An Inverse Linear Model of a Vehicle

SUMMARY It is common to use linear differential equations of vehicle motion to procure descriptions of vehicle performance. The solution to these equations describes the motion of the vehicle, usually given in terms of lateral acceleration, yaw rate, and sideslip angle, as a function of a steer angle. The equations many be termed open-loop in the sense that we give the steer angle and find out how the vehicle responds. This paper presents equations which we refer to as the inverse of the open loop procedure. In particular, the solution of the equations is steer angle, yaw rate and sideslip angle given as a function of lateral acceleration. The real part of the eigenvalues of these equations indicates that the model is always stable and well damped, and the imaginary part indicates that routine path-following tasks require only low frequency steer angles.