The influence of the sideslip target on the performance of vehicles with actively controlled handling
The influence of sideslip on the handling capability of a four wheeled vehicle is investigated. Both nonlinear, steady-state and linear, transient analyses are conducted on simple models in order to understand how the geometric and inertial effects of sideslip control influence the maneuvering capability of the vehicle. Nonlinear performance analyses confirm the findings of the literature, that constant sideslip angle at the centre of mass is required if it is desired to maintain consistent vehicle 'balance' with increasing lateral acceleration, and the reason for this is explained using simple mathematics. Analyses of energy flow between the power source and the various sinks of the vehicle show that for a typical modem vehicle, the power dissipated in a steady turn near the limiting lateral acceleration is approximately comparable in magnitude to that dissipated by aerodynamic drag near the maximum speed of the vehicle. Additionally, it shown that whenever brake control, rather than steering control, is employed to generate a yawing moment, the component of dissipated energy associated with this yaw demand is larger by at least an order of magnitude. It is concluded that whenever the required dynamic behaviour can be delivered by means of steering alone pure steering control should be preferred over the use of direct yaw control. This suggests that direct yaw control should only be used when the limit of the envelope of the steered vehicle has been reached. Transient analyses of sudden turn-in events are then undertaken. The assumption is that the driver wishes to maximise the lateral displacement of the vehicle as quickly as possible. Vehicle handling models with A WS are linearised and discretised, and Linear Progranuning is used to identifY the optimal turn-in maneuver. The objective is to understand how to make a vehicle perform well against such a target without any use of any energy-dissipating direct yaw control. It is observed that the optimal controls usually involve an immediate step to the limiting force that the front axle is able to deliver. It is shown that for vehicles with yaw dynamics where this input does not lead to saturation of the rear tyres, the transient performance is totally insensitive to changes in the enforced sideslip control. The form of this optimal force input is then used in a further mathematical analysis of the optimal obstacle avoidance maneuver. It is shown that in the case mentioned above, where sufficient friction is available at the rear axle, the time taken to build up lateral acceleration and yaw rate for a turn is a simple function of the geometric and inertial properties of the vehicle, and unrelated to rear tyre cornering stiffness, rear camber or rear steering control. It is shown also shown that for an equal level of limit over- or under-steer, 2WS vehicles that are limit over-steering are able to turn in more quickly than those which are limit under-steering, since the excess friction is available at the front axle, and can be used during the turn-in phase. Further, it is shown that both commonly adopted sideslip targets for 4WS vehicles and responses that often result from 2WS vehicles can easily be 'incompatible' with the handling envelope of a steered vehicle from an optimal obstacle avoidance point of view. This means that for some vehicles, strict enforcement of such sideslip targets directly increases the time taken to transfer such a vehicle to the limiting lateral acceleration. This limit of 'compatibility' of the sideslip target and vehicle envelope is confirmed analytically. It is then shown, that the zero sideslip target which is commonly adopted for A WS vehicles in the literature, and which was previously shown to be the ideal for consistent vehicle stability and 'balance', is only able to deliver the optimal turn-in behaviour when the underlying vehicle has a limit-neutral or limit under-steering balance. Further, the zero sideslip target requires a strongly limit under-steering balance if the sideslip target is to be maintained when the vehicle is rnaneuvered from turning quickly in one direction to turning quickly in the other without compromising the time taken to complete the maneuver. However, it is also shown that either a controlled front differential, or front axle direct yaw-moment control are each able to extend the envelope of the vehicle in the necessary direction that maintaining zero sideslip throughout such transients may become feasible, albeit at an energy cost that increases as the vehicle is maneuvered more rapidly. Additionally, an alternative sideslip target is presented, that allows optimal maneuvering to take place whilst the sideslip target is simultaneously maintained, without requiring the intervention of controlled differentials or direct yaw control.