Optimal preview speed-tracking control for motorcycles

Prior work on the application of optimal linear preview control to road vehicle steering is extended to deal with speed-profile tracking as opposed to path tracking. The focus here is on motorcycles. An elaborate multibody motorcycle ride and handling model from the literature is used as a basis for the development. This model is reduced from its general form to allow only in-plane motions. A speed-controlled nonlinear version of the model is used to establish quasi-equilibrium or trim states for running through a full speed range and a corresponding linear model for small-perturbations from any trim state, with simple engine dynamics included, 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 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 motorcycle motions in tracking a speed-profile of sinusoidal form.