Coordinated longitudinal and lateral vehicle stability control based on the combined-slip tire model in the MPC framework

•The developed tire lateral force considers yaw, lateral and longitudinal dynamics.•The vehicle yaw and lateral motions are related to the acceleration as a disturbance.•Balancing multiple objectives/constraints to improve vehicle overall stability. In extreme driving situations, the coupling between the longitudinal and lateral vehicle motion becomes significant with the highly nonlinear tire forces and influences vehicle overall stability. To address the above problem, a model predictive controller is proposed for four wheels independent motor-drive electric vehicles. Firstly, a LuGre combined-slip tire model is developed to describe the coupling nonlinearity of the tire. The variation of longitudinal velocity is considered a disturbance term in the vehicle dynamics model to consider its effect on vehicle stability. Then, the multiple objectives, including tracking the reference values of the yaw rate and lateral velocity, suppressing the tire slip ratios, and reducing the torque energy consumptions, are balanced by the additional torque generated by the designed model-based controller. The safety and actuator constraints are considered concurrently. Finally, the proposed controller is tested via co-simulation with CarSim and MATLAB/Simulink, and a hardware-in-loop system with extreme maneuvers. The results show that the handling performance, longitudinal and lateral stability are effectively improved under extreme conditions.