Instantaneous optimum wheel slip estimation of anti-lock braking system based on extremum seeking algorithm and fuzzy method

The anti-lock braking system (ABS) adjusts the longitudinal wheel slip at its optimum value to achieve the maximum braking forces. The highest braking force capacity happens at a specific slip value and depends on the friction coefficient between the tire and the road, vertical tire force, and vehicle speed. Hence, using a fixed value for the desired longitudinal slip is not appropriate. To solve this problem, the instantaneous optimum wheel slip is determined via the sliding mode-based extremum seeking algorithm in combination with the fuzzy method to achieve the maximum possible brake deceleration. Then the nonlinear prediction-based controller is designed to find the braking torque by adjusting the longitudinal slip in the calculated desired value. In addition, a nonlinear half-vehicle model considering pitch dynamics is developed and validated with the Carsim software. The main contribution of the present work involves the combination of the optimal nonlinear predictive control method with the fuzzy extremum seeking algorithm to design a wheel slip controller. Additionally, the pitch dynamics has been taken into account in the design of the control system. The performance of the designed control system is investigated through conducted simulations in Matlab/Simulink software environment. The obtained results show an enhancement in the braking performance along with a considerable reduction in the stopping distance.