State-Feedback Control of Vehicle Lateral Motion Subjected to Hybrid Time-Delays in the Loop: Stability and Gain-Optimization

Vehicle stability control (VSC) plays a central role both in the current traffic safety and in the way toward autonomy. Multiple types of time delays inevitably appear within the control loop affecting the performance and even the stability of the system. These delays can be classified as discrete and continuous ones, which together result in so-called hybrid delay effects. A vehicle model is introduced with transient and combined tire slip properties to accurately reflect the dynamics and controllability of a vehicle negotiating cornering. A semi-discretization (SD) method for the hybrid delay condition is proposed, which presents stability charts in the parameter space of control gains. The charts are validated by means of the analytical delay-averaging (DA) method constructed for the limited cases of continuous delay. Introducing the decay rate of settling as the optimization goal, the stable domain is further divided into regions characterized by the degrees of robustness against state perturbations. These optimal conditions are analyzed further for various delay hybridizations. The results are also validated by simulations carried out with the mechanical model of a vehicle which was identified experimentally. The cases with multiple hybrid delays reveal that the control performance essentially depends on the ratio of the hybrid delays rather than just on an averaged delay. Finally, conclusions regarding various gain-tuning strategies w.r.t different delay hybridization are given.