Optimum Longitudinal Wheel Slip Estimation of Anti-lock Braking System Using Extremum Seeking Algorithm and Fuzzy Method

The anti-lock braking system (ABS) adjusts the longitudinal force of the tire by setting the coefficient of longitudinal slip of the car in its optimum value. This applies the proper braking torque to the car and in addition to reducing the car's stopping distance, prevents the wheels from locking. Due to the uncertainty and road conditions, the maximum length of the tire varies, so it is not appropriate to use a fixed value for the desired longitudinal slip. To solve this problem, in this paper, the desired longitudinal slip value is obtained at any moment using the sliding mode-based extremum seeking algorithm in combination with fuzzy method according to the road conditions to maximize the tire's braking force. Then the nonlinear prediction-based controller finds the right amount of braking torque at any moment by adjusting the longitudinal slip in the calculated desired value. The simulation is performed on a nonlinear vehicle model and the results of this simulation show the proper performance of the controller and the effect of using the desired instantaneous longitudinal slip to reduce the stopping distance.