced as fig 15 So, one of effect for

driver of DYC is confirmed

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

NoCtl FWD RWD

(Reference)DYC

Vehicle with FWD

DYC Vehicle

with RWD

Base Vehicle(RWD)

Frequency(Hz)

Fig 14 Steering wheel angle on frequency domain

5 CONCLUSION

A study of dynamics performance improvement by

rear right and left independent drive system was

conducted in this paper At first, a control system that

prevents a possible cause of unstable was designed in

addition to simple direct yaw control system And then,

the performance of the system and effect on driver’s

operation were carried out on computer simulation and

driving simulator.In the simulation, the possible turning

performance was checked on the steady state turning

And, control logic of preventing to become unstable

was confirmed on the acceleration turn And then, the

response of the motor that influences the performance of

the DYC was confirmed by inflicting with a sidewind

disturbance In the driving simulator, it was confirmed that DYC was possible to reduce driver’s operation and stabilize vehicle motion Therefore, the target vehicle system was confirmed to improve the performance sufficiently and to affect well for driver’s operation

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