Effect of Coulomb Friction on Feedback Posture Control of Bicycle Using Gyroscopic Moment Effect

Abstract

A mechanism has been proposed that utilizes the gyroscopic moment generated by tilting the rotation axis of a flywheel for stabilization control of unstable system. In this study, we investigate the effectiveness of feedback control which drives a gimbal mechanism to maintain the standing posture of an unstable structure such as a two-wheel vehicle. Although a simple feedback of posture angle enables a two-wheel structure to keep standing, both posture and gimbal continue shaking little by little. This is because the gimbal temporarily stays at a constant angle due to the action of Coulomb friction, and the system becomes unstable in the interim. We propose a method to estimate both the length of time when the motion of the gimbal stops and the amplitudes of the vibration of posture and gimbal. Here, we assume that the first-order mode poles obtained from the linearized model are complex numbers and that the second-order mode response converges immediately. From the experimental results, it is found that if the gimbal stays at a constant angle for a long time, the structure tends to fall over. We show that state feedback is necessary to realize to shorten the time when the gimbal stays at a constant angle and to reduce the amplitudes of oscillations at the same time.