Stability Analysis and Optimization of Vehicle Active Motion Control System with Feedback Time Delay

A delayed dynamic model of vehicle lateral motion system is established to investigate the vehicle dynamics under time delay and to optimize the effect of time delay. The dynamic model is based on the non-linear 2-dimensional vehicle equation of motions and includes an active PD torque controller with feedback time delay. The wheel rotational dynamics and the longitudinal-lateral tyre force coupling are also modelled regarding the deformation delay induced by tyre elasticity. Phase plane analysis is carried out to acquire the handling and stability properties of the uncontrolled vehicle, and on this basis, the stability analysis of the delayed system is conducted and summarized in the stability chart of two control parameters, which shows the effects of time delay on vehicle system in various driving conditions and handling characteristics. Finally, simulations validate that the stability analysis for the controlled system dynamics and the eigenvalue-based optimization method performs effectively, which can be used for many considerations in vehicle delayed systems both from theoretical and practical viewpoints.