Integrated Slip-Based Torque Control of Antilock Braking

IEEJ Journal of Industry ApplicationsVol.3 No.4 pp.318–327 DOI: 10.1541/ieejjia.3.318

Paper

Integrated Slip-Based Torque Control of Antilock Braking System forIn-Wheel Motor Electric Vehicle

Wen-Po Chiang∗a)Non-member, Dejun Yin∗∗ Non-member

Manabu Omae∗ Non-member, Hiroshi Shimizu∗ Non-member

(Manuscript received March 31, 2013, revised Jan. 17, 2014)

In electric vehicles (EVs), cooperative control between a regenerative brake system (RBS) and the conventionalhydraulic brake system (HBS) enhances the brake performance and energy regeneration. This paper presents an inte-grated antilock braking control system based on estimating the wheel slip to improve the anti-slip performance of afour wheel drive in-wheel motor EV. A novel anti-slip control method for regenerative braking was developed and inte-grated with a hydraulic antilock braking system (ABS) according to the logic threshold concept. When combined withthe features of driving motors, the proposed method can improve the brake performance under slip conditions. Com-parative simulations showed the proposed control approach provided a more effective antilock braking performancethan the conventional ABS.

Keywords: anti-slip control, antilock braking system, brake force distribution, in-wheel motor electric vehicle, regenerative brakesystem

1. Introduction

The electric vehicle (EV) as a zero carbon dioxide emis-sion automobile having superior efficiency is currently be-ing developed due to deterioration of environment issues (1) (2).Electric motor drive EV has not only the character of high ef-ficiency, but the outstanding features of rapid response, easymeasurement and accurate controllability by comparing to in-ternal combustion engine vehicle (ICEV) (3) (4). The regenera-tive brake system (RBS) that drives motor as a generator toconvert moving kinetic energy into the electric energy storingin the battery pack has been researched widely to improve en-ergy efficiency.

In the early research works, the RBS and hydraulic brakesystem (HBS) are coordinated to concentrate on either energyregeneration in normal braking or vehicle stability perfor-mance in emergency braking. During normal braking, howto obtain the maximum energy regeneration is an interestingissue and had been respectfully studied (5)–(7). Nevertheless,some studies are devoted to anti-slip control for vehicle sta-bility regardless of energy efficiency (8)–(11). Recently, due tothe benefits of hybrid brakes, the brake control strategies haveattracted attention on coordination between energy recoveryand vehicle stability for hybrid electric vehicle (HEV) (12) (13)

and EV (14) applications. These studies have presented thatthe developed control strategies can carry out sufficient en-ergy recovery while maintaining vehicle stability.

a) Correspondence to: Wen-Po Chiang. E-mail: [email protected]∗ Graduate School of Media and Governance, Keio University

5322, Endo, Fujisawa-shi, Kanagawa 252-0882, Japan∗∗ School of Mechanical Engineering, Nanjing University of Sci-

ence and TechnologyNo. 200, Xiaolingwei, Nanjing 210094, China

The productions of HEV and EV in current automotivemarket obviously have also taken advantage of regenerativetechnology to enhance the energy efficiency. However, dur-ing the emergency braking i.e. the slip condition, commer-cial EVs or HEVs do not reply on the regenerative brakingbut the antilock braking system (ABS) of HBS. The ABScontrol algorithm makes braking force and cornering forceto be well used as possible by monitoring wheel accelera-tion and slip ratio based on the logic threshold control (LTC)method. When control unit detects the potential sliding, con-trol system reduces regenerative braking force and reverts tothe hydraulic braking only so that the hydraulic ABS can takefull responsible during the skidding. The main purpose isthat the brake performance is prior to the energy regenera-tion. However, conventional hydraulic ABS leads to the os-cillatory deceleration causing unfavorable ride comfort andthe advantages of the motor are not well utilized. Neverthe-less, because the hydraulic braking is not able to compensatethe loss of reduced regenerative braking rapidly, the decel-eration decreases suddenly causing incongruous decelerationfeeling (15).

In order to cope with problems, some research worksproposed the independently regenerative anti-slip controlmethod (9) (16) or the cooperative control strategy with hydraulicABS to maintain the vehicle stability and brake performanceduring the emergency braking (8) (13) (14) (17)–(21). In these studies,the cooperative ABS control methods are presented in sev-eral control scenarios. The first type is to propose an ABSreinforcement system to improve the traditional hydraulicABS performance by adjusting the proper regenerative brak-ing force. The regenerative braking is taken as auxiliarybrake system to support hydraulic ABS. However, these sys-tems do not contain the individual regenerative anti-slip con-trol especially on the low friction road in which there is no

c© 2014 The Institute of Electrical Engineers of Japan. 318

Integrated Slip-Based Torque Control of ABS for EV（Wen-Po Chiang et al.）

need of hydraulic braking. The second kind is to develop aleveled ABS control strategy to use either regenerative ABSor hydraulic ABS under certain brake strength for better en-ergy regeneration. However, these strategies cannot make ad-vantage of motor to improve the anti-slip ability comparingto the conventional ABS method. The third type is to con-struct a simultaneously cooperative control method betweentwo distinct brake systems. Although the ABS performanceis upgraded, but most of them use the same anti-slip controlmethod for both two brake systems, the merits of electric mo-tor are not well utilized.

This study aims to make full use of the advantages of mo-tors to achieve ABS performance improvement. We proposedan integrated antilock braking control strategy on a seriesbraking system. The control strategy includes two individualABS control systems and an integrated control method. Dur-ing slight braking (i.e., only regenerative braking is used), thedeveloped regenerative ABS works individually if wheel slipoccurs. If slip occurs during the composite braking (i.e., twobrake systems are needed), both ABS control systems worksimultaneously. Meanwhile, in order to realize better brakeperformance during the normal braking, brake force distri-bution between the front and rear wheels follows the idealbrake force distribution curve (I-curve) to ensure good us-age of road friction. A suitable distribution between RBSand HBS is determined according to the motor’s torque-speedcurve and state of charge (SOC) of battery for maximum en-ergy recovery purpose.

2. System Modeling

2.1 Vehicle Dynamics A half-car vehicle model forlongitudinal motion of a four-wheel drive in-wheel motor EVis considered on flat road surface without incline shown inFig. 1. The dynamic differential equations of the vehicle aredescribed as (1)–(5) on the basis of the assumption that thedriving resistance is considered to be small and ignorable.However, driving resistance is a variable that is related toaerodynamics, which can be synthesized in real time if higheranti-slip performance is required or if the vehicle runs at highspeed (4).

Jω f.ω f = Tm f + Th f − rFd f · · · · · · · · · · · · · · · · · · · · · (1)

Jωr.ωr = Tmr + Thr − rFdr · · · · · · · · · · · · · · · · · · · · · · · (2)

M.

Vc = Fd = Fd f + Fdr · · · · · · · · · · · · · · · · · · · · · · · · · (3)

Fd f = μ f (λ f )Nf · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (4)

Fdr = μr(λr)Nr · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (5)

where, Jω is the wheel inertia, ω is the wheel angular speed.Tm is the regenerative brake torque, Th is the hydraulic fric-tion torque, Fd is the friction force between tire and roadsureface, M is the vehicle mass, Vc is the vehicle speed, ris the wheel radius, N is the vehicle normal load, μ is thefriction coefficient, λ is the slip ratio. The subscript r and findicate front wheel and rear wheel, respectively. Here, theslip ratio is defined as

λ =Vw − Vc

max(Vc,Vw)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (6)

Vw = r · ω · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (7)

Fig. 1. Dynamic longitudinal model of vehicle

Fig. 2. Magic formula in half-car vehicle model

where Vw is the wheel speed. During longitudinal braking,load transference occurs within front and rear axles. The fol-lowing two equations describe the dynamic load transference

Nf = Mf g −(hL

)M

·Vc · · · · · · · · · · · · · · · · · · · · · · · · · (8)

Nr = Mrg +

(hL

)M

·Vc · · · · · · · · · · · · · · · · · · · · · · · · · · (9)

herein g is the acceleration of gravity, h is the center of grav-ity height, L is the wheel base. Fig. 2 shows a two-wheelvehicle model with Magic Formula for deceleration (8).

2.2 Hydraulic Brake Torque Model The actual hy-draulic brake torque can be measured directly with a sensoror estimated from hydraulic pressure of the wheel cylinder (22).The latter method is utilized in this study as

Th = BEF · Aw · re · Pw · · · · · · · · · · · · · · · · · · · · · · · · · (10)

where BEF is the brake effective factor of brake lining. Aw

is the wheel cylinder area. re is the brake effective radius.Pw is the wheel hydraulic pressure. Here, we assume that thevariation of BEF due to the brake lining wearing or ambientconditions is negligible.

Although the wheel hydraulic pressure can be estimatedaccording to hydraulic control unit (HCU) dynamic propertyand master cylinder pressure sensor which saves the cost ofmanufacturing (23), the usage of the estimated pressure must

319 IEEJ Journal IA, Vol.3, No.4, 2014


be calibrated wisely, otherwise a significantly longer stop-ping distance can result. Moreover, because the applied brakeforces are critical to ABS, it obviously would be an advan-tage to know cylinder pressure directly. Therefore, in thisstudy the wheel cylinder pressure sensor is utilized to mea-sure pressure directly.

2.3 Regenerative Brake Torque Model The transferfunction for regenerative braking between target toque andexecuted torque is described as first order delay system withdead time (4) as

Gm(s) =Tm

T ∗m=

e−τ1 s

τ2s + 1· · · · · · · · · · · · · · · · · · · · · · · · · (11)

where τ1 represents the dead time of CAN communication ormechanical response lag, τ2 represents the response time ofmotor with first order lag.

3. Brake Torque Distribution Control

3.1 Brake Torque Distribution between RBS and HBSDespite of the merits of the electric motor, the hydraulic

brake unit is reserved on considering the possible failure ofthe electric system. To employ both two brake systems, thearchitecture of the brake system needs to be changed insteadof conventional construction. There are two techniques tocoordinate the regenerative torque of the motor and frictiontorque of the hydraulic unit: parallel and series (7). In orderto recover kinetic energy as much as possible during braking,the hydraulic brake force prefers not to operate until regen-erative brake force reaches its maximum availability. Herein,the electro-hydraulic series brake system which allows inde-pendent control of the hydraulic braking according to regen-erative braking is introduced to recover more kinetic energy,Hence, the distribution between regenerative torque and fric-tion torque is described as below

if T ∗ ≤ Tm avail, then Tm = T ∗, Th = 0

if T ∗ > Tm avail, then Tm = Tm avail, Th = T ∗ − Tm

· · · · · · · · · · · · · · · · · · · (12)

where T ∗ is the target brake torque, Tm avail is the availablemotor torque. During braking, the control unit calculates thetarget deceleration as well as the target torque according tothe brake pedal stroke θ commanded by the driver. The avail-able motor brake torque is determined by the vehicle statuswhich includes the motor maximum power, the vehicle speedand the battery’s SOC (14). Eq. (13) reveals the calculation ofthe maximum motor torque. The motor characteristic curveof application motor for simulation in this study is shown inFig. 3

Tm max =

{TmN ωm ≤ ωmN

9550PmN/ωm ωm > ωmN· · · · · · · · (13)

where Tm max is the maximum motor torque. TmN is the mo-tor rated torque, ωm is the motor speed, ωmN is the motor basespeed, PmN is the motor rated power.

However, it is not available to utilize the regenerative brak-ing due to the electric recovery causing battery overchargingif SOC of battery is too high. Thus, a weighting factor WS OC

is employed to protect the battery from overcharging that maydeteriorate the battery’s life. The weighting factor for vehi-cle speed which is utilized in some studies is not considered

Fig. 3. Motor/Generator map

Fig. 4. Weighting factor of the battery SOC

in this paper. Because the regenerative torque is still avail-able, even the regenerative efficiency is low at slow speeddue to the lesser electric voltage generated (24). Accordingly,the available motor torque is obtained as (14) with a weight-ing factor WS OC . Figure 4 shows the weighting factor forbattery’s SOC. The equation of it is described as (15).

Tm avail = Tm maxWS OC · · · · · · · · · · · · · · · · · · · · · · · · (14)

WSOC =

⎧⎪⎪⎪⎨⎪⎪⎪⎩1 SOC < 0.810(0.9 − SOC) 0.8 ≤ S OC < 0.90 SOC ≥ 0.9

· · · · · · · · · · · · · · · · · · · (15)

3.2 Brake Torque Distribution between Front andRear Wheels Dynamic load transference causes rearwheels lock become easier than front wheels if brake forcesof both axles are set to be the same. The higher deceleration,the more weight transference increases. Hence, appropriatebrake force design on the front and rear wheels is essentialand required for the consideration of vehicle stability. Bysubstituting (8) and (9) to (4) and (5) respectively, a distribu-tion ratio α can be calculated as (16) which is a function ofvehicle acceleration measured by accelerometer. Therefore,with known demand of target brake torque T ∗, the appropri-ate brake torques on the front and rear wheels can be calcu-lated by (17) and (18). Front/rear brake torques distributionthat follows the distribution ratio α achieves the ideal brakeforce distribution and gives the optimal braking which makesthe front and rear wheels lock simultaneously for any roadcondition, i.e. the maximum brake effectiveness.

α =Fdri

Fd f i=

(Mrg +

(hL

Ma

)) /(Mf g −

(hL

Ma

))

· · · · · · · · · · · · · · · · · · · (16)

T f i =T ∗

1 + α· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (17)



Fig. 5. Typical μ-λ curves

Tri =α · T ∗1 + α

· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (18)

4. Proposed Anti-Slip Control Strategy

The wheel slip will increase to result in wheel lock andcause vehicle instability, once brake force is greater than fric-tion force that road surface can supply. According to the basicprinciple of conventional hydraulic ABS system, the wheeldynamics that remains at the stable region or approaches tothe unstable region can be judged by monitoring the wheelslip. Figure 5 shows four typical μ-λ curves which are in re-lation to the slip ratio and longitudinal friction coefficientson different types of road surfaces. It can be found that thevehicle is able to stay stable within a certain slip ratio valueλopt which has the maximum friction coefficient i.e. the max-imum braking force. On the contrary, when wheel slip isgreater than λopt, the vehicle turns to unstable.

The ideal anti-slip control is to keep slip ratio as λopt allthe time until vehicle stops except for the timing of slip ratioincreasing from 0 to λopt. In other words, once the wheel slipis controlled precisely, the brake performance reaches opti-mum and the stopping distance is the shortest. In this studywe utilize wheel slip as a reference parameter in the controlmethod as in the case of the conventional hydraulic ABS. Theidentical control object aids in integration of the two distinctABS control systems. Here, considering the definition of slipratio, we can rewrite (6) as (19). By taking differential of it,we can get (20)

Vw = (λ + 1) · Vc · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (19)dVw

dt= (λ + 1)

dVc

dt+ Vc

dλdt· · · · · · · · · · · · · · · · · · · · (20)

When slip occurs, if slip ratio can be maintained at value ofλopt during braking as mentioned ideal control, i.e. dλ/dt =0, (20) can be rewritten as (21).

.

Vw = (λopt + 1) · ·Vc · · · · · · · · · · · · · · · · · · · · · · · · · · · · (21)

According to Yin et al. (4), “if wheel and chassis accelera-tions are well controlled, then the difference between wheeland chassis velocities, i.e. the slip is also well controlled”.Here, by rewriting (21) into the form of (22) to describe theaccelerations of the vehicle and the wheel as a ratio. It istruth that if braking torque is controlled based on this ratio,i.e. maintain the wheel and vehicle acceleration constantlywith respect to value of λopt, the wheel slip does not become

large consequently..

Vw·

Vc

= (λopt + 1) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (22)

4.1 Vehicle Speed Calculation for Slip Ratio Estima-tion For calculation of slip ratio the vehicle speed isneeded according to (6). Considering that the driving resis-tance exits, this paper utilizes the acceleration sensor to cal-culate vehicle speed by integration based on an assumptionof flat road deceleration in short time interval as below (21)

∧Vc =

∫a · dt + Vc0 · · · · · · · · · · · · · · · · · · · · · · · · · · · · (23)

Vc0 = max(Vω f ,Vωr) · · · · · · · · · · · · · · · · · · · · · · · · · · · (24)

where Vc0 is the initial value for integral calculation. Whenbrake pedal is steeped on, Vc0 is set to be wheel speed valuewhich is a larger value between the front and rear wheels onthe instant of nonzero pedal stroke. In order to avoid accumu-lated error causing inaccurate calculation in integration, theinitial value Vc0 is acquired every single brake pedal opera-tion. Here, we assume the ineffective stroke of brake pedal tobe zero. With calculated vehicle speed, the wheel slip ratiocan be calculated as

∧λ =

Vw −∧Vc

∧Vc

· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (25)

4.2 Hydraulic Antilock Braking Control The con-trol method of conventional hydraulic ABS is so called logicthreshold control. The ABS control tries to avoid high slipoccurrence by adjusting the hydraulic pressure in the brakecalipers and consequently the brake torque clamped. Themost common ABS algorithm is based on vehicle decelera-tion and slip ratio threshold. By means of designed thresholdvalues, HUC of ABS controls increase, hold or decrease ofthe existing wheel hydraulic pressure (25). Accordingly, in thisstudy we designed an ABS control algorithm with two slipratio threshold values to achieve the equivalent operation as(26). The wheel hydraulic pressure is calculated as (27) andthe final friction torque is derived by substituting (27) into(10).

Q =

⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩k1√

(Pm − Pw) 0 ≤ ∧|λ| <∣∣∣λ∗L

∣∣∣0

∣∣∣λ∗L∣∣∣ ≤ ∧|λ| <

∣∣∣λ∗H∣∣∣

−k2√

Pw − Pr

∣∣∣λ∗H∣∣∣ ≤ ∧|λ| ≤ 1

· · · · · (26)

Pw = k3 · U = k3 ·∫

Qdt · · · · · · · · · · · · · · · · · · · · · · (27)

where Q is the hydraulic flow in brake caliper. Pm is the mas-ter hydraulic pressure. Pr is the reservoir hydraulic pressure.λ∗L and λ∗H are lower slip ratio threshold and upper slip ratiothreshold, respectively. These two thresholds are designatednearby the λopt in Fig. 5. k1 and k2 are coefficients determinedby orifice size and oil viscosity. U is the fluid capacity. k3 isa coefficient decided by characteristic of brake parts.

Furthermore, in order to increase the pressure unhurriedlyto avoid quick recovery of slip once ABS control is operated.The control technique of pulse step increasing is introduced.This control method is also wildly used in current ABS con-trol technology (24).



4.3 Regenerative Antilock Braking Control Thetarget of this study is to maintain acceleration ratio shown in(22) to be a constant to achieve anti-slip control. Based on it,Yin et al. (4) had presented a control method for slip preven-tion which provides a higher anti-slip performance for accel-erating traction control. However, in the braking behavior theacceleration ratio of wheel to vehicle will be limited all thetime so that the brake performance might be limited, becausethe brake forces will be constrained early i.e. the wheel slipis not sever enough. Moreover, the presented control methoddid not consider the effect of inaccuracy of hydraulic braketorque.

In this study, a designated value is defined for anti-slip con-trol usage and we conduct control conditions as (28) by com-paring the designated slip ratio to estimated one.

Tm =

⎧⎪⎪⎪⎨⎪⎪⎪⎩Tm 0 ≤ ∧|λ| < |λ∗|T ∗mt |λ∗| ≤

∧|λ| ≤ 1· · · · · · · · · · · · · · · · · · · (28)

where T ∗mt is the target torque for anti-slip purpose. λ∗ is thereference slip ratio, which is equal to the general value λopt

for most road surfaces showing in Fig. 5. During the nor-mal braking, i.e. a braking period without slip occurrence,the output brake torques follows the I-curve to make full useof road friction efficiently and assure that the front and rearwheels behave the same. If brake force is greater than frictionforce that road surface can supply i.e. the estimated slip ratiois greater than λ∗, the vehicle slips and wheel tends to lockand cause vehicle instable.

This study proposed a novel control approach to limit thebrake torques by derived a target motor torque T ∗mt, calledideal allowable torque. By substituting the reference slip ra-tio λ∗ into (22), the target wheel angular acceleration can becalculated as (29). Although the implement of accelerationestimation on the EV is possible, but the anti-slip perfor-mance will be affected severely if vehicle acceleration is notsensed directly, especially braking on slope or the hydraulicfriction torque calculation exits inaccuracy. Therefore, theaccelerometer is utilized.

·ω∗t =

a(λ∗ + 1)r

· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (29)

With target wheel angular acceleration, calculated frictiontorque and estimated friction force, the ideal allowable torquecan be derived by (30). The estimated friction force of wheelbetween tire and road surface is derived as (31) by observeraccording to (1) and (2).

T ∗mt = Jω·ω∗t +

∧rFd −Th · · · · · · · · · · · · · · · · · · · · · · · · · (30)

∧Fd =

Tm + Th − Jω.ω

r· · · · · · · · · · · · · · · · · · · · · · · · · · (31)

With the derived ideal allowable torque, the wheel angu-lar acceleration can be controlled to achieve desired anti-slipperformance by restraining the surplus regenerative torque.Figure 6 shows the block diagram of proposed regenerativeantilock braking control system for a single wheel.

4.4 Integrated Antilock Braking System By in-specting two distinct ABS systems, the regenerative ABS andthe hydraulic ABS, the same referring variable is slip ratio.

Fig. 6. Regenerative antilock braking control system

This paper adopted the control method using the logic thresh-old concept with different designed threshold values. Theregenerative ABS works at appropriate designated slip ratioand hydraulic ABS works around this slip ratio by increas-ing, holding, decreasing of hydraulic pressure. For example,if the reference slip ratio for regenerative ABS is designatedto be 0.2, the slip ratio threshold values of hydraulic ABS arebetween 0.15 and 0.25 which assists to avoid the occurrenceof slip.

When controller detects that the vehicle tends to slip, i.e.the potential lock on wheel, the integrated anti-slip controlstrategy holds the hydraulic bake pressure in advance andthen constrains regenerative torques by derived ideal allow-able torques. If regenerative ABS can suppress the wheel slipalone, the hydraulic ABS is not used to reduce the hydraulicpressure during the braking operation. On the other hand, ifthe wheel slip is not sufficiently suppressed and continues toincrease, the hydraulic ABS is used to reduce the hydraulicpressure to ensure that wheel slip stays within the desiredrange.

5. Simulation Results

This section evaluates the effectiveness of proposed con-trol strategy. The simulation environment showing in Fig. 7is constructed in MATLAB/Simulink. The vehicle model isbuilt with Magic Formula based on Fig. 2 containing the lon-gitudinal weight transference. The major specification of ap-plication vehicle is shown in Table 1. Due to the maximumtorque ability of motor, the regenerative braking is able to beutilized up to 0.4g of deceleration i.e. motors can generatemaximum total torque about 2000 Nm. The distribution ra-tio of front/rear hydraulic friction torques is set to be a fixedvalue of 1.5 which is widely used for passenger car.

The conditions of road surface are specified by the pickvalue of friction coefficient of μ-λ curves. The reference slipratio λ∗ for regenerative ABS and two slip ratio thresholds forhydraulic ABS, λ∗L and λ∗H are −0.2, −0.18 and −0.22, respec-tively. The time constants are set as following, τ1 = 0.02,τ2 = 0.01. The speed limit of hydraulic ABS is 3.6 Km/h(1 m/s). The SOC of battery is assumed to be around 50%during the braking.

5.1 Slight Braking on Low µ Road Surface Thissimulation performs the vehicle to decelerate with a decel-eration close to −0.3g (−2.94 m/s2) on jump μ road surfacewhich begins with dry concrete (μpeak = 0.8) and changes tocompacted snow road (μpeak = 0.3) at t = 2 s. Brake operation



Fig. 7. Block diagram of entire system inMATLAB/Simulink

Table 1. Specification of application vehicle

started at t = 1 s with initial speed of 60 Km/h and target braketorque is about 1645 Nm according to brake pedal input. Be-cause the deceleration of this simulation case is below 0.4g,the regenerative braking is responsible for the decelerating.

Figure 8 shows the comparison results between conven-tional hydraulic ABS method and proposed integrated ABSmethod. Figure 8(a) gives the brake performance results ofconventional hydraulic ABS. Figure 8(b) represents the sim-ulation results of proposed one. Figure 8(c) and Fig. 8(d)compare the vehicle speeds and decelerations between twoABS control methods, respectively.

As simulation results in Fig. 8(a) and Fig. 8(b), once thevehicle runs into the slippery road surface at 2 s, two brak-ing systems with different ABS control method have dis-tinct behavior of brake performance. For the brake systemwith conventional ABS, front slip ratio increases greater thenlower slip ratio threshold value λ∗L so that the regenerativetorques are turned off and hydraulic braking joins in. Then,hydraulic braking follows the hydraulic ABS control methodto avoid the front wheel lock and maintain its wheel speedoscillationally until vehicle stops. On the other hand, for thebrake system with integrated ABS it is apparent that at theproposed distribution control method distributes appropriatebrake torques on front and rear wheels so that the slip rationsare about the same during the normal braking. Because thefriction of road surface is well utilized, the wheel slips do notexceed the reference slip ratio λ∗. Unlike conventional ABS,the proposed anti-slip control is not activated.

By comparing the stopping time and deceleration betweentwo ABSs as shown in Fig. 8(c) and Fig. 8(d), the brake sys-tem with integrated ABS achieves shorter stopping time andhigher stable deceleration of 2.9 m/s2 which is close to the

(a) Conventional ABS (b) Integrated ABS

(c) Vehicle speeds (d) Accelerations

Fig. 8. Brake performance comparison on low μ roadsurface with light braking

limit of road surface. Because the brake torques of pro-posed control are distributed effectively, the stopping distanceis shortened about 3.03 m. In other words, almost 7.4% ofneeded stopping distance is reduced.

5.2 Heavy Braking on Low µ Road Surface Inthis simulation, the vehicle is performed on dry concrete-compacted snow jump μ road surface as well but with heavybrake operation of −0.7g (−6.86 m/s2). The target braketorque is about 4090 Nm. Because the deceleration is higherthan 0.4g, both the regenerative braking and hydraulic brak-ing are needed during the normal brake at initial two seconds.

As simulation results in Fig. 9(a) and Fig. 9(b), the brakesystem with conventional ABS relying on conventional ABSstops the regenerative torques and suppresses the front/rearfriction torques after entering the snowy road surface. Onthe contrary, the brake system with integrated ABS decreasesthe hydraulic braking torque to be zero and suppresses theregenerative torque according to anti-slip control when thevehicle runs into the compacted snow road. Because only re-generative braking is enough for slippery road, the hydraulicbraking is thought as redundancy.

As comparison results in Fig. 9(c) and Fig. 9(d), the brakesystem with integrated ABS achieves shorter stopping timeand shortens about 3.32 m of stopping distance which isabout 13.2% reduction. The deceleration also approaches to2.9 m/s2 stably to state that the road surface is utilized effec-tively better than conventional one.

5.3 Strong Braking on Medium µ Road Surface　　Above simulations give an example to inspect when vehicle

encounters an extreme condition, i.e. the low μ condition. Infact, the slip happens also under a normal adhesive road sur-face in common use, such as wet asphalt (μpeak = 0.5). Thissimulation performs with −0.6g (−5.88 m/s2) of decelerationon dry concrete-wet asphalt jump μ road. The target brake





Fig. 9. Brake performance comparison on low μ roadsurface with heavy braking

torque is about 3540 Nm. In this condition, the brake systemwith conventional ABS has the same operation of relying onregenerative ABS without regenerative braking usage. On thecontrary, the system with integrated ABS needs to coordinatethe regenerative ABS with hydraulic ABS to achieve anti-slipperformance because the deceleration is higher than 0.4g.

As simulation results in Fig. 10(a) and Fig. 10(b), the brakesystem with conventional ABS operates as same as previoussimulation. On the other hand, the brake system with inte-grated ABS has coordinated the hydraulic torques and regen-erative torques according to integrated ABS control method.As comparing results showed in Fig. 10(c) and Fig. 10(d),the brake system with proposed integrated ABS can achieveshorter stopping time and shorten the stopping distance about2.33 m which is about 13.7% reduction of needed stoppingdistance. The deceleration reaches to 4.8 m/s2 most of timestably to verify that the road surface is utilized effectivelybetter than conventional ABS with oscillatory deceleration.

5.4 Performance with Friction Torque Inaccuracy　　In Sect. 2, we have assumed that the friction torque of

hydraulic braking can be calculated correctly from the mea-surement of wheel hydraulic pressure. However, the uncer-tain variation of brake lining due to the wearing or ambientconditions is unpredictable especially during the long timebraking or urgent braking. In order to verify the adaptabil-ity of proposed integrated ABS control method, this simu-lation performs same scenarios in Sect. 5.2 and Sect. 5.3 butadding 30% inaccuracy d to calculated friction torque, i.e. thecalculated friction torque is 30% larger than actual one. Asvehicle speed comparison results showed in Fig. 11(a) andFig. 11(b), the proposed integrated anti-slip control method



Fig. 10. Brake performance comparison on medium μroad surface with strong braking

(a) Heavy braking on low μ road surface

(b) Strong braking on medium μ road surface

Fig. 11. Brake performance comparison with frictiontorque inaccuracy

still works effectively even with friction torques inaccuracy.The shortened stopping distance comparison is only effect of0.5% which is neglectablely small.

5.5 Performance with Vehicle Mass Variation 　　Figure 12 shows the comparative anti-slip performance

results with perturbations in vehicle mass. In a real driv-ing environment, the vehicle mass can vary significantly. Inorder to cover the variational possibility in vehicle mass,two conditions of vehicle loading are performed to evalu-ate the robustness of proposed controller. One condition isso called Light Vehicle Weight (LVW) which is mass con-tains net weight of a vehicle and driver standard mass. An-other condition is so called Gross vehicle weight (GVW) isthe maximum operating weight of a vehicle as specified by



(a) Heavy braking on low μ road surface

(b) Strong braking on medium μ road surface

Fig. 12. Brake performance comparison with variationin vehicle mass

the manufacturer. In this case, the GVW of vehicle is setto be 2025 kg. Same scenarios in Sect. 5.2 and Sect. 5.3 arealso performed in this simulation to show the comparisons.As results showed in Fig. 12(a) and Fig. 12(b), the proposedcontrol method is able to perform effectively in both caseswithout apparent changes.

6. Extended Simulation Study

6.1 Verification by using CarSim In order to verifythe proposed method on a detailed full-order model that con-tains the modeling uncertainties and non-linearity, a vehiclemodel and road model in simulation software CarSim 8.11were utilized. The built-in vehicle model of B-Class, Hatch-back (with ABS), is employed and re-built with powertrainof four in-wheel-motor drive. The road surface is with splitfriction coefficient (0.5L/0.8R). For fair comparison, the ra-tio of regenerative torque output between front and the rearwheels is 8 : 3 which is default setting of brake system on thevehicle model of B-Class, Hatchback. Because the defaultthreshold values λ∗L/λ

∗H of hydraulic ABS control of B-Class,

Hatchback are 0.2/0.1 for front wheel and 0.1/0.06 for rearwheel, the reference slip ratios λ∗ for regenerative ABS areset to be 0.15 and 0.08 for front and rear wheels, respectively.

In the following simulation, the wheels on the left side areused to evaluate. The vehicle decelerates at initial speed of80 Km/h. the regenerative braking is able to be utilized up to0.4g of deceleration.

6.2 Comparison Results Figure 13 shows the brakecomparison results for the pure hydraulic ABS and the pro-posed integrated ABS. As results showing in Fig. 13(a) andFig. 13(b), each case can retrieve the increasing slip ratios byreducing the brake torques. However, the proposed methodcan achieve less quantity of oscillation, and smaller ampli-tude as well, which benefits the anti-slip performance betterthan the hydraulic one. From Fig. 13(c) and Fig. 13(d), thestopping distance is shortened about 1.6 m, and the deceler-ation achieves to 6 m/s2 stably which is utilized effectivelybetter than conventional one (oscillates within 5 to 6 m/s2).

7. Discussion

First three simulations in section 5 are performed on thedesignated road surface to verify the effectiveness of pro-posed control strategy. The simulation results demonstrated

(a) Hydraulic ABS (b) Integrated ABS


Fig. 13. Brake performance comparison results on splitμ road surface from CarSim

the appropriate distribution and control between regenera-tive braking and hydraulic braking, and showed the betterbrake performance and anti-slip performance than conven-tional ABS control. During normal braking, the brake torquesare distributed appropriately to make full usage of frictionforce of road surface by following I-curve. During slip con-dition, the oscillatory behavior of slip ratio is improved andthe stopping distance is shortened average about 13% com-paring to conventional ABS control.

Moreover, an extened simulation study using CarSim insection 6 is performed to verify the effectiveness of proposedmethod on a detailed full-order vehicle model. The compar-ison results of shorter stopping distance and stable decelera-tion are in agreement on the simulation results in Sect. 5.

By inspecting the behavior of vehicle deceleration, the con-tinuously stable deceleration can achieve better ride comforti.e., no jerk (defined as differentiation of deceleration) (26).Furthermore, the regenerative efficiency is expected to be en-hanced because of continuous usage of regenerative braking.

In Sect. 5.4, the inaccuracy of friction torque is added toverify the robustness of proposed control strategy. By substi-tuted (31) into (30), we can know that ideal allowable torqueT ∗mt which restrains the surplus regenerative torque if wheelslip exceed reference slip ratio λ∗ is independent of calculatedfriction torque as below

T ∗mt = Jω(·ω∗t −

·ω) + Tm · · · · · · · · · · · · · · · · · · · · · · · · · (32)

The simulation results demonstrate the braking perfor-mance is nearly the same even the inaccuracy of frictiontorques is introduced. That is, the adaptability of proposedcontrol approach has proved.

Detailed analysis of control characteristics can be per-formed with a partially linearized one wheel vehicle model.When the control system falls into an anti-slip state, the entire



Fig. 14. Partially linearized control system

control system can be simplified into a closed-loop feedbacksystem shown as Fig. 14. Here, D is speed difference whichrepresents the extent of the slip, and Ku represents the rela-tion between D and friction force. Ku is assumed to be posi-tive because the discussion is limited to conditions where theslip ratio is in the unstable region. Fdo is the friction forcebetween tire and road surface when anti-slip control starts.The delay of the electromechanical system is simplified as anLPF with a time constant of τ for easy analysis.

The transfer functions from Fdo to D, from Th to D andfrom d to D are defined as TDF , TDT and TDd respectively.

TDF =−Jnτs + Jωλ∗

JωMτs2+(JωM−JnKuτ)s+JωKuλ∗

TDT =Mrτs

JωMτs2+(JωM−JnKuτ)s+JωKuλ∗· · · · · (33)

TDd = 0

where Jn is defined as the equivalent system inertia as below

Jn = Jω + Mr2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (34)

Therefore, the steady state response of the system to inputscan be described as below:

limt→∞D(t) = lim

s→0sTDF(s)Fdo(s) + lim

s→0sTDT (s)Th(s)

· · · · · · · · · · · · · · · · · · · (35)

Here, assume Fdo and Th to be a step reference, (35) canbe used to examine the relation between the friction force andthe speed difference, and the relation between friction torqueand speed difference, separately.

In the results, the speed difference is positively propor-tional to the friction force, and is not affected by frictiontorque in the steady state. Thus, the proposed control systemcan be verified that the worse slip condition has the betteranti-slip performance. Moreover, because positively propor-tional relation is only related to Ku, the effect of vehicle massvariation is negligible. The analysis results have agreed withsimulation results.

8. Conclusion

This paper presented an integrated antilock braking systembased on a series configuration for four wheel drive in-wheel

motor EVs. In the braking system, brake torque distribu-tion controls regarding to available motor torque and max-imum brake effectiveness are considered. A novel controlstrategy based on ideal anti-slip control is proposed. Weadopted the logic threshold concept as control conditionswith different designed thresholds for slip-based torque con-trol. The integrated system coordinates regenerative ABS andhydraulic ABS to improve the anti-slip performance and re-alize a good usage of road friction when vehicle encountersslippery roads. The comparative simulation results and dis-cussion demonstrated its effectiveness and adaptability withregard to the antilock braking performance. The proposedanti-slip control stably constrains the skidding superior to theconventional hydraulic ABS, which can shorten the stoppingdistance and provide better ride comfort on different road sur-faces. Moreover, the control strategy makes full use of re-generative braking so that the better energy efficiency can beexpected.

References

( 1 ) H. Shimizu, J. Harada, C. Bland, K. Kawakami, and L. Chan: “Advancedconcepts in electric vehicle design”, IEEE Trans. Ind. Electron., Vol.44, No.1,pp.14–18 (1997-2)

( 2 ) K.T. Chau, C.C. Chan, and C. Liu: “Overview of permanent-magnet brush-less drives for electric and hybrid electric vehicles”, IEEE Trans. Ind. Elec-tron., Vol.55, No.6, pp.2246–2257 (2008-6)

( 3 ) S. Sakai, H. Sado, and Y. Hori: “Motion control in an electric vehicle withfour independently driven in-wheel motors”, IEEE/ASME Trans Mechatron-ics, Vol.4, No.1, pp.9–16 (1999-3)

( 4 ) D.J. Yin, S. Oh, and Y. Hori: “A novel traction control for EV based on Max-imum Transmissible Torque Estimation”, IEEE Trans Ind. Electron., Vol.56,No.6, pp.2086–2094 (2009-6)

( 5 ) Z.C. Sun, Q.H. Liu, and X.D. Liu: “Research on electro-hydraulic paral-lel brake system for electric vehicle”, International Conference on VehicularElectronic and Safety, pp.376–379 (2006)

( 6 ) H. Yeo, S. Hwang, and H. Kim: “Regenerative braking algorithm for a hybridelectric vehicle with CVT ratio control”, J. Autom. Eng., Vol.220, pp.1589–1600 (2006-8)

( 7 ) G. Xu, W. Li, K. Xu, and Z. Song: “An intelligent regenerative braking strat-egy for electric vehicles”, Energies, Vol.4, pp.1461–1477 (2011-9)

( 8 ) S.I. Sakai and Y. Hori: “Advanced vehicle motion control of electric vehiclebased on the fast motor torque response”, 5th International Symposium onAdvanced Vehicle Control, pp.729–536 (2000)

( 9 ) T. Suzuki and H. Fujimoto: “Slip ratio estimation and regenerative brake con-trol for decelerating electric vehicles without detection of vehicle velocity andacceleration”, IEEJ Trans. on IA, Vol.130, No.4, pp.512–517 (2010)

(10) N. Mutoh, Y. Hayano, H. Yahagi, and K. Takita: “Electric braking con-trol methods for electric vehicles with independently driven front and rearwheels”, IEEE Trans Ind. Electron., Vol.54, No.2, pp.1168–1176 (2007-4)

(11) D.H. Kim, J.M. Kim, S.H. Hwang, and H.S. Kim: “Optimal brake torquedistribution for a four-wheel drive hybrid electric vehicle stability enhance-ment”, Proceedings of the Institution of Mechanical Engineers, Part D: J.Autom. Eng., Vol.221, No.11, pp.1357–1366 (2007-11)

(12) E. Cacciatori, B. Bonnet, N.D. Vaughan, M. Burke, D. Price, and K.Wejizanowski: “Regenerative braking strategies for a parallel hybrid pow-ertrain with torque controlled IVT”, SAE Technical Paper, 2005-01-3826(2005)

(13) J. Zhang, X. Lu, J. Xue, and B. Li: “Regenerative braking system for se-ries hybrid electric city bus”, World Elect. Veh. J., Vol.2, No.4, pp.128–134(2008-12)

(14) L. Zhou, Y. Luo, K. Li, and X. Lian: “A novel brake control strategy forelectric vehicle based on slip trial method”, IEEE International Conferenceon Vehicular Electronic and Safety, pp.1–6 (2007)

(15) G. Zhuo and H. Li: “Research on Electro-hydraulic parallel brake systembased on ABS”, International Conference on Electrical and Control Engi-neering, pp.782–787 (2011)

(16) Y. Zhou, S. Li, Z. Fang, and Q. Zhou: “Control strategy for ABS of EVwith independently controlled four in-wheel motors”, 4th IEEE Conference



on Industrial Electronics and Applications, pp.2471–2476 (2009)(17) C. Song, J. Wang, and L. Jin: “Study on the composite ABS control of vehi-

cles with four electric wheels”, J. Comput, Vol.6, No.3, pp.618–626 (2011-3)(18) C. Mi, H. Lin, and Y. Zhang: “Iterative learning control of antilock braking

of electric and hybrid vehicles”, IEEE Trans. Veh. Technol., Vol.54, No.2,pp.486–494 (2005-5)

(19) D. Peng, Y. Zhang, C.-L. Yin, and J.-W. Zhang: “Combined control of a re-generative braking and anti-lock braking system for hybrid electric vehicles”,International J. Autom. Technol., Vol.9, No.6, pp.749–757 (2008-5)

(20) H. Zhang and X. Chen: “Study on the Electronic-hydraulic Compound Anti-lock Braking System for Four In-Wheel Motor Driving Vehicle”, Interna-tional Conference on Electric Information and Control Engineering (ICE-ICE), pp.6176–6183 (2011)

(21) T. Suzuki and Fujimoto: “Regenerative braking control based on slip ratiowith integrated accelerometer for short time interval for electric vehicle”, IEEof Japan Industry Applications Society Conference, pp.1–6 (2008)

(22) T. Ishige, H. Furusho, Y. Aoki, and K. Kawagoe: “Adaptive slip control usinga brake torque sensor”, 9th International Symposium on Advanced VehicleControl, Vol.1, pp.417–422 (2008)

(23) O’Dea and Kevin: “Anti-Lock Braking Performance and Hydraulic BrakePressure Estimation”, SAE Technical Paper, 2005-01-1061 (2005)

(24) J. Guo, J. Wang, and B. Cao: “Regenerative braking strategy for electric ve-hicles”, Intelligent Vehicles Symposium, pp.864–868 (2009)

(25) Japan. ABS Co., Ltd.: “ABS Research for Automobile”, Sankaido, pp.59–70(1993)

(26) F. Wang, K. Sagawa, and H. Inooka: “A study of the relationship between thelongitudinal acceleration/deceleration of automobiles and ride comfort”, Jpn.J. Ergon, Vol.36, No.4, pp.191–200 (2000)

Wen-Po Chiang (Non-member) received a M.S. degree in Mechan-ical Engineering from the Michigan TechnologicalUniversity, MI, United States in 2004. He was asenior engineer and worked on brake system designand development at China Motor Corp., Taiwan for6 years. He studies his Ph.D. degree at Keio Univer-sity since 2011, performing research on vehicle mo-tion control, especially in the field of brake system fornext generation electric vehicles.

Dejun Yin (Non-member) received his B.S. and M.S. degrees in Elec-trical Engineering from the Harbin Institute of Tech-nology, China in 1999 and 2001, respectively. He re-ceived another M.S. degree in Electronics Engineer-ing from Chiba Institute of Technology, Japan, in2002. Then, he worked on embedded control sys-tem design in Mechanical-Electronics Engineeringfor nearly 5 years. In 2006, he entered the Universityof Tokyo and received his Ph.D. degree in ElectricalEngineering in 2009. He is currently a professor of

Nanjing University of Science and Technology in China performing researchand development on vehicle control and drive system design for next gener-ation electric vehicles.

Manabu Omae (Non-member) is a professor of the Graduate Schoolof Media and Governance, Keio University. He re-ceived his Ph.D. in Mechanical Engineering from theUniversity of Tokyo in 2000. His major research in-terests are advanced vehicle control and safety sys-tems, and automatic driving.

Hiroshi Shimizu (Non-member) is a professor emeritus of Keio Uni-veisity. He earned his Ph.D. from the GraduateSchool of Engineering of Tohoku University in 1975.In 1976 he began his work as a researcher at the Na-tional Institute for Environmental Studies. He be-came a professor in the Faculty of Environment andInformation Studies at Keio University in 1997. Hehas been a leading figure in Japan for electric vehicledevelopment, working on development of 8 conceptcars in 30 years. He was a technology leader in the

Eliica project. The Eliica concept car which utilizes next generation “in-wheel motor” technology reached a speed of 370 km/h in 2004 tests. AuthorName (Membership Category of IEEJ) the quick brown fox jump over thelazy dog. The quick brown fox jump over the lazy dog. The quick brown foxjump over the lazy dog. The quick brown fox jump over the lazy dog. Thequick brown fox jump over the lazy dog. The quick brown fox jump overthe lazy dog. The quick brown fox jump over the lazy dog. The quick brownfox jump over the lazy dog. The quick brown fox jump over the lazy dog


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Integrated Slip-Based Torque Control of Antilock Braking