Knowledge of the tyre-road interface traction limit during braking of a road vehicle can drastically improve safety and ensure stable braking on varied road conditions. This study proposes an optimal reference slip algorithm that determines the road surface while the vehicle is braking, by implicitly tracking the traction limit. It presents wheel slip variance regulation as a potential approach towards reference wheel slip estimation for wheel slip regulation (WSR). The variance regulation approach computes reference wheel slip using past wheel slip estimates and regulates wheel slip variation at a set point. This variance regulation problem was solved using least-squares estimation, yielding reference slip dynamics. A 3-staged nested control architecture was developed with reference slip dynamics to yield an anti-lock braking system (ABS) algorithm consisting of a brake controller, WSR algorithm and reference slip estimation. The algorithm was experimentally corroborated in a Hardware-in-Loop setup consisting of the pneumatic brake system of a heavy commercial road vehicle, and IPG TruckMaker®, a vehicle dynamics simulation software. The proposed ABS algorithm was tested on straight roads with homogeneous surfaces, split friction surfaces, and transition friction surfaces. It ensured stable braking in all road cases, with a 7%–18% reduction in braking distance on homogeneous road surfaces compared to the same vehicle without ABS. The vehicle directional stability was retained on a split-friction surface, and the ABS algorithm was observed to adapt to sudden transitions in the road surface.

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Wheel Slip Regulation (WSR) is one of the Active Vehicle Safety Systems (AVSSs) for maintaining vehicle stability and maneuverability during emergency braking An approach for wheel slip prediction is proposed in this paper, which involves Auto-Regressive (AR) Time-Series modelling of longitudinal vehicle acceleration. This technique allows the usage of linear longitudinal vehicle dynamics for wheel slip estimation. A wheel slip prediction model was developed considering measurements from accelerometer and wheel speed sensor. This modified the Model Predictive Control (MPC) formulation to a univariate control input problem, involving braking torque. The objective function was devised for solving a least-squares reference tracking problem. An analytical solution for the MPC optimization problem was derived and implemented towards WSR. The proposed framework was programmed in MATLAB Simulink® and co-simulated with IPG TruckMaker® (a vehicle dynamic simulation software). The algorithm was tested in a Hardware-in-Loop (HiL) setup consisting of a pneumatic air brake system interfaced with IPG TruckMaker®. Open loop studies from HiL led to the inclusion of Kalman filter for estimate tuning and PID inner loop control for brake pressure transients, which improved wheel slip regulation.

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