Central Differential Control of an Active Four Wheel Drive Vehicle

Abstract

Four Wheel Drive (4WD) vehicles are almost as old as the automobile itself, however for more than half a century the main use case of a 4WD system was to improve traction on off-road terrains. The advancement in technology over the recent decades resulted in more advanced and light weight solutions shifting the focus more towards sports cars and performance passenger vehicles. Furthermore, the advancements in electronic actuators paved the way for more attractive 4WD solutions for such vehicles. The trend continues to progress as top racing formulas, such as Formula 1 and Le Mans Prototypes, have embraced 4WD systems over the past few years and all major car manufactures recently brought road vehicles with 4WD systems to the market. In many of these vehicles, the drivelines are electronically controllable introducing new possibilities and engineering challenges. In this thesis a control system for an Active Central Differential (ACD) will be developed in order to improve the handling and performance of a 4WD vehicle. The central differential distributes the engine torque to the front and rear axle; the ACD is a controllable central differential for which the front to rear torque distribution can be varied electronically. Three different vehicle models are used in this work with varying complexity: single track model, two track model and multibody dynamics model. The single track model is used to study the influence of the actuator on the longitudinal and lateral dynamics in Quasi Steady State (QSS). Furthermore, this model is used for the sensitivity analysis of potentially varying vehicle parameters. The two track model forms the basis for the presented control system and vehicle state estimator. The multibody dynamics model is a close virtual representation of a real passenger vehicle and hence used for validation of the proposed control system. All models use a nonlinear tyre model (Magic Formula (MF) based), longitudinal and lateral load transfer (single track only longitudinal). The multibody dynamics model also simulates engine characteristics, drive train and differential inertia, clutch dynamics, suspension characteristics, pitch and roll dynamics, etc. These effects are neglected for obvious simplicity reasons in the single and two track models. The most relevant dynamics for the handling and stability of the vehicle lie in the vehicle yaw plane. Unlike differential braking or torque vectoring, the ACD can not directly generate a yaw moment; instead any yaw moment obtained from torque distribution changes is the result of combined slip effects (i.e. indirect actuation). Nonetheless, the torque distribution can significantly influence the performance, stability and understeer characteristics of the vehicle. To develop a better understanding of the complex dynamics involved, the system dynamics are studied by means of a QSS analysis and linearization. By studying the system at hand in QSS, key aspects (i.e. torque distribution) of the complete dynamic system can be isolated and analyzed without being affected by coupled dynamics. Furthermore, linearization of the nonlinear system is employed to study the dynamic system poles of the resulting linear parameter varying system. These system poles give insight in the stability of the system for a variety of torque distributions. A novel control system for the central differential is presented which improves the handling and performance of the vehicle for (combined) acceleration maneuvers. The control system is composed of a slip reference generator and a closed loop slip controller. Since only one control variable is available, the system controls the portion of the engine torque which is redirected to the rear axle in order to reduce the slip error of said axle in finite time. The controller type is a gain scheduled proportional integral controller with an anti integrator wind-up scheme to deal with actuator saturation. The classical problem of vehicle control systems, namely the inability to measure essential signals for the control system (i.e. tyre slip, stiffness and peak friction) is addressed with an Unscented Kalman Filter (UKF) based vehicle state estimator. The dynamic model of the state estimator is composed of a two track model and nonlinear normalized MF tyre model. The performance of the control system was assessed on a multibody vehicle model and the state estimator was assessed on experimental data.