IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 54, …

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 54, NO. 6, NOVEMBER 2005 1937

A Fuzzy Logic Control for Antilock Braking SystemIntegrated in the IMMa Tire Test Bench

Juan A. Cabrera, Antonio Ortiz, Juan J. Castillo, and Antonio Simon

Abstract—The use of fuzzy control strategies has recently gainedenormous acknowledgement for the control of nonlinear and time-variant systems. This article describes the development of a fuzzycontrol method for a tire antilock system in vehicles while braking,integrated in a tire test bench, thereby allowing us to imitate thefunctioning and to understand the behavior of these systems in areliable way. One of the inconveniences found in the developmentof these systems has been the difficulty of adjustment to the realconditions of a functioning vehicle. The main advantage obtainedwhen using the tire test bench is the possibility of being able toreproduce the conditions established as fundamental to the opera-tion of the antilock brake system (ABS) in a reliable and repetitiveway, and to adjust these systems until optimal performance is ob-tained. The fuzzy control system has been developed and tested inthe tire test bench to be able to refine its fundamental parameters,obtaining adequate results in all the studied conditions. The easeof the bench for the development and verification of new controlsystems for ABS has been demonstrated.

Index Terms—Antilock braking system (ABS), fuzzy control, tiretest bench.

I. INTRODUCTION

THE antilock braking system (ABS) is widely used in au-tomobiles. In an emergency braking situation the wheels

of a vehicle tend to lock quickly, increasing the longitudinalslip ratio of the vehicle. The slip ratio, while braking, is de-fined as the difference between the speed of the vehicle and thecircumferential speed of the tire, divided by the speed of thevehicle:

s =vveh − wwhl · re

vveh. (1)

When the lock of the wheel is total (s = 1), vehicle steeringcontrol and stability diminishes, and the braking distance nor-mally increases. Therefore, the goal of the braking control sys-tem is to maintain the slip ratio within the values which obtainthe maximum adherence coefficient (see Fig. 1) [1]. Achiev-ing this goal is difficult, because the maximum adherence zonevaries with many parameters, for example adherence conditionsbetween the road and the wheel, vertical load, inflation pressure,slip angle, and so on. Therefore, the ABS control systems needto know the exact point within the adhesion curves [µ-s] [2];

Manuscript received March 16, 2004; revised January 17, 2005, March 31,2005. This work was supported in part by the Government of Spain. Ministeriode Educacion y Ciencia, Comision Interministerial de Ciencia y Tecnologia(CICYT): Modelo Dinamico de Robots Moviles. Modelizacion de Neumaticos,TAP95-0383. The review of this paper was coordinated by Dr. M. Abul Masrur.

The authors are with the Mechanical Engineering Departament, Universityof Malaga, Plaza El Ejido s/n 29013 Malaga, Spain (e-mail: [email protected];[email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TVT.2005.853479

that is, we need to know the longitudinal slip ratio, friction co-efficient, and the conditions of real adherences. Achieving thistarget with accuracy is a difficult task in ABS systems. To ob-tain the real longitudinal slip ratio that each wheel of the vehicleis undergoing, it is necessary to know the linear speed of thevehicle and the angular speed of the wheel; however, in com-mercial braking control systems, there is only one parameter atour disposal—the angular speed of each of the wheels. Thereis no other sensor that measures the speed of the vehicle. Moststudies carried out so far try to estimate the speed of the vehicleor the friction coefficient, but each one includes some kind ofsensor which allows them to know another parameter that playsa role in the dynamics of the vehicle.

For example, in [3], the linear speed of the vehicle is es-timated by using a fuzzy control, but it introduces the linearacceleration of the center of gravity in the longitudinal direc-tion and the angular acceleration of the turn in relation to thevertical direction (yaw) as a known parameter. In [4], the slipreference is also obtained through a nonderivative optimizer,needing the linear acceleration of the center of gravity in thelongitudinal direction. This slip reference is used in a fuzzycontrol to obtain the brake torque. In [5] an RLS estimatoris used to obtain the adhesion characteristics, which needs toknow the brake pressure and the angular speed of the wheel asparameters. In [6], by using an extended Kalman filter, the stateof forces in each wheel is estimated, and by using a Bayesianmethod, the slip coefficient is determined, requiring knowledgeof, apart from the angular speeds of each wheel, the longitu-dinal and lateral and angular accelerations. In [7], an observeron a dynamic friction model between the road and the wheelis defined to estimate the speed of the vehicle and a parame-ter that defines the different types of roads, requiring the braketorque and the angular speed of the wheel as input to the sys-tem. Finally, in [8], by using an extended Kalman filter, theslope in the origin of the adhesion characteristic curve, [µ-s],is obtained, and with this parameter and the longitudinal slipratio, s, the type of road on which the vehicle runs is identi-fied, requiring knowledge of the longitudinal slip ratio for everyinstant.

As we can see, the summarized investigations in the previousparagraph are focused on determining the exact point within theadhesion curves [µ-s] and also the kind of surface in the road-wheel contact in a precise way. One of the problems found inthe works carried out in ABS systems is the disposition of testbenches to be able to evaluate and compare the behavior of theproposed algorithms in a real way. An example can be foundin [9], wherein a test bench consisting of an electrical traction en-gine connected to an induction machine is developed, and whichis used to simulate the road behavior. The bench developed in [9]

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1938 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 54, NO. 6, NOVEMBER 2005

Fig. 1. Adhesion characteristic curves.

has the limitation that it does not allow simulation of the lat-eral dynamics of the vehicle, variations in the inflation pressure,variations in the camber angle, variation in the adhesion of brakepads, and it does not take into consideration the real responseof a hydraulic brake system.

This article has two aims: the first one is to describe thedevelopment of a test bench [10] to be able to evaluate and verifybraking control algorithms. The test bench which is presentedreproduces the dynamic behavior of a vehicle circulating alonga road taking into consideration longitudinal behavior. Due tothe use of a conventional brake system, a dynamic responsecloser to reality is obtained. The second part of the work is theimplementation of a new ABS control system. In this controlsystem, the measurement that we need to know is the angularvelocity of the wheel, and knowing the control signal, whichis obtained from the system, we can obtain the brake pressure.With these two parameters and by means of an RLS estimationtechnique, with forgetting factor, the friction coefficient and thelinear speed of the vehicle is obtained, which in our case is thelinear speed of the flat belt. Once the linear speed is known,and according to (1), we calculate the longitudinal slip ratio.Therefore, with the friction coefficient and the longitudinal slipratio we can identify a point within the adhesion characteristiccurve [µ-s] (see Fig. 1). Now we only have to identify the kindof road. To achieve it, we use a first fuzzy block that obtains theexisting kind of road in the wheel-road contact with these twoparameters. This information is used to know the optimal slipreference, which serves to define the inputs in the second fuzzycontrol block that obtains the necessary braking pressure in thesystem.

Section II of this paper describes the brake system devel-oped in the test bench. The fuzzy braking control is describedin Section III. This braking control system is tested using thetest bench, obtaining the results that are shown in Section IV.Conclusions are given in Section V.

Fig. 2. IMMa tire test bench.

TABLE IINPUT VARIABLES

II. DESCRIPTION OF THE BRAKE SYSTEM

The developed brake system has been incorporated in the tirebench at the Department of Mechanical Engineering, Universityof Malaga (IMMa) (see Fig. 2) [10]. The fundamental advan-tages of using a test bench that simulates the dynamic behaviorof the wheel in contact with the road are 1) the possibility tocarry out tests repetitively and with all the possible variables(see Table I) varying according to the indicated function dur-ing the testing time and 2) our ability to obtain the values oflongitudinal and lateral forces, longitudinal slip ratio, and otherparameters as shown in Table II.

The brake system consists of a hydraulic circuit, which feedsa conventional brake piston which applies its force by meansof the brake pads to a brake disc. The disc has some notches atequal distances made along its circumference, where an induc-tive sensor at an appropriate distance is placed, for the reading ofthe angular velocity of the wheel. In the hydraulic circuit thereis also a sensor to measure braking pressure PB (see Fig. 3).The braking control is carried out through a proportional valve,activated by an amplifier card that allows establishing the law ofcontrol that we consider to be convenient. This valve is activatedby means of the main application that controls the tire test benchusing a known voltage-pressure relationship.

As we mentioned before, the brake system is totally integratedin the test bench and is consequently controlled by means of themain application which carries out the control of the whole testbench (see Fig. 4). This application allows us to establish thekind of test that we are going to perform, such as a test wherea sudden braking situation in curve is established, obtaining

CABRERA et al.: FUZZY LOGIC CONTROL FOR ANTILOCK BRAKING SYSTEM INTEGRATED IN THE IMMa TIRE TEST BENCH 1939

TABLE IIOUTPUT VARIABLES

Fig. 3. Brake system scheme.

information from all the sensors that we have established withinthe test (see Table II).

As described in Fig. 4, the main application carries out a seriesof independent processes in real time. Every process runs simul-taneously and has an assigned objective. When the informationof a test to be carried out has been recorded in the application,we proceed to the performance of it. The program carries outthe four processes which can be seen in the diagram:

1) Braking control process: this process is in charge of per-forming the braking control, establishing for this purposean optimal control law. This process handles the propor-tional valve of the hydraulic circuit in Fig. 4, which actsdirectly on the brake calliper installed on the wheel hub.

2) Movement actuators running process: this process is incharge of carrying out the movements that have beenestablished in the test. These can be movements in thetire (camber angle, slip angle, vertical position) or lateralmovement of the flat belt. It is also possible to change thevertical or the lateral load.

3) Erroneous parameters control process: it verifies that theparameters that are established in the test are within theranges of the flat belt and tire movement.

Fig. 4. Computer software diagram.

4) Data reading process: this process is in charge of the dataacquisition of the different sensors selected for the test.This data will be stored in the memory of the computerand afterwards recorded on the main hard disc.

As can be seen, the application has a set of processes whichallow carrying out the necessary movements in a predeterminedtest, reading the data that are programmed in it (see Table II),and performing, by means of the established rules, a controlaction in the brake system. Therefore, we have developed thewhole system necessary to be able to determine and check themost optimal braking process in our test bench.

III. FUZZY LOGIC ABS CONTROL

The use of fuzzy logic has gained great acknowledgementrecently as a methodology to design robust controllers of non-linear and time-variant systems. There are numerous works re-lated to braking fuzzy control [3], [4], [11]–[18]. In this work,an ABS control system has been developed and implemented inthe test bench. This system, as can be observed in the controlscheme described in Fig. 5, obtains information about the typeof road by means of a fuzzy logic block as an innovation of thepreviously mentioned works. Once the type of road is known,we establish the reference slip ratio adapted to such conditions.Another fuzzy logic block is used to determine the brake pres-sure using two inputs, the error between the reference and theactual slip ratio, and its variation in time. Our control diagramhas three clearly differentiated parts (see Fig. 5). In the firstpart, the adhesion characteristics are estimated by means of anRLS technique, and the speed of the belt is calculated. To dothis, we need to create a model of dynamic behavior of the testbench. In this work, the braking of the wheel will be developedfollowing a straight line. Therefore, the lateral dynamic of thewheel is not considered. Besides, measurements in the benchshow that slippage between the steel belt and the drums is verysmall, so its influence is not considered. Hence, the belt speed


Fig. 5. Pressure control scheme.

Fig. 6. Test bench scheme.

can be expressed as: v = wT · RT , where wT and RT are theangular velocity and radius of the driver drum, respectively.From Fig. 6, the following equations that create a model of thedynamic behavior of the tire and the flat belt are obtained:

Iw · ω = FX · re − TB

IB · ν

RT= TM − FX · RT . (2)

As can be seen in Fig. 6, the hydrodynamic bearing exerts aforce, NH , equal in magnitude to FZ , so there is no deformationin the steel belt, and friction between the steel belt and thebearing can be neglected. Also, rolling resistance force is notincluded in the previous equations, because these terms are smalland ignored in most ABS development works [2], [5], [6], [8],[9], [11], [13], [16]–[18].

The brake torque is expressed as a linear function with regardto the braking pressure; this is a simple model that is widely usedin ABS simulations, although other works [19], [20] use morecomplex expressions for the brake torque. Using the expres-sion of the longitudinal force, F X = µX · F Z , the following

equations are obtained:

Iw · ω = µX · FZ · re − PB · KB

IB · v

RT= TM − µX · FZ · RT . (3)

Focusing on the first equation of (3), and by means of anRLS regression technique with forgetting factor λ, the frictioncoefficient is obtained. The regression model would be Φt ·θ + εt = Y t , where Yt is the measurement vector, Φt is theregression vector, εt is the error, and θ is the parameter vector tobe estimated, which in our case is:

Yt =[wr (t) − wr (t − 1)

tm+

PB (t) · KB

Ir

]

Φt =[Fz · re

Ir

], θ = [µx(t)]. (4)

To obtain the measurement vector Yt , a sample time, tm =0.01 s, is established. This sample time is also used in thecontrol time of the braking control system. To update the co-variance [21] and the Kalman constant in the RLS algorithm,the following equations are used:

K(t) =P (t − 1) · Φt

λ + Φt · P (t − 1) · Φt

P (t) =P (t − 1)

λ· (1 − K(t) · Φt)

+ 1000 · (Y (t) − Φt · θ(t))2 (5)

where λ = 0.9 and initial condition θ(0) = 0, andP (0) = 10. Once the friction coefficient is known, the belt speed(v), integrating (3), is calculated:

v(t) = v(t − 1) +RT

IB·∫ t

t−1

(TM (t) − (µx(t) · FZ ) · RT ) · dt.

(6)The following parameters of this expression are known: RT

(radius of the driver drum), IB (inertia moment of the system),and FZ (vertical load). Vertical load is kept constant in thiswork, although the bench allows us to simulate vertical load


Fig. 7. Membership functions in road type fuzzy control. (a) Adhesion coef-ficient input. (b) Slip input. (c) Road type output.

TABLE IIIMEMBER FUNCTIONS VALUES. (A) ADHESION COEFFICIENT VALUES. (B) SLIP

VALUES. (C) ROAD TYPE VALUES

changes. A model for vertical load that only needs to know thevalue of the friction coefficient to simulate vertical load changesis proposed in [22].

As during braking, the clutch is usually disengaged [23],and we can consider the engine torque TM (t) = 0. The frictioncoefficient µX (t)is known in every instant because we haveestimated it previously. Therefore, we will know the value ofthe linear speed of the flat belt. Once we have obtained thevalue of the speed, v(t), we will be able to obtain the valueof the longitudinal slip ratio directly, by simply applying (1).Knowing both the s(t) and µX (t) values, a point of the adhesioncharacteristic curve is determined.

The second part of the control diagram is a fuzzy identifi-cation block to obtain the type of road. Once the point [µ-s]in the characteristic curve is determined, we have to know towhich curve it belongs; that is, which is the kind of wheel-roadcontact at that moment. This control block has two input mem-bership functions called ‘adhesion coefficient’ and ‘slip,’ andone output membership function called ‘road type,’ which areshown in Fig. 7.

The membership functions are triangular and trapezoidal (seeFig. 7) and their values are determined in Table III.

The performance of this fuzzy identification block wouldbe, in a summarized way, the following: the inputs defined as‘adhesion coefficient’ and ‘slip’ are real values (crisp) and ob-tained in the first part of the control system. These values arefuzzified in a first phase; that is, the input values are turned

into diffuse sets, for example, for a slip input of 0.4 (seeFig. 7(b)), the fuzzifier turns this value into the following mem-bership grades: µ(slip = zero) = 0, µ(slip = mid) = 0.67 andµ(slip = high) = 0.5. Once we have the diffuse set values, weapply the existing rules in the knowledge base. These rules arethe if-them type. More than one of the rules in the knowledgebase can be activated at the same time and have logical opera-tors like AND, OR and NOT in the antecedent, the same as inclassical logic. In our inference system, the logical operators aredefined as follows:

{µ(slip = mid) = 0.67 AND µ(slip = high) = 0.5}= min(0.67, 0.5)

{µ(slip = mid) = 0.67 OR µ(slip = high) = 0.5}= max(0.67, 0.5)

{NOT µ(slip = mid) = 0.67} = (1 − 0.67).

Once the antecedent is solved with the logical operators ofthe rule, the implication is carried out and the consequent isobtained from each of the rules, which are truncated diffusesets, by the value of the antecedent. These are added up, andthen we go on to the defuzzification phase. In this phase, we goon from a diffuse set to an exact real value (crisp). In our case,we have used a centroid method.

At this moment, only the rules for the road type fuzzy iden-tification block have to be defined. The control rules and themembership functions have been adjusted in the test bench.The rules have been obtained according to the slip behavior inthe adhesion characteristic curves. These curves clearly havethree performance zones shown in Fig. 8. As we can observe inFig. 8(b), in the A zone of the curve, the variation of the slopeis always positive and we are within the linear part of the curve.In the B zone, which is the maximum slip zone and where thebrake control must work, the variation of the slope becomeszero and finally, in the C zone, the variation is negative and thatis when the maximum slip takes place in the wheel.

With this knowledge of the adhesion curves, the rules havebeen established. In Fig. 8, two studied cases are shown whichproduce a similar performance in the brake system. For thisreason, only the slip in the braking control system has beenconsidered as input (see Fig. 5). In Fig. 8(a) the fuzzy controlrules are shown in the case where the variable input is the slip. Inthis case, the slip has been divided in three zones (zero, middle,and high), making them coincide with the three differentiatedzones in the adhesion characteristic curve.

Finally in Fig. 8(b), the slope of the characteristic curve isused as the input in the fuzzy control. This slope is obtainedby subtracting the friction coefficient in the studied instant andthe friction coefficient in the previous instant, and dividing itby the difference between the slip in that instant and the slipin the previous instant. Once the slope is obtained, we divide itin three zones (positive, zero, and negative), obtaining the rulesthat are shown in the figure.

It can be observed that the rules are the same in both cases.Only the input membership functions change (slip or slope). Asreflected in the rules, when the slip is in the A zone of the curve,


Fig. 8. (a) Determination of fuzzy rules with slip membership function. (b) Fuzzy rules for slope membership function.

the curve is of a major adherence, so in this part the brakingcontrol can raise the braking pressure. Once the slip enters theB or C zone, the kind of road depends on the adhesion values;that is, the more adhesion there is, the more adherence there isto the road.

Once the rules have been established, the surface that gen-erates the inference system with the different values of theoutput variables and the input variable for the two studiedcases are obtained. These surfaces have been calculated usingMATLAB’s Fuzzy Logic Toolbox with the Mamdani’s fuzzyinference system (see Fig. 9).

The third and last part of the control diagram is a fuzzy controlblock which is in charge of obtaining the braking pressure.According to Fig. 5, inputs are established as:

e(t) = sref(t) − s(t)

de(t) = e(t) − e(t − tm ). (7)

The first equation determines the existing error between theslip reference, obtained from the kind of road, and the slipestimated in that instant. The fuzzy logic block that determinesthe kind of road gives a value between 0 and 1, meaning 0


Fig. 9. (a) Fuzzy logic controller’s 3-D input-output map, case I. (b) Fuzzy logic controller’s 3-D input-output map, case II.

Fig. 10. Membership functions in the second fuzzy control. (a) Error input.(b) Error difference input. (c) Pressure output.

a low adherence road and 1 a high adherence road, and wemultiply this value by 0.3 (slip to obtain the maximum adhesioncoefficient in a high adherence road) to obtain the slip reference.So we have established a relationship between the kind of roadand the slip where the adhesion coefficient is maximum. Thesecond equation determines the difference between the error inthat instant of time and the error in the previous instant of time.The membership functions for the established parameters are,in this case.

As we can observe in Fig. 10, the membership functions arealso triangular and trapezoidal, and the values for each of thevariables are reflected in Table IV.

It should be noted that the membership functions for theerror input variable are not symmetrical with regard to theY-axis. This is due to the fact that according to (7), the existingdifference between the slip reference sref(t) and the slip in thatinstant s(t) is not in the same order, because the slip referencedoes not reach a value of more than 0.1–0.3. Therefore, the

TABLE IVMEMBERSHIP FUNCTION VALUES. (A) ERROR VALUES. (B) DIFERROR

VALUES. (C) PRESSURE VALUES

negative values of the error will be higher than the positiveones.

The inference system used in this fuzzy control block is thesame as the one used in the previous case. Once the input andoutput variables have been established to the control, a study ofthe behavior required for the control is carried out to be ableto define the rules that govern it. To establish the control rules,six differentiated cases of behavior of the input variables areestablished (see Fig. 11).

In the first case in Fig. 11(a), the error is positive or largepositive, and the pressure will be high because we are in thepart of the curve where we have not reached the maximum slipcoefficient. In the second case [Fig. 11(b)], the error is largenegative which means that the wheel is locked so we have tomake the pressure zero. These are the two simplest cases forwhich to establish the rules. For the following rules we have totake the difference of the committed error into consideration,and they are rules to establish the behavior when we are nearthe reference slip; that is, when the error is zero or when weslightly exceed the limit of the reference slip.

First we establish the rules when the error is negative. Thatis, we have slightly exceeded the limit of the reference slip.To establish the rules, we must observe Fig. 11(c) and (d).In Fig. 11(c) the error is negative and the error difference ispositive. In this case, the error was bigger in the previous instantthan the existing error in this instant of time. This means that wecome from a situation of low pressure and we are diminishingthe slip, which means that we can increase the braking pressurea little. In case the slip in the previous instant is the same asin this instant; that is, the error difference is zero, we can also


Fig. 11. Error and error difference behavior. (a) Positive error. (b) Large negative error. (c) Negative error and positive error difference. (d) Negative error andnegative error difference. (e) Zero error and positive error difference. (f) Zero error and negative error difference.


Fig. 12. Fuzzy logic pressure controller’s 3-D input-output map and rules.

increase the pressure a little, but less than in the previous cases.Fig. 11(d) shows the case in which the error continues being lownegative and the error difference is negative too. In this case,in the previous instant we are in the zone where we have notexceeded the slip limit or we have exceeded it but less than in thestudied instant, so we are applying a high pressure, which meansthat if we have exceeded the slip limit more in the following timeincrease, we have to reduce the pressure.

Finally, we establish the rules for the case in which the com-mitted error is zero; that is, when the slip in that instant of timeis equal to the slip limit. This is shown in Fig. 11(c)–(f). Inthe first case, when the error is zero and the slip in the pre-vious instant is superior to the slip limit [Fig. 11(e)]; that is,the error difference is positive, then the same thing happens asin the previous cases. In other words, we were in a situationin which the pressure was low and we have managed to re-duce the slip, so we increase the braking pressure, but with avalue which is a little higher than in the negative error case. Incase the slip in the previous instant is also the slip limit, then weincrease the braking pressure, but in this case with a very lowvalue.

Finally, in the case in which the error is zero and the slip in theprevious instant is inferior to the slip limit [Fig. 11(f)], in thiscase we were in a situation in which the pressure was increasedand we achieved an increase in the slip, so the braking pressurehas to be reduced.

Once the conditions of each rule have been established,the rules for the developed fuzzy control and the surfacethat the inference system generates are shown in Fig. 12. Asin the previous case, the surface has been obtained using MAT-LAB’s Fuzzy Logic Toolbox and Mamdani’s fuzzy inferencesystem.

IV. RESULTS

In this section, a series of results obtained with the proposedbrake control and the test performed in the previously describedtest bench are shown. The computer application developed tocarry out the control of the test bench and to obtain the results

TABLE VMODEL PARAMETERS

of the tests, as they were described in Fig. 4, has been pro-grammed with C++ language, although the simulation of thetest bench and the proposed control have been carried out withMATLAB’s Simulink Toolbox. For both cases, a series of pa-rameters that need the proposed control have been used, some ofwhich have been obtained in the test bench from tests, and oth-ers read directly from the sensors of the bench. The parametersare reflected in Table V.

The first test carried out is a brake test with the developedcontrol and with a Michelin MTX R14 65 tire. In this case,the test is carried out with a flat belt whose adhesion charac-teristics were found by performing tests of longitudinal forcein the test bench. Later, the encountered curve is introduced inthe test bench model and the brake control for its simulation.Therefore, we have three different named speeds: real, simu-lated, and estimated. The real speed is obtained in the test benchby means of a sensor, which reads it directly when the test iscarried out. In this case, the programmed brake control startsto work in the main application as described in Fig. 4. The es-timated speed is the one obtained by means of (6), previouslyestimating the slip coefficient and finally the simulated speedwhich is obtained simulating the test bench and the developedcontrol with Simulink. The result of this first test is shown inFig. 13.

In Fig. 13(a), the behavior of the three previously mentionedspeeds in the test carried out can be observed. We see that the


Fig. 13. Control behavior for MICHELIN MTX R14. (a) Belt velocities graphic. (b) Brake pressures graphic. (c) Kind of road.

values of the three are similar, which validates the simulationstudied in the test. On the other side, the behavior of the brakepressure in the test bench and the estimated brake pressure canalso be observed [see Fig. 13(b)]. The estimated brake pressureis obtained by means of the brake system model, and it is similarto the real brake pressure which is measured in the test bench.According to this test, the behavior of the brake system modelis accurate. Finally, the control behavior to obtain the road typeis drawn in Fig. 13(c).

The following test was carried out changing the adhesioncharacteristics and the execution time to test the dynamic be-havior of the control system in a wide range of road conditions.This test was performed with the same tire as previously, andall start at a belt speed of 27.2 m/s.

Fig. 14 shows the control behavior in dry and wet road con-ditions. Fig. 14(c) shows how the control detects the change inadherence conditions and so the control adjust the pressure level

of the brake as it is shown in Fig. 14(b). We also observe how thecontrol adjusts the slip level seen in Fig. 14(d) ranging between0.14–0.18 for wet road conditions and 0.13 for dry road condi-tions. These slip levels depend on the adjustment of the mem-bership functions of the control which establish the road typeand the value of the maximum optimum slip (sopt). Both pa-rameters have been adapted to obtain the optimum performanceof the brake control and to maintain the slip in all the testedconditions within the appropriate values.

In Fig. 15, the behavior of the brake control, in which theadherence conditions are wet and snowy asphalt, is shown.

Fig. 15(c) shows how the control estimates the existing roadtype and how the brake pressure decreases considerably whenthe control detects snow in the wheel-road contact. In Fig. 15(d),the slip varies between 0.15–0.16 in the case of wet asphalt andbetween 0.15–0.18 in the case of snow. Finally, Fig. 16 showsthe behavior in the case of wet and icy asphalt.


Fig. 14. Control behavior in dry and wet conditions.

Fig. 15. Control behavior in wet and snow conditions.


Fig. 16. Control behavior in wet and ice conditions.

V. CONCLUSION

The key goals of this work have been the construction of atest bench capable of testing algorithms of ABS brake controlswhich adjust adequately to the real conditions of performancedemanded for vehicles, and the development of a fuzzy brakecontrol system. As the simulations show, the fuzzy brake controlsystem keeps the slip and the friction coefficient in the optimumzone of the adhesion curve and is able to detect different kindof roads and adherence changes during simulation.

The robustness of the fuzzy control and its capacity to adaptto different dynamic adherence changes have been confirmed.Additionally, the results suggest that the use of fuzzy logicfor ABS brake control improves the longitudinal behavior inbraking processes in vehicles.

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Juan A. Cabrera received the B.S., M.S., and Ph.D.degrees in mechanical engineering from the Univer-sity of Malaga, Spain.

He is currently an Associate Professor of Mechan-ical Engineering at the University of Malaga. Hisresearch interests include modeling and control ofvehicle systems, advanced vehicle systems, geneticalgorithms applied to mechanisms and tire models,and multiobjective evolutionary strategies.

Antonio Ortiz received the B.S. and M.S. degreesin mechanical engineering from the Polytechnic Uni-versity of Madrid, Spain. He is a Ph.D. candidate atthe University of Malaga.

He is currently an Associate Professor of Me-chanical Engineering at the University of Malaga.His research interests include tire models and geneticalgorithms applied to tire models, and multiobjectiveevolutionary strategies.

Juan J. Castillo received the B.S. and M.S. degreesin mechanical engineering from the University ofMalaga, Spain, and is currently pursuing the Ph.D.degree there.

He is an Associate Professor of Mechanical En-gineering at the University of Malaga. His researchinterests include control and modeling of brake andsuspensions systems, and tire parameters estimation.

Antonio Simon received the B.S., M.S., and Ph.D.degrees in aeronautical engineering from the Poly-technic University of Madrid, Spain.

He is currently a Professor of Mechanical Engi-neering at the University of Malaga, Spain, and heis the Department Head of Mechanical Engineeringat Malaga University. His research interests includemodeling and control of vehicle systems, advancedvehicle systems, genetic algorithms applied to mech-anisms, and tire models and biomechanics.

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