research article numerical simulation analysis of an oversteer in-wheel...

Research ArticleNumerical Simulation Analysis of anOversteer In-Wheel Small Electric Vehicle Integrated withFour-Wheel Drive and Independent Steering

Muhammad Izhar Ishak,1 Hirohiko Ogino,2 and Yoshio Yamamoto3

1Course of Science and Technology, Tokai University, 4-1-1 Kitakaname, Hiratsuka-shi, Kanagawa 259-1292, Japan2Department of Prime Mover Engineering, Tokai University, 4-1-1 Kitakaname, Hiratsuka-shi, Kanagawa 259-1292, Japan3Department of Precision Engineering, Tokai University, 4-1-1 Kitakaname, Hiratsuka-shi, Kanagawa 259-1292, Japan

Correspondence should be addressed to Muhammad Izhar Ishak; [email protected]

Received 22 February 2016; Revised 1 May 2016; Accepted 11 May 2016

Academic Editor: Shankar Subramanian

Copyright © 2016 Muhammad Izhar Ishak et al.This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in anymedium, provided the originalwork is properly cited.

Similar to conventional vehicle, most in-wheel small EVs that exist today are designed with understeer (US) characteristic.They aresafer on the road but possess poor cornering performance.With recent in-wheelmotor and steer-bywire technology, high corneringperformance vehicle does not limit to sport or racing cars. We believe that oversteer (OS) design approach for in-wheel small EVcan increase the steering performance of the vehicle. However, one disadvantage is that OS vehicle has a stability limit velocity. Inthis paper, we proposed a Four-Wheel Drive and Independent Steering (4WDIS) for in-wheel small EV with OS characteristic.Theaim of implementing 4WDIS is to develop a high steer controllability and stability of the EV at any velocity. This paper analysesthe performance of OS in-wheel small EV with 4WDIS by using numerical simulation. Two cornering conditions were simulatedwhich are (1) steady-state cornering at below critical velocity and (2) steady-state cornering over critical velocity. The objectiveof the simulation is to understand the behavior of OS in-wheel small EV and the advantages of implementing the 4WDIS. Theresults show that an in-wheel small EV can achieve high cornering performance at low speed while maintaining stability at highspeed.

1. Introduction

In recent years, concerns over environmental issues by petro-leum-based transportations along with the issue of fossil fueldepletion around the world have led to renewed interest overelectric vehicle (EV). Small EVs have become prominent asa means of transportation, especially in urban areas wherethere are limited spaces [1, 2]. The driving method of such anelectric vehicle can be divided into two types. The most basictype is the central motor system, where a conventional com-bustion engine is replaced with an electric motor. The othertype is the in-wheel motor system, where a driving motor islocated near the hub of each wheel. We believe that the in-wheel motor system has tremendous potential in the futureof EVs for its compact size and high-energy efficiency. In pastresearch, results show that the in-wheel motor system offers

more freedom of movement for each wheel and can be gov-erned separately by control systems such as the antilock brakesystem (ABS) and the traction control system (TCS) [3–5].

A few car manufacturers have marketed compact, cheap,and reliable in-wheel small electric vehicle that is aimed fordaily usage. Similar to conventional vehicle, most in-wheelsmall EVs that exist today are designed with understeer (US)characteristic [6]. Even though they are safer on the road,they have poor cornering performance.With in-wheel motorand steer-by-wire technology nowadays, high cornering per-formance vehicle does not limit only sport or racing cars.We believe that oversteer (OS) design approach for in-wheelsmall EV can increase the steering response and lower thesteering input with shorter cornering radius. However, onedisadvantage of OS characteristic is that it has a stability limitvelocity [7]. In this paper, we proposed a Four-Wheel Drive

Hindawi Publishing CorporationInternational Journal of Vehicular TechnologyVolume 2016, Article ID 7235471, 12 pageshttp://dx.doi.org/10.1155/2016/7235471

2 International Journal of Vehicular Technology

Yaw

rota

tiona

l spe

ed

Velocity

OS stableregion

OS unstableregion

OS

US

Vc

Figure 1: Steady-state yaw rotational speed to velocity between OSand US characteristic.

and Independent Steering (4WDIS) for in-wheel small EVthat is designed with OS characteristic. The aim of imple-menting 4WDIS is to develop a high steer controllability andstability of an OS in-wheel small EV at any velocity.

This paper analyses the performance of 4WDIS on anOS in-wheel small EV by using numerical simulation. Twocornering conditions were simulated which are (1) steady-state cornering at below critical velocity and (2) steady-statecornering over critical velocity. The objective of the simula-tion is to understand the behavior of anOS in-wheel small EVand the advantages of implementing the 4WDIS.The 4WDISis governed by an Intelligence SteeringControl System (ISCS)that evaluates the dynamics of the EV, the surroundingcondition (i.e., narrow space), the road surface (i.e., dry, wetand icy road), and vehicle stability (i.e., crosswind and softcollision) in response to the drivers driving input. The ISCSwill control the four-wheel driving and braking with eachin-wheel motor and steer angle by the steering actuatorsto ensure safe maneuverability. The results show that, byimplementing 4WDIS, an OS in-wheel small EV can achievehigh cornering performance and maintain stability at anyspeed.

2. Main Symbols

Nomenclature shows the constant parameters and variableswith the meaning, value, and unit used in this paper, respec-tively.

3. Limitations of OS and US Characteristics

A basic understanding of OS and US characteristic is neces-sary before any control method can be implemented. Figure 1shows the relationship of the steady-state yaw rotational

Side

slip

angl

e

Velocity

OS

US

OS stableregion

OS unstableregion

Vc

Figure 2: Steady-state side-slip angle to velocity betweenOS andUScharacteristic.

speed to velocity, and Figure 2 shows the relationship ofsteady-state side-slip angle to velocity between OS and UScharacteristic during steady-state cornering at constant steerangle. Based on the figure, the OS characteristic is separatedinto stable region and unstable region depending on thevelocity of the vehicle. When the vehicle velocity 𝑉 isbelow the stability limit velocity 𝑉

𝑐, OS vehicle can achieve

steady-state cornering with a higher yaw rotational speedin comparison to US characteristic. A higher yaw rotationalspeed should also mean that the vehicle can achieve a shorterturning radius. The side-slip angle becomes negative as theabsolute magnitude increases with velocity. This means thatwhen the velocity increases, the vehicle will point to the innerside of the circular path of the cornering.

However, in the case of the velocity 𝑉 ≥ 𝑉𝑐, the yaw

rotational speed and the side-slip angle will produce aninfinite value with regard to a constant steer angle. It doesnotmean that the vehicle cannot be driven above this velocitybut it is important to note that the vehicle motion is unstable.For this particular reason, most vehicles are manufacturedwith US characteristic that has no stability limit velocity asa compensation to low steering response. Nonetheless, USvehicle also has a tendency to cause accidents at high speeddue to its restrictive steering.

4. Four-Wheel Drive and Independent Steering(4WDIS) Approach

4.1. Steering Characteristics. Two-wheel steering (2WS) orfront wheel steering system (FWS) is generally known inall moving vehicles. This system works by rotating the frontwheel in an angle that produces yawmotion, which then pushthe rear wheels with no steer angle sideways. A 2WS vehiclewith oversteer characteristicwill have a shorter turning radiusbut it is difficult to stabilize with front wheel steering alone.

International Journal of Vehicular Technology 3

Phase 3

Phase 1 Phase 2

Figure 3: 4WDIS steering characteristics.

Four-wheel steering (4WS) has been introduced and mar-keted by Honda since 1987 in their Prelude model and thenwas joined by other car manufacturers to promote stabilityfor conventional vehicle.The trend was short-lived due to themechanical constrain of the system [8]. Nonetheless, with in-wheel motor system and steer-by-wire technology, a smallelectric vehicle can have the freedom of design and layoutto implement Four-Wheel Drive and Independent Steering(4WDIS). In this research, themain purpose of implementing4WDIS is to have high cornering performance for OS in-wheel small EV while maintaining stability at any speed [9].Considering that eachwheel’s driving torque can be governedseparately and the direction of the wheels can bemanipulatedwith certain control, we had concluded that the steeringmodes for 4WDIS as in Figure 3 and the descriptions are asfollows:

(a) Opposite Steering (Phase 1). The rear wheels will turnon the opposite direction as the front wheels. Thiswill increase the vehicle yaw rotational speed, whichtighten the turning radius.

(b) Parallel Steering (Phase 2).The rear wheels will rotatein the same direction parallel to the front. This steer-ing does not generate yaw rotational speed but insteadreduces the yaw rotational speed.

(c) “Zero-Radius” Steering (Phase 3). The front wheelshave to be “toe-in” position and the rear wheels in“toe-out” position. The driving direction of the leftand right is in opposite. This allows the vehicle torotate at its yaw rotational center.

4.2. Intelligence Steering Control System (ISCS). An Intelli-gence Steering Control System (ISCS) is used to govern the4WDIS. The ISCS evaluates the dynamics of the EV, thesurrounding condition (i.e., narrow space), the road surface(i.e., dry, wet, and icy road), and vehicle stability (i.e., cross-wind and soft collision) with regard to the drivers steeringinput. After the evaluation, the ISCS will choose the suitable

Figure 4: Analysis vehicle model of Toyota COMS.

steering characteristics to ensure stability and maneuverabil-ity.

In this paper, the evaluated parameter focuses on thedynamic of the in-wheel small EV and dry road surface.Thus,when studying the cornering performance of OS in-wheelsmall EV, only the alternation between phases 1 and 2 asshown in Figure 3 can be observed in the results.

5. Analysis Vehicle Model

Toyota COMS AK10E-PC shown in Figure 4, which is an in-wheel small electric vehicle manufactured by Toyota AutoBody Co., was used as an analysis vehicle model in thesimulation. The vehicle uses a 2WD in-wheel motor and hasa front wheel steering. However, in the simulation, we addedtwo in-wheel motors to the front wheels and two-steeringactuator at the rear wheels. Thus, the mass of the vehiclemodel is increased from the actual vehicle. Furthermore, theweight distribution of the vehicle model was modified so thatthe weight shifted to the rear to represents a highly OS in-wheel small EV while the dimensions of the vehicle remainthe same.

6. Simulation Block Diagram

Figure 5 shows the simulation block diagram for the vehiclemodel and the ISCS. The vehicle model, which is an OSin-wheel small EV equipped with 4WDIS, is calculated bya nonlinear system. Much of past researches adopted easyway of modelling a control system based on a vehicle withlinear characteristics. By this assumption, other parametersthat could influence the dynamic motion of the vehicle areneglected and the modelled control system is deemed to below precision [10–13]. In this paper, the purpose of adoptingnonlinear system for calculating the vehicle model is that thesystem represents more precisely an actual vehicle. However,a feedback control cannot be executed directly to nonlinearsystem because of yaw rotational speed coupling with thevelocity components as expressed in dynamic equation ofmotion in later section. As an option, the ISCS, which is astate observer unit that consist of a feedback controlled linearsystem, is used to control the vehicle model. Each modelin the simulation block will be explained in detail in thefollowing sections.


B

C

A

H

𝜃r

+

++

+

+

+

+

𝜃f

Uf

Ur

𝛾∗

𝛾

𝛽

𝛽∗xx 1

S

−

Vehicle(nonlinear model)

State observer unit

−gT

C1T

C2T

Figure 5: Simulation block diagram.

−YRL sin𝜃R

YRL cos𝜃R 𝛽RL

𝜃R

YFL cos𝜃F 𝛽FL

−YFL sin𝜃F

𝛾

dR dF

XRR sin𝜃R 𝛽RR

XRR cos𝜃R

lR lF

XFR sin𝜃F 𝛽FR

𝜃F𝜃R

𝜃F

XFR cos𝜃F

Figure 6: Force vector.

7. Vehicle Model

7.1. Nonlinear Dynamic Equations. The vehicle model hassix degrees of freedom: three translational along the 𝑥-, 𝑦-, and 𝑧-axes and three rotational about the 𝑥-, 𝑦-, and 𝑧-axes. In this study, however, a planar motion is assumed sothat a translation along the 𝑧-axis and rotations about the𝑥- and 𝑦-axes are disregarded. Figure 6 depicts the forcevector used to construct the dynamic equations of motion forthe vehicle and for the yaw rotational speed. Unlike lineardynamic equation, the vehicle side-slip angle at the centerof gravity and wheels steer angle is not considered as small.Thus, we took the consideration that the longitudinal andlateral acceleration are influenced by the yaw rotational speed,which can be seen in (1).

The assumptionsmentioned above necessitate calculatingthe dynamic equations for longitudinal and lateral velocities,

including the coupling of the yaw rotation speed with thevelocities:

𝑚(𝑑𝑢

𝑑𝑡− V𝛾)

= (𝑋𝐹𝑅+ 𝑋𝐹𝐿) cos 𝜃

𝐹+ (𝑋𝑅𝑅+ 𝑋𝑅𝐿) cos 𝜃

𝑅

− (𝑌𝐹𝑅+ 𝑌𝐹𝐿) sin 𝜃

𝐹− (𝑌𝑅𝑅+ 𝑌𝑅𝐿) sin 𝜃

𝑅,

𝑚(𝑑V𝑑𝑡+ 𝑢𝛾)

= (𝑋𝐹𝑅+ 𝑋𝐹𝐿) sin 𝜃

𝐹+ (𝑋𝑅𝑅+ 𝑋𝑅𝐿) sin 𝜃

𝑅

+ (𝑌𝐹𝑅+ 𝑌𝐹𝐿) cos 𝜃

𝐹+ (𝑌𝑅𝑅+ 𝑌𝑅𝐿) cos 𝜃

𝑅,


𝐼𝑑𝛾

𝑑𝑡

= 𝑙𝐹[(𝑋𝐹𝑅+ 𝑋𝐹𝐿) sin 𝜃

𝐹+ (𝑌𝐹𝑅+ 𝑌𝐹𝐿) cos 𝜃

𝐹]

+ 𝑙𝑅[(𝑋𝑅𝑅+ 𝑋𝑅𝐿) sin 𝜃

𝑅+ (𝑌𝑅𝑅+ 𝑌𝑅𝐿) cos 𝜃

𝑅]

+𝑑𝐹

2[(𝑋𝐹𝑅+ 𝑋𝐹𝐿) cos 𝜃

𝐹+ (𝑌𝐹𝑅+ 𝑌𝐹𝐿) sin 𝜃

𝐹]

+𝑑𝑅

2[(𝑋𝑅𝑅+ 𝑋𝑅𝐿) cos 𝜃

𝑅+ (𝑌𝑅𝑅+ 𝑌𝑅𝐿) sin 𝜃

𝑅] .

(1)

7.2. Nonlinear Tire Characteristic. In the case of linear model,the forces acting on the vehicle is determined by the motionsof the vehicle that are mainly side-slip angle and yawrotational speed at the center of gravity. In our study, theacting forces are influenced by the wheels of the vehicle.Based on Fiala’s theory, eachwheel of the vehicle aremodelledas a brush tire [14]. This theory assumes that with side-slipangle, the tire tread base deforms elastically in the lateral andlongitudinal direction of the wheel. Due to this, the equationsfor friction and lateral forces are dependent on the value ofwheels side-slip angle, slip ration, and friction coefficient.The deformation of the tire tread rubber is shown by thedimensionless variable 𝜉

𝑖𝑗:

𝜉𝑖𝑗= 1 −

𝐾𝜌𝜆𝑖𝑗

3𝜇𝑖𝑗𝑊𝑧(1 − 𝜌

𝑖𝑗)

, (2)

where

𝜆𝑖𝑗= √𝜌𝑖𝑗

2 + (

𝐾𝛽

𝐾𝜌

)

2

tan2𝛽𝑖𝑗,

𝐾𝜌=𝑏𝑙𝑇

2

2𝐾𝑥,

𝐾𝛽=𝑏𝑙𝑇

2

2𝐾𝑦.

(3)

When 𝜉𝑖𝑗> 0, the contact surface comprises adhesive and

slip region. Thus, longitudinal force and lateral force can bewritten as

𝑋𝑖𝑗= −𝐾𝜌𝜌𝑖𝑗𝜉𝑖𝑗

2

− 6𝜇𝑖𝑗𝑊𝑧

𝜌𝑖𝑗

𝜆𝑖𝑗

(1

6−1

2𝜉𝑖𝑗

2

+1

3𝜉𝑖𝑗

3

) ,

𝑌𝑖𝑗= −𝐾𝛽(1 + 𝜌

𝑖𝑗) tan𝛽

𝑖𝑗𝜉𝑖𝑗

2

− 6𝜇𝑖𝑗𝑊𝑧(

𝐾𝛽tan𝛽𝑖𝑗(1 + 𝜌

𝑖𝑗)


)

⋅ (1

6−1

2𝜉𝑖𝑗

2

+1

3𝜉𝑖𝑗

3

) .

(4)

However, when 𝜉𝑖𝑗≤ 0, the contact surface only holds the slip

region. Therefore, the longitudinal force and lateral force canbe written as

𝑋𝑖𝑗= −𝜇𝑖𝑗𝑊𝑧

𝜌𝑖𝑗

𝜆𝑖𝑗

,

𝑌𝑖𝑗= −𝜇𝑖𝑗𝑊𝑧(

𝐾𝛽tan𝛽𝑖𝑗(1 + 𝜌

𝑖𝑗)


) .

(5)

Here, the integral 𝑖 represents front and rear, while the inte-gral 𝑗 represents right and left. The side-slip angle 𝛽

𝑖𝑗which

is mainly 𝛽𝐹𝑅, 𝛽𝐹𝐿, 𝛽𝑅𝑅, 𝛽𝑅𝐿

is given as follows:

𝛽𝐹𝑅= tan−1 (

V + 𝑙𝐹𝛾

𝑢 + 𝑑𝐹𝛾/2

) − 𝜃𝐹,

𝛽𝐹𝐿= tan−1 (

V + 𝑙𝐹𝛾

𝑢 − 𝑑𝐹𝛾/2

) − 𝜃𝐹,

𝛽𝑅𝑅= tan−1 (

V − 𝑙𝑅𝛾

𝑢 + 𝑑𝑅𝛾/2

) − 𝜃𝑅,

𝛽𝑅𝐿= tan−1 (

V − 𝑙𝑅𝛾

𝑢 − 𝑑𝑅𝛾/2

) − 𝜃𝑅.

(6)

The slip ratio 𝜌𝑖𝑗can be defined as the traction between the

road and the tire surface and is written as

𝜌𝑖𝑗=

𝑟𝜔𝑖𝑗− 𝑢

𝑟𝜔𝑖𝑗

. (7)

Then, by using the slip ratio value, the coefficient of friction𝜇𝑖𝑗can be approximated by the following equation:

𝜇𝑖𝑗= −1.10𝑘 × (𝑒

35𝜌𝑖𝑗 − 𝑒0.35𝜌𝑖𝑗) , (8)

where

𝑘 = 1.0 (dry asphalt) ,

𝑘 = 0.2 (icy road) .(9)

8. State Observer Unit

8.1. Linear Dynamic Equations. The ISCS consist of a stateobserver unit.This unit uses linear dynamic equations for thetranslational motion and yaw rotational motion such as

𝑚V(𝑑𝛽∗

𝑑𝑡+ 𝛾∗

) = 2𝑌𝐹+ 2𝑌𝑅, (10)

𝐼𝑑𝛾∗

𝑑𝑡= (2𝑙𝐹𝑌𝐹− 2𝑙𝑅𝑌𝑅) cos𝛽∗. (11)

It is to be noted that there is no difference in the char-acteristics of the left and right tires due to linearity; hence,a 2-wheel model is derived from the equations. The side-slip angle 𝛽∗ is assumed to be small, which then lead to theassumption that the direction perpendicular to the travelingdirection of the vehicle almost coincides with the lateral


direction 𝑦. Therefore, no coupling exists between the yawrotational speed and the vehicle’s translational velocity.

The linear lateral force is defined by

𝑌𝐹= −𝐾𝐹𝛽𝐹= −𝐾𝐹(𝛽∗

+𝑙𝐹

V𝛾∗

− 𝜃𝐹) ,

𝑌𝑅= −𝐾𝑅𝛽𝑅= −𝐾𝑅(𝛽∗

−𝑙𝑅

V𝛾∗

− 𝜃𝑅) .

(12)

Here, the cornering stiffness of the front and rear wheelsis 𝐾𝐹and 𝐾

𝑅. These values determine the sensitivity of the

ISCS [15]. In contrast, with the tire characteristics of thenonlinear model, the actual vehicle motion determines thelinear model lateral forces, which are related to the side-slip angle, yaw rotational speed, and front and rear steeringangles.The above equations can be substituted into the lineardynamic equations of motion (10) and the yaw rotationalspeed (11).

8.2. Linearized Differential Equation. The linearized differen-tial equation represents the linear vehicle dynamic equationof motion for the state observer. It is arranged as a set of first-order ordinary differential equations in the vector state form:

�� = 𝐴𝑥 + 𝐵𝑈𝑅+ 𝐶𝑈𝐹,

𝑦𝛽= 𝛽∗

= C1

𝑇

𝑥,

𝑦𝛾= 𝛾∗

= C2

𝑇

𝑥,

(13)

where

𝑥 = [𝛽∗

𝛾∗

]𝑇

,

C1

𝑇

= [1 0]𝑇

,

𝑈𝐹= 𝜃𝐹,

C2

𝑇

= [0 1]𝑇

,

𝑈𝑅= 𝜃𝑅,

𝐴 = [

𝑎 𝑏

𝑐 𝑑]

=

[[[[

[

−2 (𝐾𝐹+ 𝐾𝑅)

𝑚V−1 −

2 (𝐾𝐹𝑙𝐹− 𝐾𝑅𝑙𝑅)

𝑚V2

−2 (𝑙𝐹𝐾𝐹− 𝑙𝑅𝐾𝑅)

𝐼

2 (𝑙𝐹

2

𝐾𝐹+ 𝑙𝑅

2

𝐾𝑅)

𝐼V

]]]]

]

,

𝐵 = [

𝑒

𝑓] =

[[[

[

2𝐾𝑅

𝑚V

−2𝑙𝑅𝐾𝑅

𝐼

]]]

]

,

𝐶 = [

𝑘

𝑙] =

[[[

[

2𝐾𝐹

𝑚V2𝑙𝐹𝐾𝐹

𝐼

]]]

]

.

(14)

Table 1: Weighting matrices characteristic.

Largevalue Constant |𝑥| |��| |𝑈|

𝑞11

𝑞22, 𝑤 Reduce Increase Increase

𝑞22

𝑞11, 𝑤 Increase Reduce Increase

𝑤 𝑞11, 𝑞22

Increase Increase Reduce

The state vector 𝑥 represents the side-slip angle and yawrotational speed of the vehicle.The steering angles of the frontand rear wheels are the inputs of this system. The value forthe front wheel angle 𝜃

𝐹is a driver-selected input whereas the

rear wheel angle 𝜃𝑅is initially 0 degrees. During high-speed

cornering, the rear wheel steering is used as the control inputby introducing a feedback gain −𝑔𝑇:

𝑈𝑅= −𝑔𝑇

𝑥 + 𝜃𝑅. (15)

8.3. Optimal Control. In order to find the optimal control forthe linearized differential equation, the following evaluationfunction 𝐽 is employed:

𝐽 = ∫

∞

0

(𝑞11𝑥2

+ 𝑞22��2

+ 𝑤𝜃2

𝑟) 𝑑𝑡

= ∫

∞

0

(𝑥𝑇

𝑄𝑥 + 𝑤𝜃2

𝑟) 𝑑𝑡,

(16)

where

𝑄 = [

𝑞11

0

0 𝑞22

] (17)

in which 𝑞11, 𝑞22, and 𝑤 are appropriately chosen constant

weighting matrices for the state vector 𝑥, the first-orderdifferential of state vector ��, and the control input 𝑈

𝑅,

respectively. Table 1 shows the characteristics of the weightingmatrices value that control the state and control value. Thecontrol input has its own high gain𝐻 and thus the weightingmatric𝑤 = 1.Theweightingmatrices of 𝑞

11and 𝑞22were used

to stabilized the state vector, which is yaw rotational speedand side-slip angle to prevent it from reaching infinite valueby the oversteering characteristic of the vehicle. The controlinput weighting matric 𝑤 = 1.

The optimal solution for 𝐽 can be designed if 𝑄 is apositive definite matrix and the state observer control input𝑈𝑅is given by

𝑈𝑅= −

1

𝑤𝐵𝑇

𝑃𝑥 + 𝜃𝑅, (18)

where−𝑔𝑇

= −1

𝑤𝐵𝑇

𝑃. (19)

With 𝑃 = 𝑃𝑇

≥ 0 being the unique positive-semidefinitesolution of the algebraic Riccati equation,

𝐴𝑇

𝑃 + 𝑃𝐴 − 𝑤−1

𝑃𝐵𝐵𝑇

𝑃 = −𝑄,

[

𝑎 𝑏

𝑐 𝑑]

𝑇

𝑃 + 𝑃[

𝑎 𝑏

𝑐 𝑑] − 𝑤

−1

𝑃[

𝑒

𝑓] [𝑒 𝑓]

𝑇

𝑃

= −[

𝑞10

0 𝑞2

] .

(20)


The unique positive-semidefinite 𝑃 can also be expressed as

𝑃 = [

𝜀 𝜙

𝜓 𝜖] . (21)

Thus, (20) can be expanded as

𝑎𝜀 + 𝑐𝜓 + 𝑎𝜀 + 𝑐𝜙

−1

𝑤([𝑒2

𝜀 + 𝑒𝑓𝜙] 𝜀 + [𝑒𝑓𝜀 + 𝑓2

𝜙]𝜓) = −𝑞11,

𝑎𝜙 + 𝑐𝜖 + 𝑏𝜀 + 𝑑𝜙

−1

𝑤([𝑒2

𝜀 + 𝑒𝑓𝜙] 𝜙 + [𝑒𝑓𝜀 + 𝑓2

𝜙] 𝜖) = 0,

𝑏𝜀 + 𝑑𝜓 + 𝑎𝜓 + 𝑐𝜖

−1

𝑤([𝑒2

𝜓 + 𝑒𝑓𝜖] 𝜀 + [𝑒𝑓𝜓 + 𝑓2

𝜖] 𝜓) = 0,

𝑏𝜙 + 𝑑𝜖 + 𝑏𝜓 + 𝑑𝜖

−1

𝑤([𝑒2

𝜓 + 𝑒𝑓𝜖] 𝜙 + [𝑒𝑓𝜓 + 𝑓2

𝜖] 𝜖) = −𝑞22.

(22)

Finally, the output of the vehicle model and the stateobserver was compared to form a close loop system. Ingeneral, there is no other method to directly measure theoutput of side-slip angle. However, yaw rotational speed of avehicle can be calculatedwith gyro sensors. In this system, theestimated yaw rotational speed output of state observer unitand the measured yaw rotational speed output of the vehiclemodel are compared and multiplied by high gain 𝐻. Then,this gain is fed back into the linear model. The linearizeddifferential equation of (13) becomes

𝑥 = 𝐴𝑥 + 𝐵𝑈𝑅+ 𝐶𝑈𝑓+ 𝐻��,

�� = 𝛾 − 𝛾∗

= C2

𝑇

�� − C2

𝑇

𝑥 = C2

𝑇

(�� − 𝑥) .

(23)

The renewed state observer control input can also be rede-fined as follows:

𝑈𝑅= −

1

𝑟𝐵𝑇

𝑃 (�� − 𝑥) + 𝜃𝑅. (24)

With this equation, the FFC for the 4WDIS in-wheel smallEV can be changed to a FBC that gives greater precision.

9. Simulation Procedures

9.1. Determine the Vehicle Model Steering Characteristic. Inthe previous section, we mentioned that the vehicle modelused the Toyota COMS specification and modified it to rep-resent anOS in-wheel small electric vehicle in the simulation.A simulation of a steady-state cornering at various velocitieswith regard to a constant front steer angle was done to deter-mine the stability limit velocity of the vehicle model before4WDIS could be implemented.The constant front steer angleis fix at 10∘ at 𝑡 = 10 s. When the yaw rotational speed andthe side-slip angle give an infinite value, the velocity beforethat moment is acknowledged as the stability limit velocity.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

10 20 30 40 50 60

Yaw

rota

tiona

l spe

ed (r

ad/s

)

Time (s)

Stability velocity limit

16km/h

10km/h

5km/h

15.5km/h

13km/h

15km/h

Figure 7: Steady-state yaw rotational speed to time change with2WS.

9.2. Implementation of 4WDIS with ISCS. A 4WDIS for OSin-wheel small EV was constructed as shown is previoussimulation block diagram. In order to investigate the perfor-mance of 4WDIS in depth, we have divided the simulation asfollows:

(1) Steady-state cornering below stability limit velocity.(2) Steady-state cornering over stability limit velocity.

Similar to previous simulation condition, a steady-statecornering of a 4WDIS in-wheel small EV at below stabilitylimit velocity and over stability limit velocity, with regard to aconstant front steer angle, was carried out.The constant frontsteer angle is fix at 10∘ at 𝑡 = 10 s. The results of the steady-state yaw rotational speed and steady-state side-slip angle for4WDIS are compared to the previous simulation.

10. Results and Discussion

10.1. Stability Velocity Limit of the OS Vehicle Model during2WS Cornering. A simulation of steady-state cornering wascarried out to determine the stability limit velocity of the OSvehicle model. Figures 7 and 8 show the results of the steady-state yaw rotational speed and steady-state side-slip anglewith regard to constant front wheel steer angle, respectively.Based on both of these graphs, in regard to constant frontsteer angle of 10∘, the stability limit velocity 𝑉

𝑐is 15.5 km/h.

At this velocity, the vehicle is stable and can reach themaximum steady-state yaw rotational speed of 1.01 rad/s witha maximum absolute magnitude of the steady-state side-slipangle of 0.301 rad. When the velocity is above 15.5 km/h, theyaw rotational speed and the side-slip angle will give aninfinite value. However, the vehicle can still be driven but it isvery unstable. This shows that we have successfully modelleda highly OS in-wheel small EV.

Nonetheless, we believe that even in the stable regionwhich is below the stability limit velocity, the OS small EVcan be improved. In Figure 7, when the constant velocity


Stability velocity limit

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

10 20 30 40 50 60

Side

-slip

angl

e (ra

d) Time (s)

15.5 km/h

13km/h

10km/h

15km/h

16km/h

5km/h

Figure 8: Steady-state side-slip angle to time change with 2WS.

Yaw

rota

tiona

l spe

ed (r

ad/s

)

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15Velocity (m/s)

Figure 9: Steady-state yaw rotational speed to velocity with 2WS.

increased, the vehicle model took longer time to generate aconstant yaw rotational speed. This is due to the increase inside-slip angle to the constant velocity. The relation betweensteady-state yaw rotational speed and velocity is plotted inFigure 9, while the relation between steady-state side-slipangle and velocity is plotted in Figure 10.

10.2. Steady-State Cornering below Stability Limit Velocity with4WDIS. Theoretically, OS vehicles can already produce highyaw rotational speed and stability when cornering below thestability limit velocity. Logically, any control system is unnec-essary in the stable region. We can assume that the corneringperformance in the stable region of the OS in-wheel small EVwill be suppressed by implementing the 4WDIS.

In this section, the control effect of 4WDIS implemen-tation onto an OS in-wheel small EV during steady-statecornering below the stability limit velocity in regard toconstant front steer angle 10∘ is examined. Figures 11 and12 show the results of the steady-state yaw rotational speedand steady-state side-slip angle for the vehicle model with4WDIS, respectively. The average time for the yaw rotational

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0 5 10 15

Slid

-slip

angl

e (ra

d) Velocity (m/s)

Figure 10: Steady-state side-slip angle to velocity with 2WS.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10 15 20 25 30

Yaw

rota

tiona

l spe

ed (r

ad/s

)

Time (s)

13km/h

15km/h

10km/h

5km/h

Figure 11: Steady-state yaw rotational speed to time change for thevehicle model with 4WDIS.

−0.24

−0.2

−0.16

−0.12

−0.08

−0.04

010 15 20 25

Side

-slip

angl

e (ra

d)

Time (s)

13km/h

15km/h

10km/h

5km/h

Figure 12: Steady-state side-slip angle to velocity for the vehiclemodel with 4WDIS.


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15

Yaw

rota

tiona

l spe

ed (r

ad/s

)

Velocity (km/h)

4WDIS

2WS

Figure 13: Comparison of steady-state yaw rotational speed tovelocity for 2WS and 4WDIS.

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0 5 10 15

Side

-slip

angl

e (ra

d)

Velocity (km/h)

2WS

4WDIS

Figure 14: Comparison of steady-state side-slip angle to velocity for2WS and 4WDIS.

speed to reach a constant value was also reduced to 25 s incomparison to the 2WS vehicle model. Even with high yawrotational speed, the steady-state side-slip angle also remainsconstant. The steady-state side-slip angle was in negativevalues which indicate that the vehicle was facing the innercircle of the cornering direction as the cornering initiated.

For better comparison, the relation between steady-stateyaw rotational speed to velocity and steady-state side-slipangle to velocity for vehicle model with 4WDIS and 2WS wasplotted in Figures 13 and 14. The steady-state yaw rotationalspeed of the vehicle model with 4WDIS was approximatelytwofold the value of vehicle model with normal 2WS at veloc-ity range of 0 to 10 km/h. When the velocity of the vehicle

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

10 15 20 25 30Time (s)

Rear

whe

el st

eerin

g an

gle (

rad)

15km/h

13km/h

10km/h

5km/h

Front wheel steering

Figure 15:The front and rearwheel steering angle during the steady-state cornering at below stability limit velocity for the vehicle modelwith 4WDIS.

increased from 10 km/h to 15 km/h, the steady-state yaw rota-tional speed gradually decreased. A similar pattern occurredfor the side-slip angle if we observe in absolute magnitude.

In order to comprehend these matters, we have to exam-ine the output of the ISCS. Figure 15 shows the rear wheelsteering angle during the steady-state cornering of the4WDIS vehicle model. As soon as the front wheel steer inputinitiated at 𝑡 = 10 s, the rear wheel steer initiated at the oppo-site direction as the front wheel. The rear wheel steeringangle maintained an opposite angle as the front wheel whichincreased the yaw rotational speed. As the velocity approachnear the stability limit, the opposite angle of the rear wheeldecreased.

10.3. Steady-State Cornering over Stability Limit Velocity with4WDIS. The stability limit velocity of the modelled OSin-wheel small EV has been determined in the previoussimulation. The previous simulation also proves that theimplementation of 4WDIS is able to improve the maneuver-ability of the OS small electric vehicle even at stable region.The more anticipated matter is the control of 4WDIS for theOS small electric vehicle during cornering above the stabilityvelocity limit.The previous steady-state cornering simulationcondition is repeated again for this vehicle model.

In this section, the control effect of the 4WDIS on anOS in-wheel small EV during steady-state cornering overthe stability limit velocity in regard to constant front steerangle 10∘ is investigated. Figure 16 shows the result of thesteady-state yaw rotational speed for the vehicle model with4WDIS. From this figure, the yaw rotational speed decreasedas the velocity of the vehicle model increased. However, ifwe observe closely, the time to produce a constant steady-state yaw rotational speed is instantaneous and maintainsthe average time of 25 s, especially at velocity range of 30 to50 km/h. The results of steady-state side-slip angle for thissimulation in Figure 17 show a reverse pattern from the yawrotational speed. The side-slip angle increased as the velocityof the vehicle model increased. Based on these results, we canassumed that the 4WDIS control input suppressed the outputmore as the velocity of the vehicle model increased.


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10 15 20 25

Yaw

rota

tiona

l spe

ed (r

ad/s

)

Time (s)

50km/h40km/h

30km/h

20km/h

15km/h

Figure 16: Steady-state yaw rotational speed to time change for thevehicle model with 4WDIS.

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

10 15 20 25

Side

-slip

angl

e (ra

d)

Time (s)

50km/h

40km/h

30km/h

20km/h

15km/h

Figure 17: Steady-state side-slip angle to time change for the vehiclemodel with 4WDIS.

In order to understand the control method of the 4WDISby the ISCS, we have to examine the output of the system.Figure 18 shows the front and rear wheel steering angleduring the steady-state cornering simulation of the 4WDISvehicle model. In the first few second after the front wheelsteering angle initiated, the ISCS produced a rear wheelsteering angle in minus value that gave the instantaneousyaw rotational speed mentioned before. The minus angleof the rear wheel was smaller as the steady-state velocityincreased because the excess yaw rotational speed producedby OS vehicle model also increased. As time progressed, theISCS gradually increased the rear wheel steering angle tocounter the excess yaw rotational speed and sustain a constantvalue. The angle of the rear wheel is higher for velocity rangeover 15 km/h which proves that our early assumption wascorrect.

−0.13

−0.08

−0.03

0.02

0.07

0.12

0.17

0.22

10 15 20 25Time (s)

Rear

whe

el st

eerin

g an

gle (

rad)

Front wheel steering angle

50km/h40km/h

20km/h

15km/h

30km/h

Figure 18:The front and rearwheel steering angle during the steady-state cornering at over stability limit velocity for the vehicle modelwith 4WDIS.

10.4. Overall Comparison of Steady-State Cornering with 2WSand 4WDIS. Figures 19(a) and 19(b) show the characteristicsof the steady-state yaw rotational speed and side-slip angle foran in-wheel small EV integrated with our modelled 4WDIScontrol in comparison to the conventional 2WS vehicle,respectively. This figure is a combination of the simulationresults of the 4WDIS control simulation.

Based on these results, an OS in-wheel small EV canachieve a stable steady-state cornering evenwhen the velocityis over the stability limit velocity with the implementationof 4WDIS. Simply put, the 4WDIS eliminate the stabilityvelocity that was present in the OS small electric vehiclewith 2WS. The 4WDIS control input suppressed the yawrotational speed and side-slip angle during high speed byrotating the rear wheels at the same direction as the frontwheels. Additionally, it can also improve the maneuverabilityof the vehicle at low speed by rotating the rear wheels at theopposite direction of the front wheels.

11. Conclusion

There are various methods to design an OS vehicle. In thispaper, we chose the transfer of weight distribution methodto model an OS in-wheel small EV. There are also a fewways to recognize an OS vehicle and one of them is that thevehicle will have a stability limit velocity.When a steady-statecornering simulation was carried out below the stability limitvelocity 𝑉

𝑐, the OS in-wheel small EV can achieve steady-

state corneringwith a higher yaw rotational speedwith regardto constant low steering input. However, when the vehiclevelocity 𝑉 ≥ 𝑉

𝑐, the yaw rotational speed and the side-slip

angle produced an infinite value in regard to the same con-stant steer angle.

The main objective of implementing 4WDIS onto an OSin-wheel small EV is to ensure stability during cornering atany velocity. The 4WDIS utilized the opposite at low speedto gain yaw motion and parallel steering to reduce the yawmotion of the vehicle.

In this paper, the Intelligence Steering Control System(ISCS) evaluated the dynamic of the in-wheel small EV anddry road surface. In the future, other parameters such as


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45 50

Yaw

rota

tiona

l spe

ed (r

ad/s

)

Velocity (km/h)

4WDIS

2WS

(a)

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0 10 20 30 40 50

Side

-slip

angl

e (ra

d)

Velocity (km/h)

2WS

4WDIS

(b)

Figure 19: (a) Steady-state yaw rotational speed to velocity for the vehicle model with 4WDIS. (b) Steady-state side-slip angle to velocity forthe vehicle model with 4WDIS.

lateral disturbance or icy road surface which has effect on thedriving or the vehicle will be taken into consideration in thesimulation analysis.

Nomenclature

Constant Parameters Symbols, Meaning, Value, and Unit

𝑏: Width of wheel interact surface, 0.1, m𝑑𝐹: Front tread, 0.840, m

𝑑𝑅: Rear tread, 0.815, m

𝐼: Yaw inertia moment at gravity point ofvehicle, 1470, kgm2

𝐾𝑥: Longitudinal tread rubber stiffness, 3.33 ×106, N/m3

𝐾𝑦: Lateral tread rubber stiffness, 3.33 × 106,N/m3

𝐾𝐹: Front wheel cornering stiffness, 2000.00,N/rad

𝐾𝑅: Rear wheel cornering stiffness, 2612.62,N/rad

𝑙𝑇: Length of wheel interact surface, 0.15, m

𝑙𝐹: Length from front axle wheel to gravity

point of vehicle, 0.725, m𝑙𝑅: Length from rear wheel axle to gravity

point of vehicle, 0.555, m𝑙: Length from front axle to rear axle of the

wheel, 1.28, m𝑚: Mass of the vehicle, 421.61, kg𝑟: Radius of the wheel, 0.23, m.

Variables Symbols, Meaning, Value, and Unit

𝑢: Longitudinal velocity, m/sV: Lateral velocity, m/s𝑉: Velocity at center gravity, m/s𝑉𝑐: Stability limit velocity, m/s

𝑋𝐹𝑅, 𝑋𝐹𝐿, 𝑋𝑅𝑅, 𝑋𝑅𝐿: Friction force for each tire, N

𝑌𝐹𝑅, 𝑌𝐹𝐿, 𝑌𝑅𝑅, 𝑌𝑅𝐿: Lateral force for each tire, N

𝑊𝑧: Wheels load subject to load transfer,N

𝛽: Side-slip angle of vehicle, rad𝛽∗: Side-slip angle of state observer, rad𝛽𝐹𝑅, 𝛽𝐹𝐿, 𝛽𝑅𝑅, 𝛽𝑅𝐿: Side-slip angle of each wheel, rad

𝜇: Friction coefficient𝜃𝐹, 𝜃𝑅: Front and rear wheels steer angle, rad

𝛾: Yaw rotational speed of vehicle body,rad/s

𝛾∗: Yaw rotational speed of state observer,

rad/s𝜌: Slip ratio𝜔: Wheel rotational speed, rad/s.

Competing Interests

The authors declare that they have no competing interests.

References

[1] Ministry of Land Infrastructure and Transport Department ofMunicipal Affairs and Automobile Station, “Towards the real-ization of a new social life through the development and utiliza-tion of new (mobility) guidelines for the introduction of ultra-smallmobility,” 2010, http://www.mlit.go.jp/common/001129801.pdf.

[2] Y. Hori, “Future vehicle driven by electricity and control—research on four wheel motored ‘UOT Electric March II’,” inProceedings of the 7th International Workshop on AdvancedMotion Control (AMC ’02), pp. 1–14, Maribor, Slovenia, July2002.

[3] M. Izhar, H. Ogino, and Y. Oshinoya, “Research on motioncontrol of 4 wheels steering vehicles-effect of regeneraive brakeon vehicles motion,” Proceeding of The School of Engineering,Tokai University, vol. 53, no. 2, pp. 99–103, 2013.

[4] M. Izhar, H. Ogino, and Y. Oshinoya, “Research on 4 wheelsindependent steering for small electric vehicle (effect of stabilityclearance speed),” in Proceedings of the Japan Society of Mechan-ical Engineers Annual Yearly Conference, No. 14, 2014.


[5] H. Ogino, M. Izhar, and Y. Oshinoya, “Stability analysis ofsmall electric vehicle (effect of hysteresis of friction brake forcefor regenerative braking force),” Proceeding of The School ofEngineering, Tokai University, vol. 52, pp. 55–64, 2012.

[6] R. Bundorf, “The influence of vehicle design parameters oncharacteristic speed and understeer,” SAE Technical Paper670078, 1967.

[7] M. Abe, “Vehicle handling dynamics: theory and application,”in Vehicle Handling Dynamics: Theory and Application, p. 61,Butterworth-Heinemann, 2nd edition, 2009.

[8] T.Murphy andB.Corbett, “Quadrasteer off course,”Ward’s AutoWorld, 2005.

[9] E. Ona, Y. Hattori, H. Aizawa, H. Kato, S. Tagawa, and S. Niwa,“Clarification and achievement of theoratical limitation in vehi-cle dynamics integrated management,” Journal of Environmentand Engineering, vol. 4, no. 1, pp. 89–100, 2009.

[10] F. Du, J.-S. Li, L. Li, andD.-H. Si, “Robust control study for four-wheel active steering vehicle,” in Proceedings of the InternationalConference on Electrical and Control Engineering (ICECE ’10),pp. 1830–1833, June 2010.

[11] N. Hamzah, M. K. Aripin, Y. M. Sam, H. Selamat, and M.F. Ismail, “Yaw stability improvement for four-wheel activesteering vehicle using sliding mode control,” in Proceedings ofthe IEEE 8th International Colloquium on Signal Processing andIts Applications (CSPA ’12), pp. 127–132, IEEE,Melaka,Malaysia,March 2012.

[12] J. Tian, N. Chen, J. Yang, and L. Wang, “Fractional order slid-ing model control of active four-wheel steering vehicles,” inProceedings of the International Conference on Fractional Dif-ferentiation and Its Applications (ICFDA ’14), pp. 1–5, IEEE,Catania, Italy, June 2014.

[13] S.-H. Yu and J. J. Moskwa, “A global approach to vehicle control:coordination of four wheel steering and wheel torques,” Journalof Dynamic Systems, Measurement, and Control, vol. 116, no. 4,pp. 659–667, 1994.

[14] M. Abe, Vehicle Handling Dynamics: Theory and Application,Butterworth-Heinemann, Boston, Mass, USA, 2nd edition,2009.

[15] M. Izhar, H. Ogino, and Y. Oshinoya, “Research on 4 wheeldrive and independent steering for small electric vehicle: activestability control during high speed cornering,” Proceeding of theSchool of Engineering, Tokai University, vol. 40, pp. 63–70, 2015.

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation http://www.hindawi.com

Journal ofEngineeringVolume 2014

Submit your manuscripts athttp://www.hindawi.com

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation http://www.hindawi.com

Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

SensorsJournal of


Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks


research article numerical simulation analysis of an oversteer in-wheel...

Documents