The objective of this paper is to propose a modified optimal sliding mode control method for the hydraulic anti-lock braking system of a vehicle to achieve both robustness and optimal control performance. The longitudinal dynamic model of a vehicle, tyre model and hydraulic anti-lock braking system model are established, and the weakness of the common optimal sliding mode control method in designing the anti-lock braking system controller is analysed synthetically. The analyses form the basis for tracking an ideal slip ratio. A new modified optimal sliding mode controller is proposed to regulate the hydraulic anti-lock braking system for a better braking performance and robustness: the optimal sliding mode manifold function includes several virtual damping elements and infinitely small-sized items to meet the working conditions of the current optimal sliding mode control method. The control results of the proposed controller are compared with those of the common sliding mode controller. Simulation results under various road conditions demonstrate that the modified optimal sliding mode controller not only has strong robustness against uncertainties in the road adhesion coefficient but also achieves better control performance of the slip ratio.
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