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For the vehicle dynamic control system, to guarantee directional stability in risky maneuvers, the side-slip angle should be restricted to the admissible range when the yaw rate tracks the proposed desired response for enhanced steerability. Meanwhile, the control input of the external yaw moment produced by asymmetric braking forces should be calculated in the practical range according to the capacity of tire forces. In the present study, a novel constrained controller with input and state constraints is developed. To this aim, a cost function consisting of predicted continuous response of yaw rate tracking error is expanded in terms of current control signal. Concurrently, the state constraint of side slip is transformed to the equivalent constraint of control signal by a novel nonlinear prediction approach. After that, the expanded performance index is analytically minimized in the presence of all input constraints to obtain the control law. The computed yaw moment is optimally distributed to asymmetric braking forces by designing a wheel slip control system. Simulation studies are conducted to evaluate the performance of proposed constrained controller compared with the unconstrained controller and a conventional nonlinear model predictive controller developed in the recent papers using a 14-degree-of-freedom vehicle model which includes suspension system dynamics. The results show that the proposed controller is much faster and easy to solve and implement.

This paper looks into the energy management and directional stability of four-in-wheel driven electric vehicles, simultaneously. In the proposed strategy, the optimal driving torques are initially distributed between the wheels by considering the condition for minimum losses of motors using the motor efficiency model. In risky maneuvers, a novel optimal torque vectoring system is developed to intentionally change the initial optimal torques for the generation of required stabilizing yaw moment. For designing the stability controller, a new constrained control method is analytically developed based on the prediction of continuous nonlinear vehicle models. The proposed control method restricts the side-slip angle to guarantee the stability. Also, the required control torque for each motor is restricted within the admissible range according to the motor map. As another result of the constrained strategy, a small change in the optimal energy consumption is occurred for improved stability because of using minimum external yaw moment. In simulation studies, a good performance of the developed control system to provide both directional stability and drivability of electric vehicle with high energy efficiency is presented at different driving conditions using 14-degrees-of-freedom vehicle model. A comparative study with the conventional model predictive control method indicates the speed of the proposed constrained control method and the ease of its solution and implementation.

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