A Fuzzy Logic Control for Antilock Braking System ... - Semantic Scholar

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

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A Fuzzy Logic Control for Antilock Braking System Integrated in the IMMa Tire Test Bench Juan A. Cabrera, Antonio Ortiz, Juan J. Castillo, and Antonio Simón

Abstract—The use of fuzzy control strategies has recently gained enormous acknowledgement for the control of nonlinear and timevariant systems. This article describes the development of a fuzzy control method for a tire antilock system in vehicles while braking, integrated in a tire test bench, thereby allowing us to imitate the functioning and to understand the behavior of these systems in a reliable way. One of the inconveniences found in the development of these systems has been the difficulty of adjustment to the real conditions of a functioning vehicle. The main advantage obtained when using the tire test bench is the possibility of being able to reproduce the conditions established as fundamental to the operation of the antilock brake system (ABS) in a reliable and repetitive way, and to adjust these systems until optimal performance is obtained. The fuzzy control system has been developed and tested in the tire test bench to be able to refine its fundamental parameters, obtaining adequate results in all the studied conditions. The ease of the bench for the development and verification of new control systems for ABS has been demonstrated. Index Terms—Antilock braking system (ABS), fuzzy control, tire test bench.

I. INTRODUCTION HE antilock braking system (ABS) is widely used in automobiles. In an emergency braking situation the wheels of a vehicle tend to lock quickly, increasing the longitudinal slip ratio of the vehicle. The slip ratio, while braking, is defined as the difference between the speed of the vehicle and the circumferential speed of the tire, divided by the speed of the vehicle: vveh − wwhl · re . (1) s= vveh

T

When the lock of the wheel is total (s = 1), vehicle steering control and stability diminishes, and the braking distance normally increases. Therefore, the goal of the braking control system is to maintain the slip ratio within the values which obtain the maximum adherence coefficient (see Fig. 1) [1]. Achieving this goal is difficult, because the maximum adherence zone varies with many parameters, for example adherence conditions between the road and the wheel, vertical load, inflation pressure, slip angle, and so on. Therefore, the ABS control systems need to 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. Ministerio de Educacioń y Ciencia, Comisioń Interministerial de Ciencia y Tecnologiá (CICYT): Modelo Dinámico de Robots Mo´viles. Modelizacioń de Neumáticos, TAP95-0383. The review of this paper was coordinated by Dr. M. Abul Masrur. The authors are with the Mechanical Engineering Departament, University of Málaga, Plaza El Ejido s/n 29013 Málaga, 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 coefficient, and the conditions of real adherences. Achieving this target with accuracy is a difficult task in ABS systems. To obtain the real longitudinal slip ratio that each wheel of the vehicle is undergoing, it is necessary to know the linear speed of the vehicle and the angular speed of the wheel; however, in commercial braking control systems, there is only one parameter at our disposal—the angular speed of each of the wheels. There is no other sensor that measures the speed of the vehicle. Most studies carried out so far try to estimate the speed of the vehicle or the friction coefficient, but each one includes some kind of sensor which allows them to know another parameter that plays a role in the dynamics of the vehicle. For example, in [3], the linear speed of the vehicle is estimated by using a fuzzy control, but it introduces the linear acceleration of the center of gravity in the longitudinal direction and the angular acceleration of the turn in relation to the vertical direction (yaw) as a known parameter. In [4], the slip reference is also obtained through a nonderivative optimizer, needing the linear acceleration of the center of gravity in the longitudinal direction. This slip reference is used in a fuzzy control to obtain the brake torque. In [5] an RLS estimator is used to obtain the adhesion characteristics, which needs to know the brake pressure and the angular speed of the wheel as parameters. In [6], by using an extended Kalman filter, the state of forces in each wheel is estimated, and by using a Bayesian method, the slip coefficient is determined, requiring knowledge of, apart from the angular speeds of each wheel, the longitudinal and lateral and angular accelerations. In [7], an observer on a dynamic friction model between the road and the wheel is defined to estimate the speed of the vehicle and a parameter that defines the different types of roads, requiring the brake torque and the angular speed of the wheel as input to the system. Finally, in [8], by using an extended Kalman filter, the slope in the origin of the adhesion characteristic curve, [µ-s], is obtained, and with this parameter and the longitudinal slip ratio, s, the type of road on which the vehicle runs is identified, requiring knowledge of the longitudinal slip ratio for every instant. As we can see, the summarized investigations in the previous paragraph are focused on determining the exact point within the adhesion curves [µ-s] and also the kind of surface in the roadwheel contact in a precise way. One of the problems found in the works carried out in ABS systems is the disposition of test benches to be able to evaluate and compare the behavior of the proposed algorithms in a real way. An example can be found in [9], wherein a test bench consisting of an electrical traction engine connected to an induction machine is developed, and which is used to simulate the road behavior. The bench developed in [9]

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Fig. 2.

Fig. 1.

Adhesion characteristic curves.

has the limitation that it does not allow simulation of the lateral dynamics of the vehicle, variations in the inflation pressure, variations in the camber angle, variation in the adhesion of brake pads, and it does not take into consideration the real response of a hydraulic brake system. This article has two aims: the first one is to describe the development of a test bench [10] to be able to evaluate and verify braking control algorithms. The test bench which is presented reproduces the dynamic behavior of a vehicle circulating along a road taking into consideration longitudinal behavior. Due to the use of a conventional brake system, a dynamic response closer to reality is obtained. The second part of the work is the implementation of a new ABS control system. In this control system, the measurement that we need to know is the angular velocity of the wheel, and knowing the control signal, which is obtained from the system, we can obtain the brake pressure. With these two parameters and by means of an RLS estimation technique, with forgetting factor, the friction coefficient and the linear speed of the vehicle is obtained, which in our case is the linear 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 slip ratio we can identify a point within the adhesion characteristic curve [µ-s] (see Fig. 1). Now we only have to identify the kind of road. To achieve it, we use a first fuzzy block that obtains the existing kind of road in the wheel-road contact with these two parameters. This information is used to know the optimal slip reference, which serves to define the inputs in the second fuzzy control block that obtains the necessary braking pressure in the system. Section II of this paper describes the brake system developed in the test bench. The fuzzy braking control is described in Section III. This braking control system is tested using the test bench, obtaining the results that are shown in Section IV. Conclusions are given in Section V.

IMMa tire test bench. TABLE I INPUT VARIABLES

II. DESCRIPTION OF THE BRAKE SYSTEM The developed brake system has been incorporated in the tire bench at the Department of Mechanical Engineering, University of Malaga (IMMa) (see Fig. 2) [10]. The fundamental advantages of using a test bench that simulates the dynamic behavior of the wheel in contact with the road are 1) the possibility to carry out tests repetitively and with all the possible variables (see Table I) varying according to the indicated function during the testing time and 2) our ability to obtain the values of longitudinal and lateral forces, longitudinal slip ratio, and other parameters as shown in Table II. The brake system consists of a hydraulic circuit, which feeds a conventional brake piston which applies its force by means of the brake pads to a brake disc. The disc has some notches at equal distances made along its circumference, where an inductive sensor at an appropriate distance is placed, for the reading of the angular velocity of the wheel. In the hydraulic circuit there is 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 of control that we consider to be convenient. This valve is activated by means of the main application that controls the tire test bench using a known voltage-pressure relationship. As we mentioned before, the brake system is totally integrated in the test bench and is consequently controlled by means of the main application which carries out the control of the whole test bench (see Fig. 4). This application allows us to establish the kind of test that we are going to perform, such as a test where a 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

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TABLE II OUTPUT VARIABLES

Fig. 4.

Computer software diagram.

4) Data reading process: this process is in charge of the data acquisition of the different sensors selected for the test. This data will be stored in the memory of the computer and afterwards recorded on the main hard disc. As can be seen, the application has a set of processes which allow carrying out the necessary movements in a predetermined test, reading the data that are programmed in it (see Table II), and performing, by means of the established rules, a control action in the brake system. Therefore, we have developed the whole system necessary to be able to determine and check the most optimal braking process in our test bench. Fig. 3.

Brake system scheme.

III. FUZZY LOGIC ABS CONTROL information from all the sensors that we have established within the test (see Table II). As described in Fig. 4, the main application carries out a series of independent processes in real time. Every process runs simultaneously and has an assigned objective. When the information of a test to be carried out has been recorded in the application, we proceed to the performance of it. The program carries out the four processes which can be seen in the diagram: 1) Braking control process: this process is in charge of performing the braking control, establishing for this purpose an optimal control law. This process handles the proportional valve of the hydraulic circuit in Fig. 4, which acts directly on the brake calliper installed on the wheel hub. 2) Movement actuators running process: this process is in charge of carrying out the movements that have been established in the test. These can be movements in the tire (camber angle, slip angle, vertical position) or lateral movement of the flat belt. It is also possible to change the vertical or the lateral load. 3) Erroneous parameters control process: it verifies that the parameters that are established in the test are within the ranges of the flat belt and tire movement.

The use of fuzzy logic has gained great acknowledgement recently as a methodology to design robust controllers of nonlinear and time-variant systems. There are numerous works related to braking fuzzy control [3], [4], [11]–[18]. In this work, an ABS control system has been developed and implemented in the test bench. This system, as can be observed in the control scheme described in Fig. 5, obtains information about the type of road by means of a fuzzy logic block as an innovation of the previously 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 pressure using two inputs, the error between the reference and the actual slip ratio, and its variation in time. Our control diagram has three clearly differentiated parts (see Fig. 5). In the first part, the adhesion characteristics are estimated by means of an RLS technique, and the speed of the belt is calculated. To do this, we need to create a model of dynamic behavior of the test bench. In this work, the braking of the wheel will be developed following a straight line. Therefore, the lateral dynamic of the wheel is not considered. Besides, measurements in the bench show that slippage between the steel belt and the drums is very small, so its influence is not considered. Hence, the belt speed

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Fig. 5.


Pressure control scheme.

equations are obtained: Iw · ω˙ = µX · FZ · re − PB · KB IB ·

Fig. 6.

can be expressed as: v = wT · RT , where wT and RT are the angular velocity and radius of the driver drum, respectively. From Fig. 6, the following equations that create a model of the dynamic behavior of the tire and the flat belt are obtained: Iw · ω˙ = FX · re − TB ν˙ = T M − FX · R T . RT

(3)

Focusing on the first equation of (3), and by means of an RLS regression technique with forgetting factor λ, the friction coefficient is obtained. The regression model would be Φt · θ + εt = Y t , where Yt is the measurement vector, Φt is the regression vector, εt is the error, and θ is the parameter vector to be estimated, which in our case is: wr (t) − wr (t − 1) PB (t) · KB Yt = + tm Ir Fz · re Φt = (4) , θ = [µx (t)]. Ir

Test bench scheme.

IB ·

v˙ = TM − µX · FZ · RT . RT

(2)

As can be seen in Fig. 6, the hydrodynamic bearing exerts a force, NH , equal in magnitude to FZ , so there is no deformation in the steel belt, and friction between the steel belt and the bearing can be neglected. Also, rolling resistance force is not included in the previous equations, because these terms are small and 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 regard to the braking pressure; this is a simple model that is widely used in ABS simulations, although other works [19], [20] use more complex expressions for the brake torque. Using the expression of the longitudinal force, F X = µX · F Z , the following

To obtain the measurement vector Yt , a sample time, tm = 0.01 s, is established. This sample time is also used in the control time of the braking control system. To update the covariance [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) · (1 − K(t) · Φt ) λ + 1000 · (Y (t) − Φt · θ(t))2

(5)

where λ = 0.9 and initial condition θ(0) = 0, and P (0) = 10. Once the friction coefficient is known, the belt speed (v), integrating (3), is calculated: t RT · (TM (t) − (µx (t) · FZ ) · RT ) · dt. v(t) = v(t − 1) + IB t−1 (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 this work, although the bench allows us to simulate vertical load


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into diffuse sets, for example, for a slip input of 0.4 (see Fig. 7(b)), the fuzzifier turns this value into the following membership grades: µ(slip = zero) = 0, µ(slip = mid) = 0.67 and µ(slip = high) = 0.5. Once we have the diffuse set values, we apply the existing rules in the knowledge base. These rules are the if-them type. More than one of the rules in the knowledge base can be activated at the same time and have logical operators like AND, OR and NOT in the antecedent, the same as in classical logic. In our inference system, the logical operators are defined 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). Fig. 7. Membership functions in road type fuzzy control. (a) Adhesion coefficient input. (b) Slip input. (c) Road type output.

TABLE III MEMBER FUNCTIONS VALUES. (A) ADHESION COEFFICIENT VALUES. (B) SLIP VALUES. (C) ROAD TYPE VALUES

changes. A model for vertical load that only needs to know the value of the friction coefficient to simulate vertical load changes is proposed in [22]. As during braking, the clutch is usually disengaged [23], and we can consider the engine torque TM (t) = 0. The friction coefficient µX (t)is known in every instant because we have estimated it previously. Therefore, we will know the value of the linear speed of the flat belt. Once we have obtained the value of the speed, v(t), we will be able to obtain the value of the longitudinal slip ratio directly, by simply applying (1). Knowing both the s(t) and µX (t) values, a point of the adhesion characteristic curve is determined. The second part of the control diagram is a fuzzy identification block to obtain the type of road. Once the point [µ-s] in the characteristic curve is determined, we have to know to which curve it belongs; that is, which is the kind of wheel-road contact at that moment. This control block has two input membership functions called ‘adhesion coefficient’ and ‘slip,’ and one output membership function called ‘road type,’ which are shown in Fig. 7. The membership functions are triangular and trapezoidal (see Fig. 7) and their values are determined in Table III. The performance of this fuzzy identification block would be, in a summarized way, the following: the inputs defined as ‘adhesion coefficient’ and ‘slip’ are real values (crisp) and obtained in the first part of the control system. These values are fuzzified in a first phase; that is, the input values are turned

Once the antecedent is solved with the logical operators of the rule, the implication is carried out and the consequent is obtained from each of the rules, which are truncated diffuse sets, by the value of the antecedent. These are added up, and then we go on to the defuzzification phase. In this phase, we go on 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 identification block have to be defined. The control rules and the membership functions have been adjusted in the test bench. The rules have been obtained according to the slip behavior in the adhesion characteristic curves. These curves clearly have three performance zones shown in Fig. 8. As we can observe in Fig. 8(b), in the A zone of the curve, the variation of the slope is always positive and we are within the linear part of the curve. In the B zone, which is the maximum slip zone and where the brake control must work, the variation of the slope becomes zero and finally, in the C zone, the variation is negative and that is when the maximum slip takes place in the wheel. With this knowledge of the adhesion curves, the rules have been established. In Fig. 8, two studied cases are shown which produce a similar performance in the brake system. For this reason, only the slip in the braking control system has been considered as input (see Fig. 5). In Fig. 8(a) the fuzzy control rules are shown in the case where the variable input is the slip. In this case, the slip has been divided in three zones (zero, middle, and high), making them coincide with the three differentiated zones in the adhesion characteristic curve. Finally in Fig. 8(b), the slope of the characteristic curve is used as the input in the fuzzy control. This slope is obtained by subtracting the friction coefficient in the studied instant and the friction coefficient in the previous instant, and dividing it by the difference between the slip in that instant and the slip in the previous instant. Once the slope is obtained, we divide it in three zones (positive, zero, and negative), obtaining the rules that 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). As reflected in the rules, when the slip is in the A zone of the curve,

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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 braking control can raise the braking pressure. Once the slip enters the B or C zone, the kind of road depends on the adhesion values; that is, the more adhesion there is, the more adherence there is to the road. Once the rules have been established, the surface that generates the inference system with the different values of the output variables and the input variable for the two studied cases are obtained. These surfaces have been calculated using MATLAB’s Fuzzy Logic Toolbox with the Mamdani’s fuzzy inference system (see Fig. 9).

The third and last part of the control diagram is a fuzzy control block 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 the slip reference, obtained from the kind of road, and the slip estimated in that instant. The fuzzy logic block that determines the kind of road gives a value between 0 and 1, meaning 0


Fig. 9.

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(a) Fuzzy logic controller’s 3-D input-output map, case I. (b) Fuzzy logic controller’s 3-D input-output map, case II. TABLE IV MEMBERSHIP FUNCTION VALUES. (A) ERROR VALUES. (B) DIFERROR VALUES. (C) PRESSURE VALUES

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 we multiply this value by 0.3 (slip to obtain the maximum adhesion coefficient in a high adherence road) to obtain the slip reference. So we have established a relationship between the kind of road and the slip where the adhesion coefficient is maximum. The second equation determines the difference between the error in that 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 are also triangular and trapezoidal, and the values for each of the variables are reflected in Table IV. It should be noted that the membership functions for the error input variable are not symmetrical with regard to the Y-axis. This is due to the fact that according to (7), the existing difference between the slip reference sref (t) and the slip in that instant s(t) is not in the same order, because the slip reference does not reach a value of more than 0.1–0.3. Therefore, the

negative values of the error will be higher than the positive ones. The inference system used in this fuzzy control block is the same as the one used in the previous case. Once the input and output variables have been established to the control, a study of the behavior required for the control is carried out to be able to define the rules that govern it. To establish the control rules, six differentiated cases of behavior of the input variables are established (see Fig. 11). In the first case in Fig. 11(a), the error is positive or large positive, and the pressure will be high because we are in the part of the curve where we have not reached the maximum slip coefficient. In the second case [Fig. 11(b)], the error is large negative which means that the wheel is locked so we have to make the pressure zero. These are the two simplest cases for which to establish the rules. For the following rules we have to take the difference of the committed error into consideration, and they are rules to establish the behavior when we are near the reference slip; that is, when the error is zero or when we slightly exceed the limit of the reference slip. First we establish the rules when the error is negative. That is, 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 is positive. In this case, the error was bigger in the previous instant than the existing error in this instant of time. This means that we come from a situation of low pressure and we are diminishing the slip, which means that we can increase the braking pressure a little. In case the slip in the previous instant is the same as in this instant; that is, the error difference is zero, we can also

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


Fig. 12.

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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 low negative and the error difference is negative too. In this case, in the previous instant we are in the zone where we have not exceeded the slip limit or we have exceeded it but less than in the studied instant, so we are applying a high pressure, which means that if we have exceeded the slip limit more in the following time increase, we have to reduce the pressure. Finally, we establish the rules for the case in which the committed error is zero; that is, when the slip in that instant of time is equal to the slip limit. This is shown in Fig. 11(c)–(f). In the first case, when the error is zero and the slip in the previous instant is superior to the slip limit [Fig. 11(e)]; that is, the error difference is positive, then the same thing happens as in the previous cases. In other words, we were in a situation in which the pressure was low and we have managed to reduce the slip, so we increase the braking pressure, but with a value which is a little higher than in the negative error case. In case the slip in the previous instant is also the slip limit, then we increase the braking pressure, but in this case with a very low value. Finally, in the case in which the error is zero and the slip in the previous instant is inferior to the slip limit [Fig. 11(f)], in this case we were in a situation in which the pressure was increased and we achieved an increase in the slip, so the braking pressure has to be reduced. Once the conditions of each rule have been established, the rules for the developed fuzzy control and the surface that the inference system generates are shown in Fig. 12. As in the previous case, the surface has been obtained using MATLAB’s Fuzzy Logic Toolbox and Mamdani’s fuzzy inference system. IV. RESULTS In this section, a series of results obtained with the proposed brake control and the test performed in the previously described test bench are shown. The computer application developed to carry out the control of the test bench and to obtain the results

TABLE V MODEL PARAMETERS

of the tests, as they were described in Fig. 4, has been programmed with C++ language, although the simulation of the test bench and the proposed control have been carried out with MATLAB’s Simulink Toolbox. For both cases, a series of parameters that need the proposed control have been used, some of which have been obtained in the test bench from tests, and others read directly from the sensors of the bench. The parameters are reflected in Table V. The first test carried out is a brake test with the developed control and with a Michelin MTX R14 65 tire. In this case, the test is carried out with a flat belt whose adhesion characteristics were found by performing tests of longitudinal force in the test bench. Later, the encountered curve is introduced in the test bench model and the brake control for its simulation. Therefore, we have three different named speeds: real, simulated, and estimated. The real speed is obtained in the test bench by means of a sensor, which reads it directly when the test is carried out. In this case, the programmed brake control starts to work in the main application as described in Fig. 4. The estimated speed is the one obtained by means of (6), previously estimating the slip coefficient and finally the simulated speed which is obtained simulating the test bench and the developed control with Simulink. The result of this first test is shown in Fig. 13. In Fig. 13(a), the behavior of the three previously mentioned speeds in the test carried out can be observed. We see that the

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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 simulation studied in the test. On the other side, the behavior of the brake pressure in the test bench and the estimated brake pressure can also be observed [see Fig. 13(b)]. The estimated brake pressure is obtained by means of the brake system model, and it is similar to the real brake pressure which is measured in the test bench. According to this test, the behavior of the brake system model is accurate. Finally, the control behavior to obtain the road type is drawn in Fig. 13(c). The following test was carried out changing the adhesion characteristics and the execution time to test the dynamic behavior of the control system in a wide range of road conditions. This test was performed with the same tire as previously, and all start at a belt speed of 27.2 m/s. Fig. 14 shows the control behavior in dry and wet road conditions. Fig. 14(c) shows how the control detects the change in adherence conditions and so the control adjust the pressure level

of the brake as it is shown in Fig. 14(b). We also observe how the control adjusts the slip level seen in Fig. 14(d) ranging between 0.14–0.18 for wet road conditions and 0.13 for dry road conditions. These slip levels depend on the adjustment of the membership functions of the control which establish the road type and the value of the maximum optimum slip (sopt ). Both parameters have been adapted to obtain the optimum performance of the brake control and to maintain the slip in all the tested conditions within the appropriate values. In Fig. 15, the behavior of the brake control, in which the adherence conditions are wet and snowy asphalt, is shown. Fig. 15(c) shows how the control estimates the existing road type and how the brake pressure decreases considerably when the 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 and between 0.15–0.18 in the case of snow. Finally, Fig. 16 shows the 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.

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Fig. 16.


Control behavior in wet and ice conditions.

V. CONCLUSION The key goals of this work have been the construction of a test bench capable of testing algorithms of ABS brake controls which adjust adequately to the real conditions of performance demanded for vehicles, and the development of a fuzzy brake control system. As the simulations show, the fuzzy brake control system keeps the slip and the friction coefficient in the optimum zone of the adhesion curve and is able to detect different kind of roads and adherence changes during simulation. The robustness of the fuzzy control and its capacity to adapt to different dynamic adherence changes have been confirmed. Additionally, the results suggest that the use of fuzzy logic for ABS brake control improves the longitudinal behavior in braking processes in vehicles. REFERENCES [1] M. Buckhardt. “Fahrwerktechnick: Würzburg, Vogel Fachbuch, 1993.

Radschlupf-Regelsysteme,”

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Antonio Ortiz received the B.S. and M.S. degrees in mechanical engineering from the Polytechnic University of Madrid, Spain. He is a Ph.D. candidate at the University of Malaga. He is currently an Associate Professor of Mechanical Engineering at the University of Malaga. His research interests include tire models and genetic algorithms applied to tire models, and multiobjective evolutionary strategies.

Juan A. Cabrera received the B.S., M.S., and Ph.D. degrees in mechanical engineering from the University of Malaga, Spain. He is currently an Associate Professor of Mechanical Engineering at the University of Malaga. His research interests include modeling and control of vehicle systems, advanced vehicle systems, genetic algorithms applied to mechanisms and tire models, and multiobjective evolutionary strategies.

Antonio Simoń received the B.S., M.S., and Ph.D. degrees in aeronautical engineering from the Polytechnic University of Madrid, Spain. He is currently a Professor of Mechanical Engineering at the University of Malaga, Spain, and he is the Department Head of Mechanical Engineering at Malaga University. His research interests include modeling and control of vehicle systems, advanced vehicle systems, genetic algorithms applied to mechanisms, and tire models and biomechanics.

Juan J. Castillo received the B.S. and M.S. degrees in mechanical engineering from the University of Malaga, Spain, and is currently pursuing the Ph.D. degree there. He is an Associate Professor of Mechanical Engineering at the University of Malaga. His research interests include control and modeling of brake and suspensions systems, and tire parameters estimation.