A Study on Swing up Control for Rotation of Parametric Pendulum

A parametric pendulum inherently demonstrates a conversion from external vibration to rotational motion and this property is applicable to energy scavenging from vibration of external source in nature. The periodic rotation of the parametric pendulum has a benefit to convert the mechanical energy to electric energy through conventional electric machines. On the other hand, the onset of the periodic rotation depends on the initial condition. We propose a control method for starting up the parametric pendulum to the periodic rotations based on an external force input with time delay. The feasibility of proposed method is verified numerically and experimentally. The results show that there exists a certain range of control gain to achieve the control from any initial condition. This paper advocates that the proposed method is suitable for crossing over a separatrix which governs the dynamics.