# Individual Drive-Wheel Energy Management for Rear-Traction Electric Vehicles with In-Wheel Motors
## 2 State of the Art in EDS  
Many studies have been conducted about EV efficiency [12; 13; 14], but few focus on the particular case of IWMEVs [15]. The Ackermann steering geometry is the starting point of most proposed models for wheel speed differentiation [16]. It specifies the geometric relationships that should be complied with to achieve an optimum vehicle performance during turning maneuvers, as stated in the vehicle dynamics literature [17]. The essential inputs for the EDSs proposed in other works are the steering angle and the throttle position [18]. For the EDS presented in this work, the inputs mentioned earlier are also used, complete with the vehicle's longitudinal speed information. The modeling of the IWMEV results in a complex nonlinear system due to the tire characteristics during a turning or direction-changing process [19]; rapid steering or a low-adhesion-coefficient road can cause vehicle instability like tire slipping causing the driver to lose control. The testing of the EDS proposed in this work was performed at low speeds and maintaining low mechanical power demand on the testing vehicle; this guaranteed vehicle stability and eliminated the possibility of slipping during testing [20], simplifying the vehicle dynamics modeling and allowing for energy interactions to be better observed. The dynamics stability control approach is used by [PERSON] et al. in their work [21]. Their proposed EDS follows the yaw rate's value closely and distributes the torque on both sides to ensure steering performance and driving stability. Using an input signal, the steering angle values, and the vehicle speed, their proposed fuzzy logic controller calculates the additional yaw moment necessary to maintain the vehicle's stability. Another proposed approach is the one presented by [PERSON] et al. [22]. They introduce an EDS based on wavelength control, transforming the steering angle and the throttle input into frequency components to calculate the respective gains fed into the system as input to the motors. [PERSON] et al. also compare the wavelength controller with their own PID controller. It is noticeable that the wavelength controller provides a smoother response with less overshot and a faster settling time than the PID controller. [PERSON] et al. [23] acknowledge the nonlinearity of the vehicle dynamics in their proposed EDS, including the combined effects and interactions of the longitudinal, lateral, and yaw dynamics together with tire dynamics. The EDS calculations are made by a Model Predictive Control (MPC) controller that processes the vehicle dynamics variables, achieving suitable stability parameters. MPC theory is a recurrent method in vehicle dynamics control [24]. [PERSON] et al. [25] used MPC for torque distribution in a IWMEV that included the motor's efficiency map to reduce energy consumption, achieving savings of 4.5% and 0.8% for lane changing and straight acceleration maneuvers, respectively. [PERSON] et al. [26] also used MPC for torque control in their IWMEV simulation model to optimize their in-wheel motors' regenerative braking function. EDS works focus on vehicle dynamics; however, there have been efforts in combining dynamics control with energy optimization since both tasks imply powertrain control and actuation. [PERSON] et al. [27] use torque allocation to reduce side slipping by implementing a penalty function within its controller; reducing side slip angle has positive effects on the vehicle dynamics and reduces energy losses in the tire due to tire wear. [PERSON] et al. [28] proposed a system with a dynamics stability approach, using a holistic corner controller for a vehicle with four in-wheel motors to reduce tire slipping and thus tire wear, controlling the yaw rate of the car and finally achieving a reduction of tire slip energy of 16.62%. This paper's main contribution consists of an EDS focused on energy management and implementation in an IWMEV test car.