Tracking control of wheel slip ratio with velocity estimation for vehicle anti-lock braking system

Optimal wheel slip ratio control is the key issue in an anti-lock braking system (ABS). Due to the unavailability of direct measurement of vehicle speed, which is required for a reliable computation of wheel slip ratio, and the problem of nonlinear tyre-road friction characteristic, accurate vehicle speed estimation and estimation-based slip ratio control are becoming critical for the implementation of ABS. To estimate the vehicle speed, a fuzzy observer is first designed in the paper based on the Takagi-Sugeno (T-S) fuzzy modelling of the nonlinear vehicle braking system. With the designed observer, a speed estimation-based fuzzy tracking controller is then designed with the consideration of braking torque saturation to track the optimal wheel slip ratio. Both the design of the observer and the controller are achieved by solving a set of linear matrix inequalities. Numerical simulations on a quarter-vehicle braking model are used to validate the effectiveness of the proposed approach.