**3. Fuzzy Control of ABS**

The fuzzy control of the ABS is based on a conventional ABS complemented by a fuzzy controller. The design and the subsequent verification by simulationwere carried outin CarSim andMATLAB/Simulink. The designed fuzzy ABS control system consists of three parts:


The block model of the proposed fuzzy control is shown in Figure 5.

**Figure 5.** Block scheme of ABS control with fuzzy controller.

The basic parameters for speed controller input were the values of vehicle speed and the speed values of individual wheels. As shown in Figure 6, the output of the speed controller is the value of the vehicle speed multiplied by a constant that modifies the speed value, and this then, becomes the input value to the fuzzy controller. Constant 1/200 was selected on the basis of the defined maximum speed 200 km/h. For tests involving a higher speed, this constant has to be modified. The second output is the ratio of the wheel speed and the vehicle speed. The ratio of vehicle speed and wheel speed can be in the range of values between 0 and 1, where value 0 represents an unblocked wheel (slip 0), and value 1 represents a blocked wheel (slip 1).

**Figure 6.** Block scheme of the speed controller.

The input for the fuzzy controller, shown in Figure 7, is the modified vehicle speed and speeds of the individual wheels.

**Figure 7.** Block scheme of the fuzzy controller.

The range of values for the first input is from 0 to 1. Zero value represents zero vehicle speed and 1 is the highest speed. The range of values for the second input can also be from 0 to 1. In this case, the 0 value represents zero slip and value 1 represents maximum slip value.

The fuzzy controller output value is in the range −1 to 1. Value 1 represents full brake pressure applied to the wheels and −1 represents the application of negative pressure, which means that the wheel is released. The constant output pressure ratio is 20/8 for the front/rear wheels. The constant ratio in favor of the front wheels was chosen in view of the fact that during braking, the vehicle weight is transferred forward and the rear wheels are relieved, which at full braking force would cause blocking of the wheels and subsequent loss of control over the vehicle. This ratio value has been taken as ideal from the CarSim brake pressure control actuator model. Since a fuzzy controller is used to control the braking force, a ratio of 20/8 was chosen as ideal for achieving the largest possible parameter of relative deceleration. The maximum pressure for the simulation was limited to 10 MPa. Table 2 shows the decision rules for the fuzzy controller setting.


**Table 2.** Table of rules for the fuzzy controller.

VS—very small, S—small, M—middle, H—high, VH—very high, VN—very negative, N—negative, Z—zero, P—positive, VP—very positive.

Values of the individual variables for the FIS matrix shown in Figure 8 were selected on the basis of tire slip, which was set at 20%. At such slip, the vehicle is still operable even under heavy braking. A graph showing the dependence between vehicle speed, ratio of vehicle and wheel speed and the resulting pressure is presented in Figure 9.

**Figure 8.** Setting rules of FIS matrix for fuzzy controller.

**Figure 9.** Graph showing the dependence of output variable on the input variables in the fuzzy controller.
