Optimal nonlinear control of vehicle braking torques to generate practical stabilizing yaw moments

In this paper, a new optimal strategy for differential braking is proposed to recover the vehicle stability in emergency maneuvers. Practical aspects of the problem are considered in the design of a control system with two layers. In the upper layer, an optimal nonlinear control law is analytically developed for calculating the external yaw moment and the distributed braking forces. The optimal property of the control law provides the possibility of reducing the control input to the lowest possible value to avoid undesirable effects. At the same time, considering the force capacity of each tire, a practical stabilizing yaw moment can be calculated by adjusting the weighting ratio as a free parameter of the control law. In the lower layer, a nonlinear wheel slip tracking controller is designed for the front wheels to generate the required braking forces of the upper layer. The simulation studies carried out by a nonlinear eight-degrees-of-freedom (8DOF) vehicle model indicate that the proposed control system can improve vehicular handling and stability with a practical external yaw moment and reduced differential braking forces