The Control and Stability Analysis of Two–wheeled Road Vehicles

The multibody dynamics analysis software, AUTOSIM, is used to develop automated linear and nonlinear models for the hand derived motorcycle models presented in (Sharp, 1971, 1994b). A more comprehensive model, based on previous work (Sharp and Limebeer, 2001), is also derived and extended. One version of the code uses AUTOSIM to produce a FORTRAN or C program which solves the nonlinear equations of motion and generates time histories, and a second version generates linearised equations of motion as a MATLAB file that contains the state-space model in symbolic form. Local stability is investigated via the eigenvalues of the linearised models that are associated with equilibrium points of the nonlinear systems. The time histories produced by nonlinear simulation runs are also used with an animator to visualise the result. A comprehensive study of the effects of acceleration and braking on motorcycle stability with the use of the advanced motorcycle model is presented. The results show that the wobble mode of a motorcycle is significantly destabilised when the machine is descending an incline, or braking on a level surface. Conversely, the damping of the wobble mode is substantially increased when the machine is ascending an incline at constant speed, or accelerating on a level surface. Except at very low speeds, inclines, acceleration and deceleration appear to have little effect on the damping or frequency of the weave mode. A theoretical study of the effects of regular road undulations on the dynamics of a cornering motorcycle with the use of the same model is also presented. Frequency response plots are used to study the propagation of road forcing signals to the motorcycle steering system. It is shown that at various critical cornering conditions, regular road undulations of a particular wavelength can cause severe steering oscillations. The results and theory presented here are believed to explain many of the stability related road accidents that have been reported in the popular literature. The advanced motorcycle model is improved further to include a more realistic tyre-road contact geometry, a more comprehensive tyre model based on Magic Formula methods utilising modern tyre data, better tyre relaxation properties and other features of contemporary motorcycle designs. Parameters describing a modern high performance machine and rider are also included.