Optimal handling characteristics for electric vehicles with torque vectoring.

Abstract

Torque vectoring by virtue of independent electric motors is the focus of an increasing number of studies as electric vehicles gain prominence as the chosen direction for the automotive industry. Building on active yaw control systems developed over the past decades, torque vectoring benefits from the high-responsiveness and controllability of the electric motor actuator. Furthermore, and especially in the case of vehicles equipped with one independent motor per wheel, the overall performance envelope of the vehicle is significantly improved, as well as the ability to actively shape the vehicle handling. Much attention has been focussed on controller development and control allocation aspects of torque vectoring controllers, but little on the appropriate yaw rate reference. Optimal control studies have been successfully used to mimic the expert driver in both minimum-time circuit racing and high-sideslip rally driving, and can offer insight into how to optimally tune active chassis control systems, such as torque vectoring yaw control. The main aim of this thesis was to investigate the optimal handling characteristics of an electric vehicle with four independent electric motors at the limits of performance. A TV controller was first developed for a prototype sportscar with 4 independent motors, employing a model-based design process that encompassed real-time software in the loop testing. Real-world track testing demonstrated the controller was able to successfully modify the handling characteristic of the vehicle in both understeer and oversteer directions, achieving good controller performance in steady-state and transient manoeuvres. The limit performance of the TV-controlled vehicle was subsequently investigated in the simulation domain. Numerical techniques were used to solve optimal control problems for a single-track vehicle model with linear tyres and an external yaw moment term representing the overall yaw moment arising from the difference in torques at each wheel. For a U-turn manoeuvre, it was shown that torque vectoring significantly lowers manoeuvre time in comparison with the vehicle without TV active, and that modifying the passive understeer gradient does not affect manoeuvre time. The system dynamics were reformulated to include a feedback torque vectoring controller. The target yaw rate reference was varied and it was found that the manoeuvre time was highly sensitive to the yaw rate reference. For minimising laptime, the target understeer gradient should be set to the passive understeer gradient value. The methodology was repeated for a higher fidelity model including nonlinear tyres and lateral load transfer, and found that when the torque vectoring controller was included in the system dynamics, the manoeuvre time showed little sensitivity to the target understeer gradient. Following the contradictory results of the optimal control problems, the vehicle models were investigated next. Time optimal yaw rate gain surfaces were generated from further minimum-time optimal control problems. Open-loop manoeuvres investigating effects of tyre model, lateral load transfer and torque vectoring generation mechanism found that tyre modelling was the dominant differentiator and tyre nonlinearity is an essential modelling consideration. Optimal control techniques have been used for high sideslip manoeuvring for conventional vehicles but no studies have explored the effects of torque vectoring on agility. In the final chapter, an aggressive turn-around manoeuvre was simulated and it was found that torque vectoring can significantly increase agility and reduce the space taken for an aggressive turn-around manoeuvre. Reducing yaw inertia increased agility, as well as increasing longitudinal slips limits. A critique of agility metrics in this context was given.