A Phase Portrait-Based Sliding Mode Control Method to Improve Dynamic Stability of Car-Trailer Combinations via Differential Braking

As a specific articulated vehicle, lateral stability of car-trailer combination deserves special attention because this vehicle shows catastrophic dynamic instability occasionally at high speeds. This is known as sway or flutter and might poses a serious threat to traffic safety on the highway. The problem can be attribute to complex dynamics coupling between the towing car and the trailer. This paper proposes a phase portrait-based sliding mode control method via differential braking at the towing car and the trailer simultaneously to realize the direct yaw moment control and improve dynamic stability. In this process, a nonlinear single-track model with 3 degrees of freedom is established and integrated into the controller design. The stability region of the towing car and the trailer is analyzed based on the sideslip angle - yaw rate phase portraits under different speeds. And the sliding mode surface of controller is designed based on the stability region. The Matlab/Simulink and TruckSim co-simulation is established to verify the performance of controller. The steering wheel input of simulation is designed in accordance with ISO9815 and the dynamic critical speed is determined based on the yaw damping ratio of car-trailer combination. Compared with the model predictive control-based method, the simulation results demonstrate that the phase portrait-based sliding mode control method has realized yaw damping ratio of 0.81 both in the towing car and the trailer at dynamic critical speed. The proposed method has superior performance in enhancing the dynamic stability of car-trailer combination.