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The use of electric motors to independently control the torque of two or four wheels of a vehicle has the potential to significantly improve safety and handling. One virtue of electric motors is that their output torque can be accurately estimated. Using this known output torque, longitudinal tire force and coefficient of friction can be estimated via a controller output observer. This observer works by constructing a model of wheel dynamics, with longitudinal tire force as an unknown input quantity. A known wheel torque is input to the physical and modeled system and the resulting measured and predicted wheel speeds are compared. The error between the measured and predicted wheel speed is driven towards zero by a robust feedback controller. This controller modulates an estimate of longitudinal tire force used as an input by the wheel dynamics model. The resulting estimate of longitudinal tire force quickly converges towards the actual value with minimal computational expense.

It is commonly accepted that the principal functions of an automobile suspension are to control low frequency rigid body motions, provide comfort to passengers, and to reduce tire normal force variation so that predictable handling is maintained. A good argument for reducing normal force variation is that in the extreme, if a tire is off the ground, it for certain cannot generate any lateral forces, and thus compromises lateral dynamics. The direct relationship between road holding and dynamic tire normal force variation is quantified sparsely in the literature. In this paper a relatively simple model is proposed which exposes how normal force variation at the front and rear directly affects the vehicle yaw rate and lateral acceleration. It is shown that normal force variation at the front has potentially the same effect on lateral dynamics as does the steering input.

Vehicle stability augmentation has been refined over many years, and currently there are commercial systems that control right/left braking and throttle to create vehicles that remain controlled when road conditions are very poor. These systems typically use yaw rate and lateral acceleration in their control philosophy. The tire/road friction coefficient, μ, has a significant role in vehicle longitudinal and lateral control, and there has been associated efforts to measure or estimate the road surface condition to provide additional information for the stability augmentation system. In this paper, a differential braking control strategy using yaw rate feedback, coupled with μ feedforward is introduced for a vehicle cornering on different μ roads. A nonlinear 4-wheel car model is developed. A desired yaw rate is calculated from the reference model based on the driver steering input.

In the simulation of the dynamic response of a vehicle, the accuracy of the predictions strongly depends on the tire properties. Since the physics of tire force generation is highly nonlinear and complex, semi-empirical models are used, which are mathematically curve fitted to experimental data. Although this approach yields realistic tire behavior, it requires many experimental coefficients. Even though tire forces generated by a real tire are nonlinear, there is a linear region where the slip and slip angle are low. Most normal driving is done in this region. This paper will present a new analytical tire model capable of simulating pure cornering, pure braking, and combined braking/cornering in this region. The dynamic properties of the tire are analytically derived as functions of the slip, slip angle, normal force, and road friction coefficient.