Active Braking Control of Electric Vehicles to Achieve Maximal Friction Based on Fast Extremum-Seeking and Reachability

The braking process is a race against time. By controlling the wheel slip around the optimal point, the maximal friction can minimize braking distance, and it can be achieved when the tire and the vehicle reach a state named as the optimal slip ratio. The aim of this paper is to determine the optimal slip ratio online and reach and maintain the state until the end of braking. To achieve this objective, a new control system capable of estimating friction is proposed. The proposed control system consists of two main parts: an online extremum-seeking algorithm and a controller based on reachability. The former will generate the control commands for the controller, and the latter will track the provided commands. The proposed extremum-seeking algorithm is based on the bisection method with high searching efficiency, which can tolerate the measurement inaccuracy and noise to some degree. The maximal error caused by these kinds of inaccuracy has been quantized by a formula. The reachability-based controller can achieve short settling time and be insensitive to the noise; few parameter need to be tuned and each parameter has an explicit physical meaning. The stability and robustness of the control method have been proved. The effectiveness and robustness of the proposed system is illustrated by numerical simulations. The results show that the proposed method can achieve the shortest braking distance compared with other methods, even under extreme road conditions.