A fast model predictive control allocation of distributed drive electric vehicles for tire slip energy saving with stability constraints

This paper proposes a fast model predictive control allocation (MPCA) approach to minimize the tire slip power loss on contact patches for distributed drive electric vehicles (DDEV). In this strategy, two assumptions are set up from a practical focus: (1) the vehicle acceleration and yaw rate are measurable by global position system (GPS)/ inertial navigation system (INS) and inertial measurement unit (IMU), respectively; (2) the longitudinal velocity, road adhesion factor, and vehicle yaw rate are arranged to be “already known” by advanced estimators. For the strategy design, a CarSim-embedded driver model and a linear quadratic regulator (LQR) based direct yaw moment controller, are respectively applied to calculate the desired longitudinal traction and yaw moment as a virtual input first. Then, a MPCA method is proposed to reasonably distribute the virtual input among four in-wheel motors in order to optimize the tire slip power loss and vehicle stability performance. To accurately characterize tire slip power loss in MPCA, a tire slip estimator is established for tire slip information acquirement. Moreover, addressing on the heavily computational challenge in MPCA, a modified continuation/generalized minimal residual (C/GMRES) algorithm is employed. Since the traditional C/GMRES algorithm cannot directly solve the inequality constraint problem, the barrier functions are applied for transforming the inequality constraints to equivalent cost. According to Pontryagin's minimum principle (PMP) conditions, the existence and uniqueness for solution of the modified C/GMRES algorithm are strictly proved. Subsequently, a Karush–Kuhn–Tucker​ (KKT) condition based approach is developed to fast gain the optimally initial solution in C/GMRES algorithm for extending application. Finally, numerical simulation validations are implemented and demonstrate that the proposed MPCA can ensure the compatibility between the tire slip power loss reduction and vehicle stability in a computationally efficient way.