Research on the potential of integrated vehicle control with closed-loop phase portrait analysis

The phase portrait is an important tool for analyzing vehicle stable region widely utilized in vehicle dynamic control systems. At handling limits, traditional open-loop vehicle stable region constraints will restrict the vehicle control ability, while the closed-loop actuator interventions can help states outside the open-loop stable region converge back to stable origin, which is more suitable for constraining vehicle states under extreme working conditions. This article systematically analyzes the potential of integrated vehicle control with closed-loop phase portrait. Firstly, a vehicle dynamic model considering actuator dynamics and tire transient characteristics is established. Then, a numerical optimal control method for calculating closed-loop controllability region is introduced. The controllability region under different friction coefficients, vehicle speeds, convergence time, vehicle steering response characteristics, actuator time constants, and tire transient characteristics are discussed and analyzed. In terms of different control inputs combinations, this article displays the controllability regions under different front steering angles, rear steering angles, direct yaw moments, and their synergistic performances. Control input laws derived from numerical optimization are summarized in two specific directions. Finally, a comparative analysis of open-loop stable regions and closed-loop controllability regions confirms the superiority of the proposed method. Potential applications of the systematic analysis are also discussed.