Robust Adaptive fractional-order sliding mode controller for vehicle longitudinal dynamic

For the high risk of accidents when the vehicle is under braking condition, a robust controller of the vehicle longitudinal dynamic is required. This paper presents an adaptive robust fractional-order sliding mode controller of the vehicle longitudinal dynamic that takes into account uncertainties and disturbances (such as road conditions, vehicle loading, and variable parameters) at the design stage. The controller is designed according to the sliding mode control theory and the Lyapunov stability theorem to ensure both the system stability and the tracking of the desired slip ratio. The effectiveness and high performances of the proposed control strategy are demonstrated by a simulation example. Also, a comparison with the conventional sliding mode controller has been performed, showing the advantages of our proposal.