Wheel torque proportioning, rear steering, and normal force control: a structural investigation

This paper is concerned with various analysis and design issues for a possible set of control channels which may be used to improve the maneuverability and handling of automobiles. Of the possible set of controls, the current paper is limited to variable wheel torque proportioning, rear steering, and normal force control. The analysis and design issues are studied using an extensive linear model representing the lateral, longitudinal, and vertical dynamics, including their interactions. For the investigation of the finite-time behavior of system dynamics, we first introduce the notion of a reachable set where the attainability of a particular state vector at a particular time instant is considered. Next, we examine the attainability of a particular output trajectory within a finite-time interval using the notion of output function controllability. Several structural properties of these concepts have been studied. Various degenerate operating points are identified, where the effectiveness of the control channels deteriorates. In the steady-state analysis, the reference tracking and regulation problems are considered. It is shown that for some input/output subsystems those problems are generically solvable due to the minimum phase structure of the subsystems. For some others, those problems are solvable provided that the equilibrium point is not a degenerate equilibrium point. Finally, we show that for some input/output subsystems those problems are generically unsolvable.