Modelling, analysis, and control of four-wheel independently actuated vehicles at handling limit

This study looks into the handling limit condition from a rather innovative perspective, by making use of an assumption, namely the independent wheel actuation. This assumption is recently becoming more relevant to the vehicle dynamics, as the electrified vehicles with in-wheel motors are getting a more common type of passenger vehicles. The focus of this research is on passenger vehicles moving at high-speed around the handling limit. Handling limit refers to the condition where the tyre forces reach their maximum value in a particular direction. This conditions is well-observed in the practice of drifting, as performed by highly-skilled drivers, which narrows down the focus of this work to those manoeuvres. The ultimate goal of this study is providing the analysis and guidelines on how the vehicle behaviour changes with different slips under the tyres when the vehicle starts to slide. First, a thorough planar motion analysis is performed, using a simplified vehicle model and the general behaviour of the vehicle is evaluated. An effective method for path-tracking control of the vehicle is studied and further developed. A qualitative metric to measure the amount of drifting in vehicle is suggested in a mathematical form, based on the quantitative descriptions about drifting. In the next stage, a four-wheel model with 7 degrees of freedom is introduced and validated for use in vehicle sliding analysis. To capture the nonlinear behaviour of the tyre forces, an elliptic tyre model is introduced for the combined-slip conditions. The model is then used to analyse the drifting manoeuvres. Drifting is studied in detail, in terms of dynamic equilibria and stability. The four-wheel vehicle model is used to calculate the dynamic equilibria in planar motion, numerically, by introducing an assumption on constant longitudinal tyre slips. This assumption enables studying the system effectively with three state variables. Other than the unstable drifting points that were reported by previous researchers, a new pair of drifting equilibria are identified and the difference of the two types is studied. The phase portrait approach is used to identify the type of these equilibria. The two-by-two phase portraits reveal the type of instability in the primary and the secondary drifting points and provide control suggestions to stabilise the drifting equilibria. Finally, general remarks on using the primary drifting for path-tracking during drifting are stated.