Karush–Kuhn–Tuckert based global optimization algorithm design for solving stability torque allocation of distributed drive electric vehicles

Abstract

This paper presents a Karush–Kuhn–Tuckert (KKT) based global optimization algorithm for solving torque allocation, which aims at improving the stability performance of distributed drive electric vehicles (DDEVs). The driver desired traction and direct yaw moment, from the driver model and the direct yaw moment controller, are taken as the generalized force that needs to be distributed among four wheels. An optimization term is introduced from the perspective of the tire grip margin to construct a stability objective function. According to KKT conditions, the nonlinear objective function is transformed into the eigenvalue problem, thereby making the solving process independent of the initial guess of the optimal solutions. Afterwards, to guarantee the global minima acquisition, two phases of optimization are designed, namely the preliminary and secondary optimization. The preliminary optimization is developed regardless of the realistic boundary of the actuators, while the secondary optimization takes the physical constraints into account. Additionally, an active-set method is introduced as a comparative allocation algorithm. The proposed KKT-based algorithm and active-set method are applied to a detailed vehicle model, which is built in CarSim combining with Simulink. The simulation under a double-lane-change test is carried out to evaluate the proposed algorithm. The results show that the KKT-based algorithm is able to find the global optimum and accurately allocate the generalized force. More importantly, it highly reduces the computational efforts, providing the potential for the real vehicle application.