Extremum Seeking and Sliding Mode Control Applied to Anti-lock Braking Systems

The Anti-lock Braking System (ABS) is a widely used device, with applications in a variety of automotive applications. Its operation consists in controlling the wheel slip, thus preventing the wheels from locking up during braking, maximizing the friction force and shortening the braking distance while maintaining maneuverability. The nonlinear nature of the road-tire interaction as well as the uncertainties related to each particular road condition make this a challenging problem. In this paper, a new design is proposed to control the wheel slip. An extremum seeking controller strategy for the external loop is designed to estimate the optimum slip value to each road condition in real time, and a sliding mode control approach for the internal loop is employed to regulate the desired slip value. The stability analysis of the closed-loop system is developed. Numerical simulations show a good performance of the proposed control scheme.