Stabilization Control of Parametric Resonance in Flexible Structure

本文从理论上提出了一些参数共振的稳定控制方法，并通过实验验证了它们的有效性。首先，提出了一种采用小静摩擦摆的稳定方法。从理论上阐明了以激励幅频平面上的分岔集为界的不稳定区域被被动自动移位，使激励幅频组合不再处于不稳定区域。其次，利用电机驱动摆，提出了一种基于分岔控制的参数激励单自由度系统主动控制方法，使控制系统对较大的外部干扰具有更强的鲁棒性。我们将这种针对单自由度系统的主动控制方法推广到分布参数系统，并建立了参数激励悬臂梁的稳定方法。电机驱动摆使控制系统的自由度增加了一个，即由于摆的运动，控制系统的自由度比梁的自由度大。为了防止这种自由度的增加，我们提出了一种稳定控制方法，即使用压电陶瓷作为致动器而不是电机驱动摆。通过实验结果与理论结果的比较，证实了该方法的有效性。

In this research, some stabilization control methods for parametric resonance are theoretically proposed, and their validity is experimentally confirmed. First, a stabilization method using a pendulum with small static friction at its pivot is proposed. It is theoretically clarified that the unstable region, which is bounded by the bifurcation set on the excitation amplitude-frequency plane, is passively and automatically shifted so that the combination of the excitation amplitude and frequency is no longer in the unstable region. Next, using a motor actuated pendulum, we propose an active control method based on bifurcation control for a parametrically excited single degree of freedom system to make the control system be more robust with respect to the large external disturbance. We expand this active control method proposed for a single degree of freedom system to the distributed-parameter system and establish a stabilization method for the parametrically excited cantilever beam. The motor actuated pendulum increases the degrees of freedom in the control system by one, i.e., the degrees of freedom in the control system are more than those of the beam due to the motion of the pendulum. In order to prevent such increase in the degrees of freedom, we propose a stabilization control by using the piezoceramic as an actuator instead of a motor actuated pendulum. The validity of this method is confirmed by comparing the experimentally obtained results to those of theoretically ones.