Contents I. Introduction
Environmental concerns along with the shortage and the uncertainty of the supply of fossil fuels have led the automotive industry to increasingly consider alternative vehicular drivetrains, such as hybrid, plug-in hybrid, and electric. Studies show that with improvements in batteries, electric motor drives, and power electronics, these environmentally friendly vehicles are able to perform satisfactorily and at times even better than conventional vehicles. In more-electric vehicles certain mechanical components are replaced with electric or electronic components that perform the same task. In an electric vehicle (EV), conventional (mechanical) differential must be replaced with an electric differential (ED), which performs the task of adjusting the torque applied to each wheel based on the present driving conditions. A well-designed electronic differential can make the vehicle both lighter and more stable in handling. Electric vehicles are expected to have faster torque response than conventional vehicles due to advanced motor-control methods (e.g., direct torque control), which allows the motor to generate rapidly varying amounts of torque. Use of regenerative braking enables the kinetic energy in the moving vehicle to be recuperated in the battery during braking periods, thereby increasing the efficiency of the drivetrain [1]. Different electric motors with high negative and positive torque characteristics have been investigated including switched reluctance and permanent-magnet synchronous motors [2], [3]. Drive-train layouts including one, two or four independently controlled motors have been considered. Use of four independent in-wheel motors provides the opportunity to generate different torque (speed) references to each wheel independently; this not only leads to better differential operation, but also has considerable potential for improved yaw-motion stability control [4]. In-wheel motor controllers have been considered for various aspects of motion stability such as yaw control, lateral control, and anti-skid braking systems [5]–[8]. Different topologies and aspects of electronic differential, such as master-slave control or synchronization structure, and sliding mode yaw motion control, have been investigated in the literature. In [9], the authors investigate the advantages of the ED in vehicle motion stability. Chen and Wang investigate an over-actuated ground electric differential with four independent In-wheel motors in [10]. This paper proposes an ED based on solid and provable geometric expressions' which describe the motion of the vehicle and its four wheels in a turn. Using a purely mathematical procedure in section II, the paper shows that addition of an ED requires simple modifications to the existing electric vehicle drive-train controller structure. Additionally the method proposed herein considers the slippage of the wheels in the design of the ED and proposes a novel method of yaw motion stability. In some parts of this paper it is assumed that the yaw rate and the ground vehicle speed are available through continuous sensing. Ground speed sensors using optical means are found in [11], [12]. Other speed estimation methods have also been proposed in the literature including in [13]. The paper continues with an introduction to ED and its necessity. Basic geometric equations that underline the turning action are then presented and used to derive a controller that generates different power commands for different wheels during cornering. In section III an algorithm for operation at optimal wheel slippage is developed using curves of adhesion friction versus wheel slippage. This allows for maximizing the traction force without excessive power consumption by each motor. In section IV, the action of the ED in preventing over- and under-steering and in increasing stability is discussed. Computer simulation and experimental results of the proposed methods are also given followed by conclusions
