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Slip rate control is important in improving vehicle stability and driving efficiency. In this paper, a robust slip rate control system is designed for distributed drive electric vehicles that consists of two slip rate estimators for multi-driving conditions, a vehicle speed estimator, and an anti-windup robust variable structure slip rate tracking controller. Because there is no driven wheel in a four-in-wheel-motor distributed drive electric vehicle, the estimators for small and large slip rates are designed based on dynamic and kinematic methods, respectively, which can switch according to the slip conditions. The convergence of the estimation error is discussed with the Lyapunov stability law and is less than 2% under the condition of acceleration on a low-friction road. The slip rate tracking controller is designed based on the sliding mode control law and the proportional-integral (PI) control method to handle model nonlinearity, modelling and estimation errors, and disturbances and to control the input chattering and saturation. The asymptotic stability of the tracking error is proven by Lyapunov theory. A joint control variable composed of the wheel angular acceleration and slip rate is designed to improve the robustness of the controller against the slip rate estimation error. Simulations and experiments under various conditions are performed to verify the proposed anti-slip control method. The results show that compared with a distributed drive vehicle without a slip rate controller, the controlled vehicle can prevent serious wheel skid on low-adhesion roads and improve the driving performance.

\ud \ud 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.