**5. Discussion**

The CarSim and MATLAB/Simulink programs were used to verify the design of the vehicle's fuzzy ABS controller. The main goal of this work was to improve the braking properties of the vehicle by using fuzzy logic for the brake pressure regulator. We have chosen three types of operating states for testing the fuzzy ABS. The first was to test the vehicle's braking behavior on dry roads at speeds of 100 and 140 km/h.

In this test, the shortest braking distance was the main criterion for assessing the quality of the proposed fuzzy ABS controller. The value of the braking distance of a vehicle with a classic ABS was taken as a reference value for comparison, as we wanted to improve the properties of this ABS by using a fuzzy logic.

As can be seen from the comparison in Table 9 and Figure 17, the ABS with the fuzzy controller achieved better properties with all monitored parameters, i.e., directional stability, braking time and braking distance than when using ABS without a fuzzy controller.

**Table 9.** Comparison of parameters when braking on dry road.

**Figure 17.** Graphical comparison of the test on dry road.(**a**): Graphical comparison of the braking distance during a dry road test at a vehicle speed of 100 km/h; (**b**): Graphical comparison of the braking time during a dry road test at a vehicle speed of 100 km/h; (**c**): Graphical comparison of the vehicle rotation in z-axis during a dry road test at a vehicle speed of 100 km/h; (**d**): Graphical comparison of the braking distance during a dry road test at a vehicle speed of 140 km/h; (**e**): Graphical comparison of the braking time during a dry road test at a vehicle speed of 140 km/h; (**f**): Graphical comparison of the vehicle rotation in z-axis during a dry road test at a vehicle speed of 140 km/h.

In the second test, we observed the braking behavior of the vehicle on the road with different adhesion on the right and left side. In this test, in addition to monitoring the shortest braking distance, the ABS's ability to maintain the vehicle in a straight line when braking was also monitored. Again, as in the previous test, the reference values were obtained by simulating a conventional ABS. As can be seen from the comparison shown in Table 10 and Figure 18, the ABS with the fuzzy controller achieved better results also in this case.

**Table 10.** Comparison of parameters when braking on road with combined adhesion.

**Figure 18.** Graphical comparison of the test on road with combined adhesion. (**a**): Graphical comparison of the braking distance during a test on a road with combined adhesion at speed of 100 km/h; (**b**): Graphical comparison of the braking time during a test on a road with combined adhesion at speed of 100 km/h; (**c**): Graphical comparison of the vehicle rotation in z-axis during a test on a road with combined adhesion at speed of 100 km/h; (**d**): Graphical comparison of the braking distance during a test on a road with combined adhesion at speed of 140 km/h; (**e**): Graphical comparison of the braking time during a test on a road with combined adhesion at speed of 140 km/h; (**f**): Graphical comparison of the vehicle rotation in z-axis during a test on a road with combined adhesion at speed of 140 km/h.

In the last test, we observed the behavior of the vehicle during braking and simultaneously avoiding an obstacle in the roadway. In this test, we monitored the vehicle's ability to maintain within the prescribed path, and the reference value in this test was the value of the maximum deviation from the prescribed path for a vehicle with a conventional ABS. As Table 11 and Figure 19 demonstrates, although the vehicle without ABS had the shortest braking distance at speed 130 km/h, this vehicle was not able to avoid the obstacle and continued straight on, which would eventually cause the vehicle to collide with the obstacle.


**Table 11.** Comparison of parameters during avoiding an obstacle on the road.

**Figure 19.** Graphical comparison of the maneuverability test on road. (**a**): Graphical comparison of the braking distance during a manoeurability test on a dry road at speed of 100 km/h; (**b**): Graphical comparison of the braking time during a manoeurability test on a dry road at speed of 100 km/h; (**c**): Graphical comparison of the vehicle deviation from the prescribed road during a manoeurability test on a dry road at speed of 100 km/h; (**d**): Graphical comparison of the braking distance during a manoeurability test on a dry road at speed of 140 km/h; (**e**): Graphical comparison of the braking time during a manoeurability test on a dry road at speed of 140 km/h; (**f**): Graphical comparison of the vehicle deviation from the prescribed road during a manoeurability test on a dry road at speed of 140 km/h.

Based on the previous results, we made a percentage comparison of the improvement in the performance of the ABS with the fuzzy controller compared to the classic ABS. The result of this comparison is shown in Table 12.


**Table 12.** Percentage comparison of the improvement of key indicators.

It is shown in Table 11 that by using a fuzzy controller for the vehicle's ABS, we can achieve up to a 6% reduction in braking distance when braking on a road with combined adhesion. In the simulations, however, we achieved much more significant results in the directional stability of the vehicle or when avoiding an obstacle.
