Fixed-Time Slip Control With Extended-State Observer Using Only Wheel Speed for Anti-Lock Braking Systems of Electric Vehicles

In this paper, we propose a fixed-time slip control with an extended-state observer (ESO) using only wheel speed for anti-lock brake systems (ABS) in electric vehicles. In the proposed control strategy, the longitudinal tire-road friction is defined as the disturbance. The ESO is designed to estimate the wheel speed, longitudinal tire-road friction, and longitudinal vehicle speed. Based on the estimated longitudinal tire-road friction, an optimal desired slip generator is designed, which provides optimal desired slip in real-time to maintain a nearly maximum tire-road friction coefficient (TFC), according to road surface conditions. A fixed-time controller is developed to guarantee an upper bound of convergence time determined regardless of the initial slip tracking errors. The proposed method guarantees a uniform ultimate boundedness of the wheel-slip tracking error based on an analysis of closed-loop stability. The performance of the proposed method is validated via simulations by using CarSim and MATLAB/Simulink for three scenarios on a jump TFC road surface, on a split TFC road surface, and on a suddenly cornering jump TFC road surface. The proposed method, which only employs a wheel speed sensor, achieves a shorter braking distance and stopping time in comparison with classical ABS.