The capability of a road vehicle equipped with an anti-lock braking system (ABS) comes to a safe stop depends on factors such as dynamic force between tire and road surface adhesion coefficient, and the vertical profile of the road. When in panic, a driver’s reaction is to step hard on the brakes to make the vehicle stop as soon as possible. Although the use of modern technologies such as ABS has reduced the number of accidents significantly, any further improvement in stopping distance would only complement these technologies. Mathematical simulation of an ABS has been implemented in Matlab, which employs a quarter car vehicle's model undergoing a straight line braking maneuver. The model also incorporates a hydraulic brake valve dynamics and road-tire interaction. The road-tire interaction model is given in the form of an empirical function (Magic formula) describing the nonlinear relation between adhesion (rolling) coefficient and wheel slip. A Bang-Bang controller has been implemented with the above model for controlling wheel slip at given desired reference value. The braking performances in both assisted ABS mode and non-ABS mode have been evaluated by simulation. Simulated results of stopping distances were confirmed using a road test setup. The results indicate that the braking performance of automotive assisted ABS was improved significantly, the braking time advanced, and the stopping distance shorten consequently, the braking safety of vehicle can be improved.

Bang-Bang controller, Anti-locked Braking System, straight line braking maneuver, hydraulic brake actuator dynamics, road-tire friction, wheel slip