Application of optimal preview control to speed-tracking of road vehicles

Abstract

Previous research on the application of optimal linear preview control to road vehicle steering is now extended to deal with speed-profile tracking as opposed to path tracking. After a brief review of the existing theory, a simple trolley model and a more elaborate but planar multi-body car model are described. The equilibrium or trim states of the simple trolley are trivial but those for the car need to be found through simulation, for the purpose of obtaining a linear, small-perturbation model, to which the control theory can be applied. Such a linear model for small-perturbations from any trim state is used for the linear optimal control computations. It is shown how the speed-tracking problem can be put into optimal linear preview control form and controls are derived and shown as functions of speed and control authority or tightness. As established in previous work, the optimal controls are demonstrated to have state-feedback and preview parts. Diminishing returns for additional preview of the speed-demand are obtained, reinforcing the notion that only finite preview is needed for full system performance. The preview needs of representative systems are found. For very tight control, the necessary preview is short but a wide range of behaviours is possible, depending on the balance between tracking precision and control power. In this instance, control power means engine power. Frequency responses of some optimally controlled systems are calculated and near-perfect speed-tracking is demonstrated for suitably band-limited and amplitude-limited demands. A simulation study shows the car motions in tracking a speed-profile of sinusoidal form.