Fuzzy knowledge-based model for prediction of traction force of an electric golf car

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Journal

www.elsevier.com/locate/jterra

Journal of Terramechanics 49 (2012) 13–25

ofTerramechanics

Fuzzy knowledge-based model for prediction of traction forceof an electric golf car

Ataur Rahman a,⇑, Altab Hossain a, Zahirul Alam A.H.M. b, Mabubur Rashid c

a Department of Mechanical Engineering, International Islamic University Malaysia, 50728 KL, Malaysiab Department of Electrical and Communication Engineering, International Islamic University Malaysia, 50728 KL, Malaysia

c Department of Mechatronics Engineering, Faculty of Engineering, International Islamic University Malaysia, 50728 KL, Malaysia

Received 14 March 2011; received in revised form 3 July 2011; accepted 15 August 2011Available online 4 November 2011

Abstract

The methods of artificial intelligence are widely used in soft computing technology due to its remarkable prediction accuracy. How-ever, artificial intelligent models are trained using large amount of data obtained from the operation of the off-road vehicle. In contrast,fuzzy knowledge-based models are developed by using the experience of the traction in order to maintain the vehicle traction as requiredwith utilizing optimum power. The main goal of this paper is to describe fuzzy knowledge-based model to be practically applicable to areasonably wide class of unknown nonlinear systems. Compared with conventional control approach, fuzzy logic approach is more effi-cient for nonlinear dynamic systems and embedding existing structured human knowledge into workable mathematics. The purpose ofthis study is to investigate the relationship between vehicle’s input parameters of power supply (PI) and moisture content (MC) and out-put parameter of traction force (TF). Experiment has been conducted in the field to investigate the vehicle traction and the result hasbeen compared with the developed fuzzy logic system (FLS) based on Mamdani approach. Results show that the mean relative errorof actual and predicted values from the FLS model on TF is found as 7%, which is less than the acceptable limit of 10%. The goodnessof fit of the prediction value from FLS is found close to 1.0 as expected and hence shows the good performance of the developed system.� 2011 Published by Elsevier Ltd. on behalf of ISTVS.

Keywords: Artificial intelligent system; Traction; Fuzzy logic system

1. Introduction

The tyre–surface friction and rolling resistance are thedeciding factors of vehicle dynamics models. However,most of the known models do not take into account therelation between these factors and the impact of externaloperating and environmental conditions that create diffi-culties for the prediction of vehicle traction. Traction con-trollers improve a driver’s ability to control a vehicle underadverse conditions, such as a wet or icy road. The fast andstable acceleration and deceleration can be maintained bycontrolling the traction force between the vehicle’s tires

0022-4898/$36.00 � 2011 Published by Elsevier Ltd. on behalf of ISTVS.

doi:10.1016/j.jterra.2011.08.001

⇑ Corresponding author. Tel.: +60 3 3691 4550; fax: +60 3 6196 4455.E-mail addresses: [email protected], [email protected] (A. Rah-

man).

and the road [10,11,13,19]. The steerability of the vehiclecan be improved significantly by preventing the wheelsfrom slipping [10,18]. Since effective control of a vehicle’straction is essential for lateral and longitudinal guidancesystems, artificial traction control system becomes animportant option for controlling the vehicle. Traction con-trollers regulate wheel slip with normalizing the differencebetween wheel and vehicle speed. Wheel slip strongly influ-ences the tyre–road adhesion coefficient. The traction con-trol system is complicated to establish especially for off-road vehicle as it is highly nonlinear due to the changingof road conditions significantly with time. Moreover, thetyre–road interaction is difficult to measure and to estimate[10,11,13,19]. The uncertainty and nonlinearity associatedwith traction control make a fuzzy-logic control approachappealing [11,12,14,15]. Fuzzy-logic-based traction control

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14 A. Rahman et al. / Journal of Terramechanics 49 (2012) 13–25

could substantially improve longitudinal performance andoffer significant potential for optimal control of drivenwheels [9].

Over the years, fuzzy logic techniques have been appliedto a wide range of systems, with many electronic controlsystems in the automotive industry, such as automatictransmission, engine control and antilock braking systems(ABSs). These electronically controlled automotive systemsrealize superior characteristics through the use of fuzzy-logic-based control, rather than traditional control algo-rithms [4]. Moreover, the fuzzy logic controller deals withinexactness in a rigorous manner and it is effective at han-dling the uncertainties and non-linearity associated withcomplex control systems such as traction control system.The aim of the fuzzy controller to control the wheel slipsat an optimum value that can provide desired traction forceregardless of road conditions.

This paper presents fuzzy knowledge based model forprediction the traction force and justify the traction con-troller development for investigate the vehicle longitudinaltraction performance. A fuzzy logic approach is appealingfor traction control because of the nonlinearity and time-varying uncertainty involved in traction control systems.The controller is attractive because of its ability to maxi-mize acceleration and deceleration regardless of road con-ditions. However, it is found through simulations thecontroller’s performance to regulate vehicle dynamic trac-tion at any desired value of wheel slip.

The mathematical model has also been presented in thisstudy to simulate the vehicle contact area, slippage andtraction force with taking accounts into the vehicle tyreradius, total weight and the kinematics of vehicle at thetires-road interfaces.

1.1. Electric golf car configuration

The electric golf car as shown in Fig. 1, has been givenby Jabson and Janshon for the establishment of optimumpower management system. The car is operated with aDC motor of 48 V DC, series wound, 3.1 kW@2400RPMpowered by a battery pack of Six 48 V, 117 min @ 56

Fig. 1. Photo of the Golf car.

amp. It is reported that the vehicle is powered by the powerpack only for one and half hours instead of two hours. Thisstudy is conducted on the effectiveness of fuzzy knowledgebased model for prediction the traction force and justifythe traction controller development for investigate thevehicle longitudinal traction performance and power opti-mization. The establishment of optimum power manage-ment system is considered as the further study on thisvehicle. The specification of the golf cart is stated inTable 1.

1.2. Mathematical model for traction

The traction control prevents the wheel from spinningwhen moving off or when accelerating sharply. Tractioncontrols intervene to maintain stability, reduction of yaw-ing moment reactions, provide optimum propulsion at allspeed, and reduce driver workload. We consider two forcesacting on the vehicle body: driving (longitudinal) and side(lateral) forces. As depicted in Fig. 3, these force character-istics strongly depend on the slip. Slip is one of the func-tional parameters for the vehicle traction mechanism. Asthe traction force developed by a tire is proportional tothe applied wheel torque under steady state conditions, slipis a function of traction force. The slip is defined as the ratio

of the linear velocity at the tire center to the spin velocity of

straight free-rolling tire expressed as a percentage. If thevehicle remains stuck and wheel slip continues, the drivingforce is reduced drastically. The slip of the wheel coulddetermine by using the cycloid principle. A cycloid is thecurve defined by a fixed point on a rim of the wheel as it rolls,

or, more precisely, the locus of a point on the rim of a circle

rolling along a straight line. Points of rolling rim describe a

cycloid. Consider a wheel of radius R0 which is free to rollalong the x-axis as shown in Fig. 2.

As the wheel turns, a point P on the tire traces out acurve. Assume P is initially at the origin and let C and T

are located as indicated in Fig. 2, with / denoting theradian measure of angle TCP. Then the arc PT and the seg-ment OT have the same length such that the center C of therolling circle is at (R0/, R0). Using trigonometry, it couldbe concluded that

x ¼ R0/� R0 sin / ¼ R0ð/� sin /Þ ð1Þy ¼ R0 � R0 cos / ¼ R0ð1� cos /Þ ð2Þ

It is assumed that the driving wheels operate with exert-ing a longitudinal force (traction force) due to the applieddriving torque at the wheel, and its elastic deformation andthe accompanying soil deformations create a condition as ifthe wheels roll with slip radius Rz. The radius Rz can bemeasured by using the following equation:

Rz ¼ R0ð1� irdÞ ð3ÞIn Eq. (3), ird is the slippage of wheel relative to the terrainin percentage which is induced due to the friction at theinterface between driving wheel and terrain, V is the linearspeed at the wheel in m/s, and x is the angular speed of the

Table 1Specification.

Drive motor 48 V DC, series wound, 3.1@2400RPM(continuous)

Horsepower 10.0@1125RPM (intermittent)Drive unit 12.3–1 direct drive axle, double reduction helical

gearElectrical system 48 VBatteries Six 8 V, 117 min @ 56 ampKey or pedal start PedalSteering Self adjusting rack and pinionFront suspension Independent leaf spring with dual hydraulic shocksRear suspension Leaf Springs with dual hydraulic shocks.Brakes Self adjusting rear wheel mechanical drumFrame/chassis Aluminum I-BeamFront and rear tires 24 � 14.4 wideOverall length 91.5in (232 cm)Overall width 47.25in (120 cm)Wheelbase

differential65.5in (166.4 cm)

Overall height 68.5 in (174 cm)Ground clearance 4.5in (11.4 cm)

A. Rahman et al. / Journal of Terramechanics 49 (2012) 13–25 15

tyre in rad/s. The resulting slip radius Ri can be calculatedby using the following equation:

Ri ¼ Rzð1� iÞ ¼ R0ð1� irÞ ð4Þ

Fig. 2. Typical cycloid for the wheele

Fig. 3. Tire–terrain in

In Eq. (4), ir is the resultant slippage, ir ¼ iþ ird and

i:ird ffi 0 with ir ¼ 1� VRix

� �When the driving wheel is in longitudinal slip, the dis-

placement of the vehicle due to the slippage (i.e., slip dis-placement) of the wheel can be represented by rewritingthe Eq. (4):

x ¼ U � H=2 ¼ Ri/� H=2 ¼ R0/ð1� irÞ � H=2 ð5ÞThe resultant slippage, ir is caused by the tangential

force and tire deformation and x is the slip displacement.Eq. (5) represents slip displacement when considering thekinematics interaction at the tyre–terrain interface.

When the deformable tire rolls with radius R0, the resul-tant slippage is zero, or ir ¼ 0. The displacement of the tirecan be written as

x0 ¼ R0/� H=2 ð6Þ

In Eq. (6), x0 is the displacement at zero resultant slip-page.

It is noted that when i ¼ 0, the slip displacement of thetire will be zero (x = 0), and Eq. (6) can be rewritten as

x ¼ R0/ð1� irdÞ � H=2 ¼ 0

d vehicle rolling on peat terrain.

teraction model.


ird ¼ ir ¼ 1� Hð2R0/Þ

¼ 1� VRzx

� �� 100%

¼ 1� VRix

� �� 100% ð7Þ

It is noted that the vehicle ground contact pressure (Pc)is higher than the normal ground pressure (Pg) when thetires of the car are inflated by 100%. In this case the vehiclewould have higher sinkage and leads the higher motionresistance. The inflation pressure of the tire is reduced by5%, 10%, 15%, 20% and 25% for the moisture content of40%, 50%, 60%, 70% and 80% respectively. The tire deflec-tion and contact length increase significantly with decreas-ing the inflation pressure of the tires. The contact length ofthe tire H can be computed by considering the verticalequilibrium of the tire. The length of the contact surfaceis definitely the function of the tire deflection. Therefore,H is computed by considering the tire deflection d,

H ¼ 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½ðdÞðD� dÞ�

p¼ 2ðRo/Þ; 1� 1� V

Rix

� �ð100%Þ

� �ð8Þ

where D is the diameter of the tire in meter. In Fig. 3, thepoint ‘D’ is the normal force acting point on the curve BCof the wheel and ‘z’ is defined as the depth of the normalforce acting point (i.e., z ¼

HðPosition of DÞ. The slip sink-

age of the vehicle is computed in this study by usingz0 ¼ zo � z. The slip sinkage is defined as the sinkage of the

vehicle due to the slippage. It is earlier mentioned that theslippage of the vehicle increases with stucking the vehicle.If the slip sinkage of the vehicle equals to zero (i.e.z0 ¼ 0), the point ‘D’ would be at the point B which indi-cates that the inflation pressure of the tire should be100%. While, the position of point D in any point of thecurve BC means the inflation of the tire needs to decrease.In this study the inflation of the tire has been changed man-ually. However, the moisture content is an importantfactor of the terrain to determine the traction force of thecar as the tire inflation pressure is reduced based on the ter-rain moisture contents. Furthermore, the changing infla-tion pressure changes the position of point ‘D’ and tirescontact length (H). The sinkage of the golf cart is com-puted by using the Bekker’s equation [1]:

z ¼ 3Wð3� nÞðkc þ BkuÞ

ffiffiffiffiffiffiDwp

� � 22nþ1

ð9Þ

where z is the cart sinkage in m, B is the wheel width in m,kc and ku are the Bekker’s cohesive and frictional moduli ofsoil deformation in kN/mn+2, W is the normal load onwheel in kN, Dw is the diameter of the wheel in m and nis the dimensionless exponent of a load sinkage curve.

And the motion resistance by using the equation ofModest [16]:

Rc ¼k � B � znþ1

nþ 1ð10Þ

Where, Rc is the motion resistance due to the compaction.Based on the vehicle dynamics characteristics the vehiclewill be able to move forward if the vehicle traction forceis more than or equal to the motion resistanceði:e:; F P RtÞ. As the golf cart speed is considered about12 km/h, it motion resistance mainly incurred due to themotion resistance due to the compaction.

From the wheel-terrain interaction model as shown inFig. 3, the traction force of the vehicle could be determinedby applying the Newton’s motion law:

ðF t þ F nÞ sin u1 � Rc � Ra ¼Wg

ddtðvÞ

ðF t þ F nÞ sin u ¼ Rc þ Ra þWg

ddtðvÞ ð11Þ

Where, ðF t þ F nÞ sin u ¼ 2BR L

0sdx, s ¼ smaxð1� e�j=KwÞ

and F t þ F n ¼ FIn Eq. (9), Ft is the tangential force in kN, Fn is the nor-

mal force that exert from the terrain in kN, W is the totalof the vehicle weight in kN, Rc is the motion resistance dueto terrain compaction in kN, Kw is the shear deformationmodulus in m, j is the slip displacement in m, smax is themaximum shear stress, kN/m2 and v is the traveling speedof the vehicle in km/h. The maximum shear stress can becomputed by using the Bekk [1],

smax ¼ cþ r tan u ð12ÞWhere, c is the cohesion of the soil in kN/m2, r is the nor-mal shear stress in kN/m2 and u is the internal frictionalangle in radian.

By integrating the equation, F ¼ Atsin u1ðcþ r tan uÞ

R1� e�ix=KW

dx, the tractive effort equation of the tyre–terrain interfaces can be written as

F ¼ 1

ðsin u1ÞAtðcþ r tan uÞ 1� e�j=Kw

ð13Þ

where r ¼ WAt

and At ¼ BLt ¼ B H þ x� H2

¼ B H

2þ x

In Eq. (13), r is the normal stress of the vehicle on the

tyre–terrain interaction in kN/m2, i the slippage in percent-age, and Kw the shear deformation modulus in m.

1.2.1. Traction vs. Moisture content

Moisture contents and shearing strength of a Golf resortin Kuala Lumpur, Malaysia was conducted for the depthsof 10, 25, and 40 cm for developing the relationshipbetween the traction force and moisture content. Undis-turbed samples volume of 216 cm3 were taken at the men-tioned depths and different points in the fields in threereplications for the determination of moisture content,bulk density, cohesiveness, internal friction angle, sheardeformation modulus of soil. The samples were wrappedwith aluminum foil and sealed in a plastic container beforewere immediately taken to the laboratory for the relevantanalysis. The collected samples that were brought to thelaboratory were initially weighed for their wet mass beforeplacing in an electric oven at 105 �C temperatures. After


twenty-four hours, the samples were taken out from theoven and weighted for their dry mass. The moisture con-tent is determined as follows:

MC ¼ x ¼ W wss

W dwss

� �100% ð14Þ

In equation, x is the moisture content in percentage, Wwwss

is the weight of water in soil sample in kN and Wdss is thedry weight of soil sample in kN.

Fig. 4a show the moisture content of the soil in differentdepths while the Fig. 4b shows the typical trend of in-situ

shearing strength of the soil. It is noted that the tractionforce of the golf car is the main function of the soil mois-ture content and the cohesiveness. The demand of the trac-tion force of the car increases with increasing the moisturecontent of the soil which might be due to the higher com-paction resistance of the golf car and higher cohesiveness.The cohesiveness of the soil in the range of 5–10 cm depthis recorded lower than the cohesiveness of the soil in therange of 10–40 cm depth. This is mainly due to the presenceof the dense roots of the grass. Therefore, the golf cartsinkage should not be more than 10 cm. The relationshipbetween the moisture content and the traction force ofthe golf car is model by simplifying the trend lines of thecurve as follows:

F ¼ Ate½�0:0144x2þ2:29x�0:97� 1� e�j=Kw

ð15Þ

Where, F is the traction force of the golf car in kN, e is theexponential, x is the moisture content of the soil in per-centage, At is the total contact area of the car, j is the sheardisplacement and Kw is the shear deformation modulus inm.

Power required for the golf car to develop the desiredtraction force is computed as,

P r ¼ AtðeX Þ 1� e�j=Kw � �

ðvÞ ð16Þ

with

X ¼ �0:02x2 þ 2:29x� 0:97

Where, Pr is the power required for the car to develop thesufficient traction force to overcome the motion resistance

Fig. 4. Soil parameter (a) moisture

which is normally develops due to sinkage or the compac-tion of the soil in kW and v is the travelling speed of the carin m/s. It is noted that the moisture content causes the vehi-cle slip sinkage and power consumption. If the vehicle sink-age is high vehicle will be experienced high motionresistance. So the vehicle needs more power to developthe desired traction. But, the excessive sinkage the car willbe unable to traverse.

By using the empirical equation from the trend lines, therelationship between the moisture content and sinkage ismodeled as follows:

z ¼ Hðnþ 1Þk

ðeX Þ 1� e�j=Kw � � 1

nþ1

ð17Þ

Based on the Eq. (17), it could be mentioned that thetraction force of the cart is the major function of moisturecontent. To develop the sufficient traction, the cart DCmotors needs to develop desired traction torque which issubject to the power supply. In the following discussionon the development of fuzzy controller the moisture con-tent and power supply is considered the input variableswhich are defined the traction force of the cart.

2. Fuzzy Logic System

There are a number of different control techniques thatwould work here and therefore a design choice must bemade. Some of the control techniques include classical con-trol, PID control, adaptive control, and state space meth-ods require a relatively accurate model of the system inorder to develop a satisfactory controller. Fuzzy logic con-trollers usually do not require a model of the system.Instead, they rely on the knowledge of an expert on con-trolling the particular system. Therefore, with all of thesein mind, a fuzzy logic controller is introduced to predicttraction force for an electric golf car. The knowledge ofan expert can be coded in the form of a rule-base, and usedin decision making. The main advantage of fuzzy logic isthat it can be tuned and adapted if necessary, thus enhanc-ing the degree of freedom of control.

content; (b) shearing strength.


2.1. Function of Fuzzy Logic Controller

Before designing any controller, the inputs and outputsof the control process must be properly determined. Theinput variables to the controller are used to determinehow best to control the process or plant. The output vari-ables of the controller must therefore have some impacton process. Fuzzy controller used fuzzy logic system(FLS) is introduced in this study for predicting vehicletraction force. The general configuration of the fuzzyexpert system, which is divided into four main parts byKevin et al. (1998) as shown in Fig. 5 are: (1) Fuzzifica-tion – which converts controller inputs into informationthat the inference mechanism can easily use to activateand apply rules, (2) Knowledge base – which contains afuzzy logic quantification of the expert’s linguistic descrip-tion of how to obtain satisfactory control for a particularapplication, (3) Inference – which creates the controlactions according to the information provided by thefuzzification module by applying knowledge about howbest to control the plant, and (4) Defuzzification – which

Fig. 5. Basic structure of th

Fig. 6. The structure of

calculates the actual output, i.e. converts fuzzy outputinto a precise numerical value (crisp value) and then sendsthem to the physical system (plant), so as to execute thecontrol of the system.

2.2. Membership function and Fuzzification

For implementation of fuzzy values into the system byusing fuzzy logic system (FLS), moisture content (MC),sinkage (SL) and power deliver (PD) are used as inputparameters and traction force (TF) is used as outputparameter. For fuzzification of these factors the linguisticvariables low (L), medium (M), and high (H) are used forthe input parameters and very low (VL), low (L), medium(M), high (H), and very high (VH) are used as outputparameters. The logical AND is implemented with the min-imum operator, the aggregation method is maximum, andthe center of gravity defuzzification method is used becausethese operators assure a linear interpolation of the outputbetween the rules as shown in Fig. 6 [5]. The membershipfunctions most frequently used in control hypothesis are

e fuzzy logic controller.

fuzzy logic system.

Table 2Inference rules of controller parameters.

Rules Input variables Output variable

MC SL PD TF

1 L L L VL– – – – –6 L L H L– – – – –10 M L L M– – – – –13 M M L L– – – – –18 M H H H– – – – –23 H M M H– – – – –27 H H H VH

Fig. 7. Prototype membership functions for moisture content (MC).

Fig. 8. Prototype membership functions for vehicle slippage (SL).

Fig. 9. Prototype membership functions for power deliver (PD).

Fig. 10. Prototype membership functions for traction force (TF).


triangular, trapezoidal, Gaussian, Z-, S-, and bell-shapedforms [6]. Based on the expert and application, many differ-ent choices of membership functions are possible. How-ever, the triangular, Z-, and S-shaped membershipfunctions are used in this study for both input and outputvariables because of their accuracy [7]. The units of theused factors are: MC (%), SL (%), PD (kW) and TF(kN). For the three inputs and one output, a fuzzy associ-ated memory or decision is formed as regulation rules.Total of 27 rules are formed. Parts of the rules are shownin Table 2. For example, Rule 1 and 13 can be interpretedas follows:

Rule 6: If MC = L and SL = L and PD = H, thenTF = L, i.e. if the terrain’s MC is low and vehicle slippageis medium and power deliver is high, then vehicle’s tractionforce is low.

Rule 13: If MC = M and SL = M and PD = L, thenTF = L, i.e. if the terrain’s MC is medium and vehicle slip-page is medium and power deliver is low, then vehicle’straction force is low.

The first block inside the FLS is fuzzification, whichconverts each piece of input data to degrees of membershipin one or several membership functions. Fuzzifications ofthe moisture content (MC), vehicle slippage (SL), powerdeliver (PD) and traction force (TF) are made by aid fol-lows functions. These formulas are determined by usingmeasurement values.

MCði1Þ ¼i1; 40 6 i1 6 80

0; otherwise

�ð18Þ

SLði2Þ ¼i2; 20 6 i2 6 40

0; otherwise

�ð19Þ

PDði3Þ ¼i2; 4 6 i2 6 15

0; otherwise

�ð20Þ

TF ðo1Þ ¼o1; 1:5 6 o1 6 6

0; otherwise

�ð21Þ

In Eqs. (18)–(20), i1 is the first input variable (MC), i2 is thesecond input variable (SL), i3 is the third input variable

(PD), and o1 is the first output variable (TF). Prototypefuzzy sets for the fuzzy variables, namely, moisture content(MC), vehicle slippage (SL), power deliver (PD) and trac-tion force (TF) are set up using MATLAB FUZZY Tool-box. The membership values obtained from the aboveformulae are shown in the Figs. 7–10.

Table 6Coefficients of membership functions for FIS parameter of TF.

Linguistic variables Type Coefficients (kN)

c1 c2 c3

Very low Z-shaped 2 2.5 –Low Triangular 1.5 2.5 3.5Medium Triangular 2.5 3.5 4.5High Triangular 3.5 4.5 5.5Very high S-shaped 5 6 –


Within the framework of the present study, the follow-ing rules are used to create the input and output member-ship functions. Ivanov et al. [6] has reported that if there isminimal information for a particular variable and this var-iable is a responsive indicator, the range of values is dividedinto numerous identical triangular membership functions.

ltriangleðx; c1; c2; c3Þ ¼

0; xhc1

x�c1

c2�c1; c1 6 x 6 c2

c3�xc3�c2

; c2 6 x 6 c3

0; xic3

8>>><>>>:

9>>>=>>>;

ð22Þ

In this case, the edge of the variable’s interval may be rep-resented with linear Z- and S-shaped functions describedrespectively as

lZðx; c1; c2Þ ¼1; x 6 c1

c2�xc2�c1

; c1hxhc2

0; x P c2

8><>:

9>=>; ð23Þ

lSðx; c1; c2Þ ¼0; x 6 c1

x�c1

c2�c1; c1 6 x 6 c2

1; x P c2

8><>:

9>=>; ð24Þ

In Eqs. (11)–(13), x is the input and output variables, c1, c2

and c3 are the coefficients of membership functions for thedescribed input and output variables. The coefficients ofmembership functions for the input and output variablesare given in Tables 3–6.

To illustrate the fuzzification process, linguistic expres-sions and membership functions of moisture content(MC) obtained from the developed rules and above for-

Table 3Coefficients of membership functions for FIS parameter of MC.

Linguistic variables Type Coefficients (%)

c1 c2 c3

Low Z-shaped 45 55 –Medium Triangular 50 60 70High S-shaped 65 75 –

Table 4Coefficients of membership functions for FIS parameter of SL.


c1 c2 c3

Low Z-shaped 5 10 –Medium Triangular 5 17.5 30High S-shaped 25 35 –

Table 5Coefficients of membership functions for FIS parameter of PD.


c1 c2 c3

Low Z-shaped 5 7 –Medium Triangular 6 9 12High S-shaped 10 12 –

mula are presented analytically. The notation i1 indicatesthe system input (for this case MC) and it has its member-ship function values that can be computed for all fuzzy setsas follows:

lLði1Þ ¼1; i1h4555�i1

10; 45 6 i1 6 55

0; i1i55

8><>:

9>=>; ð25Þ

lMði1Þ ¼

i1�5010

; 50 6 i1 6 6070�i1

10; 60 6 i1 6 70

0; i1i70

8><>:

9>=>; ð26Þ

lH ði1Þ ¼0; i1 6 65i1�65

10; 65 6 i1 6 75

1; i1i75

8><>:

9>=>; ð27Þ

Similarly, the linguistic expressions and membershipfunctions of other parameters can be calculated.

The inference process generally involves two steps: (1)the linguistics variables of all the rules are comparedto the controller inputs to determine which rules apply tothe current situation, and (2) the conclusions (what controlactions to take) are determined by using the rules at thecurrent time. In this stage, truth degrees (l) of the rulesare determined for the each rule by aid of the min and thenby taking max between working rules.

Rajasekaran and Vijayalakshmi Pai [8] and Passino andYurkovich [3] have reported that in many conditions, fora system whose output is fuzzy, it can be simpler to receivea crisp decision if the output is represented as a single scalarquantity. This conversion of a fuzzy set to single crisp out-put in order to take action is called defuzzification. In thisstage, the output membership values are multiplied by theircorresponding singleton values and then are divided by thesum of membership values to compute TFcrisp as follows [2]:

TF crisp ¼P

ibilðiÞPilðiÞ

ð28Þ

where, bi is the position of the singleton in the ith universe,and l(i) is equal to the firing strength of truth values ofrule i.

2.3. Control surface of the fuzzy inferring system

Using MATLAB the fuzzy control surfaces are devel-oped as shown in Fig. 11 and 12. These may serve as the

Fig. 11. Control surface of the fuzzy inferring system.

Fig. 12. Control surface of the fuzzy inferring system.

(a) MC =40%

(c) MC =70%

Fig. 13. Vehicle typi


visual depiction of how FLS operates dynamically overtime. These are the mesh plot of the example relationshipbetween moisture content (MC), vehicle sinkage (SL) andpower delivering (PD) on the input side and controller out-put traction force (TF) on the output side. These controlsurfaces display the range of possible defuzzified valuesfor all possible inputs of MC, SL and PD. Both figuresdepict the impacts of terrain and vehicle parameters onthe traction force. The surface plot shown in Fig. 11 depictsthe impacts of MC and PD parameters on TF. It showsthat as the power delivering and moisture content increase,there is concomitant increase in traction force as expected.The traction force reaches the apex when the power deliv-ering and moisture content both reach their respectivemaximum level. Fig. 14 demonstrates as the power deliver-ing increases up to a certain amount, especially at lowerlevel of vehicle slippage, traction force is lower. However,traction force increases with the further increase of powerdelivering even at lower level of slippage. Hence, lowerlevel of slippage does not contribute much towards tractionforce. But it could be noted that the effect is highly signif-icant at the higher level of slippage. Traction forceincreases with the increase of vehicle slippage, althoughthe effect is less prominent at the level of power delivering.The plots are used to check the rules and the membershipfunctions and to see if they are appropriate and whethermodifications are necessary to improve the output. Whena satisfactory system is achieved, the fuzzy program is con-verted to machine language and downloaded into a micro-processor controller. The microprocessor then runs themachine based on the fuzzy program. Although the process

(b) MC =50%

(d) MC =80%

cal performance.

(a) MC = 40% (b) MC = 50%

(c) MC = 60% (d) MC = 70%

Fig. 14. Vehicle typical power requirement.


seems to be long, it actually is relatively easy to execute,and it adds intelligence to a machine.

In addition, the prediction accuracy of the developedfuzzy logic system has been investigated according to math-ematical and statistical methods [5]. In order to establishthe relative error (e) of structure, the subsequent equationis used:

e ¼Xn

i¼1

y � y^

y

�� 100%

nð29Þ

The goodness of fit (g) of the predicted system is calcu-lated by the following equation:

g ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1�

Pni¼1ðy � yÞ2Pn

i¼1ðy � ymeanÞ2

sð30Þ

where, n is the number of interpretations, y is the measuredvalue, y^ is the predicted value, and ymean is the mean ofmeasured value. The relative error provides the differencebetween the predicted and measured values and it is neces-sary to attain zero. The goodness of fit also provides theability of the developed system and its highest value is 1.

3. Results and discussions

3.1. Vehicle field performance investigation

Vehicle performance test was conducted without usingcontroller for the different moisture contents at constantspeed with two passengers after installing the importantinstrumentation system on the vehicle. The instrumenta-tion system of the vehicle was equipped with travel speed

transducers and digital meter to provide real time perfor-mance display for the vehicle. The instrumentation systemof the vehicle was made up of a set of transducer withrespective digital readouts from the data acquisition sys-tem. The traction of the vehicle is partially measured bymeasuring the output torque of the motor which is com-puted by using the mathematical model as follows:

F ¼ ðV msIsmÞN � Rw

ðMÞðgmÞ ð31Þ

where F is the measured traction by measuring the powersupply to the motor ðP sm ¼ V smIsmÞ and the motor rpm,gm is the motor efficiency in% and M is the multiplying fac-tor. Motor power supply was measured by using the digitalmeter and rpm was measured by using speed transducer.The motor efficiency was considered 90% according tothe motor specification. M is a multiplying factor whichis equal to 0.095.

The partial experimental results on vehicle traction testhave been shown in Figs. 13 and 14. Vehicle traction vari-ation was found with the variation of moisture contentwhich could be incurred due to increasing of vehicle sink-age and the cohesiveness of the terrain. The traction forceincreased with increasing vehicle slippage up to a certainlimit and then decreased with further increase of slippageas shown in Fig. 13. Vehicle slippage was measured byusing GPS. The moisture content was measured for the ter-rain before and after testing the vehicle. There was no sig-nificant difference observed on the moisture contentbetween these two instants. It is observed that the tractionforce varies from 0.688 kN to 5.541 kN. Approximately, anincreases of 70% at moisture content resulted in traction


force increases of 61% while an increases of 9 times at vehi-cle slippage caused a 48% increased of the traction force.The degree of traction force was usually larger for highermoisture content. Hence, moisture content was the majorcontributory factor on traction force as compared to vehi-cle slippage. As expected, the greatest value in tractionforce was observed at a slippage of 23% and moisture con-tent of 80%.

Fig. 14 shows the vehicle typical power requirement fordelivering. The power delivering increased with increasingvehicle slippage up to a certain limit and then decreased withfurther increase of slippage. Similar pattern is observed forthe moisture content. It is observed that the power deliver-ing varies from 4.951 kW to 14.394 kW. Approximately,an increase of 70% at moisture content resulted in a powerincrease of 59% while an increase of 9 times at vehicle slip-page caused a 50% increased of the power requirement.The degree of power requirement was again larger for highermoisture content. This conclusion is also supported by theexperimental results of Rahman et al. [17]. Hence, the mois-ture content was considered as the major parameter of theterrain on the power requirement as compared to vehicleslippage. As expected, the greatest value in power require-ment delivering was observed at a slippage of 20% and mois-ture content of 70%.

3.2. Traction force prediction and validation

The results of the developed FLS were compared withthe experimental results. Fig. 15 shows the correlationbetween actual and predicted values from FLS systemof vehicle traction force. The mean of actual and pre-dicted values are 2.18 and 2.27 kN for vehicle tractionforce. Furthermore, the correlation between actual andpredicted values (from FLS model) of vehicle tractionforce for different vehicle slippage is also examined. Thecorrelation coefficient is found as 0.93 which is significantin operation. Therefore, it can be inferred that the devel-oped fuzzy logic system can explain up to 86.5%(R2 = 0.865) of the total variability of traction force. Fur-thermore, the mean relative error of actual and predictedvalues from the FLS model on vehicle traction force isfound as 7% which is less than the acceptable limit of

Fig. 15. Correlation between actual and predicted values of traction force.

10%. Moreover, the goodness of fit of the prediction val-ues from the FLS model is found as 0.89. The value isfound to be close to 1.0 as expected.

The above results indicate that the system is qualified toreplace the work of an operator. This is a remarkable out-come, as it opens the access to agricultural application withvehicle operation in a fuzzy environment. It is worth men-tioning that predicted values are closer to the actual values.The fact that a computer has a greater ability to compare,remember, and correlate the conditions for different times,faster and more accurately than humans, reinforces thisbelief. Moreover, the more accurate traction force predic-tion, the system can be trained on scientific simulated datathat represents an optimal load, given a specific fuzzy setfor the input variables. The analysis of vehicle tractionforce and fuzzy logic system shows the good performanceof the developed electric golf car and hence warrant thenovelty of this work.

4. Adaptive fuzzy logic traction controller

An on-going research is to design and develop the fuzzylogic controller (FLC) to maintain the power deliveringfrom the battery pack to the DC motor of its optimal oper-ating point. Hence, power management of an off-road vehi-cle is established in order to minimize fuel consumption,while enhancing or maintaining the vehicle tractive perfor-mance. In this case, fuzzy logic controller is used which caneffectively control the motor output torque. A schematic ofthis control strategy is shown in Fig. 16. At any particularpoints, the power supply from the battery to the DC motoris determined based on the demand torque of the vehicle.The optimal power supply from the battery to the DCmotor optimal torque is adjusted initially with the batterypack adjusting mechanism which is mainly based on themoisture content (MC) of the terrain. The maximum powersupply is made to the DC motor for the maximum cardynamic torque development with the help of the FLC.The battery packs adjusting mechanism to control the var-iable power input (P) for the plant (motor) to develop thetraction torque (Tp) with FLC. It is noted that the sensinginputs of the wheel speed sensor (WSS), slope sensor (SS)and sinkage sensor (SiS) are effective for the car at highspeed and climbing on slope, respectively.

Consider a system with the plant model (Motor) of theform,

T p ¼ �apyp þ bpP ð32Þ

where P ¼ VI is the control variable, and Tp is the mea-sured state output torque in Nm, ap and bp are unknowncoefficient. In the model, the voltage supply is consideredas constant while the current supply is controlled by fuzzylogic controller. In equation, eventually the current is con-sidered as controlled variable. Assuming that it is desiredto obtain a closed – loop system described by

T m ¼ �amym þ bmr ð33Þ

Fig. 16. Fuzzy logic traction control system (TCS).


where r is the control variable, and Tm is the reference tor-que in Nm, am and bm are known coefficient.

After knowing the parameters of the plan, the followingcontrol law gives the model as follows:

(i) For the motor of rear left wheel motor (Motorrlw),

P 1ðtÞ ¼ brðtÞ � aT p1ðtÞ ð34Þ

(ii) For the rear right wheel motor (Motorrrw),

P 2ðtÞ ¼ brðtÞ � aT p2ðtÞ ð35Þwith b ¼ bm

bpa ¼ am�ap

bpand T p ¼ T p1

þ T p2

The output of the plant Tp1 and Tp2 are not equal all theways. It equality depends on the track conditions. Theerror variable of the control model,

eðtÞ ¼ T pðtÞ � T mðtÞ ð36ÞThe rate of change of the error can be defined as,

deðtÞdt ¼ ½�apT pðtÞ þ bpPðtÞ� � ½�amT mðtÞ þ bmrðtÞ�¼ �ameðtÞ þ ½am � ap � bpaðtÞ�T pðtÞ þ ½bpbðtÞ � bm� rðtÞ

ð37ÞEq. (37) indicates that the error of the control model will bezero if a(t) and b(t) are zero. The emphasis is given to con-struct a battery pack adjustment mechanism in MRATCSthat will drive the parameters a(t) and b(t) to appropriatevalues, such as the resulting control law for the motorforces the motor output Tp(t) to follow the model outputTm(t). In order to achieve this target, the Lyapunov func-tion is introduced,

V ðe; a; bÞ ¼ 1

2e2ðtÞ þ 1

bpcðbpaðtÞ þ ap � amÞ2 þ

1

bpcðbpbðtÞ � bmÞ2

� �ð38Þ

where c > 0. This function will be zero when e (t) is zeroand the controller parameters a(t) and b(t) are equal tothe optimal values.

5. Conclusion

Prediction of vehicle performance characteristics is nec-essary for agricultural applications. In this paper, the fuzzylogic system is presented and described its implementationon traction force prediction for an electric golf car. Thedeveloped fuzzy rules give a very good understandingabout the interaction between important soil parametersand their influence on vehicle traction. The results indicatethat the prediction accuracy of the developed fuzzy knowl-edge-based model is reasonably good. However, the mainconclusions drawn from this study are as follows:

1. The mean relative error of actual and predicted valuesfrom the FLS model on traction force is 7% which is lessthan the acceptable limit.

2. The system is quite easy to develop and it could be mod-ified easily if the soil parameters are changed in agricul-tural application.

Acknowledgement

The authors are grateful for the financial support pro-vided by International Islamic University Malaysia (IIUM)for this project.

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Fuzzy knowledge-based model for prediction of traction force of an electric golf car