An Approach to Vibration Control of Multiple-Pendulum System by Wave Absorption

Abstract

In this paper, a new wave-absorbing strategy has been studied to suppress the vibration of a multiple-pendulum system by controlling the lateral movement of the support. The wave-absorbing condition is derived from the difference between the equation of motion of the boundary pendulum and that of an inner pendulum. An online real-time simulation method using the numerical solution is proposed to control the movement that satisfies the wave-absorbing condition. According to this method, vibration of a multiple-pendulum system with arbitrary degrees of freedom can be controlled by measuring only the deflection angle of the uppermost pendulum adjacent to the support if the dimensions of the uppermost pendulum and the total mass of the system are known. Both the numerical simulations and the experiments have confirmed the effectiveness of this method. The basic idea of this control method can easily be applied to any discrete vibrating system whose equations of motion have no traveling-wave solution.