Some structural aspects of vehicle dynamics and their implications on control

A linear analytical vehicle model around a particular operating point is considered. Two sets of outputs, /spl Yscr//sub 1/, /spl Yscr//sub 2/ and two sets of inputs, /spl Uscr//sub 1/, /spl Uscr//sub 2/ are investigated where /spl Yscr//sub 1/={longitudinal velocity, yaw rate}, /spl Yscr//sub 2/={roll angle, pitch angle, vertical displacement of vehicle center of gravity, tire normal force distribution}, /spl Uscr//sub 1/={wheel torques} and /spl Uscr//sub 2/={active suspension forces}. First, a finite time control problem is examined. It is shown that the pairs (/spl Yscr//sub 1/, /spl Uscr//sub 1/), (/spl Yscr//sub 2/, /spl Uscr//sub 2/), and (/spl Yscr//sub 1//spl cup//spl Yscr//sub 2/, /spl Uscr//sub 1//spl cup//spl Uscr//sub 2/) are all output function controllable. That is, for each input/output pair, by choosing the input function suitably, the output dynamics can be made to track perfectly any desired trajectory within any finite time interval. Next, two asymptotic control problems, disturbance rejection and reference tracking, are considered. It is shown that the system matrices corresponding to the pairs (/spl Yscr//sub 1/, /spl Uscr//sub 1/), (/spl Yscr//sub 2/, /spl Uscr//sub 2/), and (/spl Yscr//spl cup//spl Yscr//sub 2/, /spl Uscr//sub 1//spl cup//spl Uscr//sub 2/) are all free of transmission zeros at the origin. Consequently, stepwise disturbances can be rejected and stepwise reference signals can be tracked asymptotically by the output variables in each pair by choosing a suitable feedback controller.