This paper proposes a real-time nonlinear model predictive control (NMPC) strategy for direct yaw moment control (DYC) of distributed drive electric vehicles (DDEVs). The NMPC strategy is based on a control-oriented model built by integrating a single track vehicle model with the Magic Formula (MF) tire model. To mitigate the NMPC computational cost, the continuation/generalized minimal residual (C/GMRES) algorithm is employed and modified for real-time optimization. Since the traditional C/GMRES algorithm cannot directly solve the inequality constraint problem, the external penalty method is introduced to transform inequality constraints into an equivalently unconstrained optimization problem. Based on the Pontryagin's minimum principle (PMP), the existence and uniqueness for solution of the proposed C/GMRES algorithm are proven. Additionally, to achieve fast initialization in C/GMRES algorithm, the varying predictive duration is adopted so that the analytic expressions of optimally initial solutions in C/GMRES algorithm can be derived and gained. A Karush-Kuhn-Tucker (KKT) condition based control allocation method distributes the desired traction and yaw moment among four independent motors. Numerical simulations are carried out by combining CarSim and Matlab/Simulink to evaluate the effectiveness of the proposed strategy. Results demonstrate that the real-time NMPC strategy can achieve superior vehicle stability performance, guarantee the given safety constraints, and significantly reduce the computational efforts.

A supervisory control strategy, including dynamic control supervisor, handling-stability controller, energy efficiency controller, and coordinated torque allocator, is proposed for distributed drive electric vehicles to coordinate vehicle handling, lateral stability, and energy economy performance. In the dynamic control supervisor, first, the phase plane analysis is implemented to accurately define the vehicle stability boundary so that the lookup table of bounds can be established for online applications. Subsequently, based on the feedback drive conditions and vehicle states, the identified boundary is dynamically quantified by the designed varying weight factor (VWF) in real time. In the handling-stability controller, a unified yaw rate reference of VWF is developed to simultaneously guarantee vehicle maneuverability and lateral stabilization. Then, a novel integral triple-step method is proposed to calculate the proper direct yaw moment for the desired vehicle motion. In the energy efficiency controller, the interaxle torque distribution map is optimized for optimal vehicle energy economy. In the coordinated torque allocator, a torque increment allocation problem is formulated and optimized to realize the desired forces, meanwhile, based on VWF to minimize energy consumption and tire workload usage. The validations of the proposed strategy are conducted under various maneuvers, yielding comprehensive improvements in terms of vehicle handling, lateral stability, and energy performance.

This paper proposes a computationally efficient path following control strategy of autonomous electric vehicles (AEVs) with yaw motion stabilization. First, the nonlinear control-oriented model including path following model, single track vehicle model, and Magic Formula tire model, are constructed. To handle the stability constraints with ease, the nonlinear model predictive control (NMPC) technique is applied for path following issue. Here NMPC control problem is reasonably established with the constraints of vehicle sideslip angle, yaw rate, steering angle, lateral position error, and Lyapunov stability. To mitigate the online calculation burden, the continuation/ generalized minimal residual (C/GMRES) algorithm is adopted. The deadzone penalty functions are employed for handling the inequality constraints and holding the smoothness of solution. Moreover, the varying predictive duration is utilized in this paper so as to fast gain the good initial solution by numerical algorithm. Finally, the simulation validations are carried out, which yields that the proposed strategy can achieve desirable path following and vehicle stability efficacy, while greatly reducing the computational burden compared with the NMPC controllers by active set algorithm or interior point algorithm.