Hybrid Sliding-Mode-Based Wheel Slip Control for Brake-by-Wire Vehicles with In-Wheel Motors

Sliding-mode control (SMC) is valued in automotive applications for its robustness and its low computational cost, although chattering remains a practical obstacle. Higher-order and adaptive formulations reduce chattering, but each carries limitations that may restrict their use in wheel slip control. This paper presents a hybrid low-level controller that combines a first-order sliding-mode (FOSM) term with a proportional–integral (PI) term acting on the same slip error. The two branches are weighted by a hyperbolic tangent function, so that the FOSM term governs the response towards the reference slip and the PI term governs it within a narrow band around the reference. Because the weighting is continuous, the transfer between branches introduces no step change in the torque demand. The controller is embedded in a three-level brake-by-wire architecture with series brake blending between in-wheel motors and friction brakes. The study uses an experimentally validated 14-DOF vehicle model and proposes a benchmarking procedure for comparison against a velocity-scheduled PI baseline. The results suggest improved slip tracking of the braking manoeuvre.