Stabilization Control of Parametric Resonance in Flexible Structure

在本研究中，从理论上提出了几种参数共振的镇定控制方法，并通过实验验证了其有效性。首先，提出了一种利用支点具有较小静摩擦的摆动系统的镇定方法。从理论上阐明了由激励幅频平面上的分叉集所限定的不稳定区域被被动地、自动地平移，使得激励幅频组合不再处于不稳定区域。其次，针对参数激励的单自由度系统，提出了一种基于分叉控制的主动控制方法，使控制系统对大的外部扰动具有更强的鲁棒性。将这种单自由度系统的主动控制方法推广到分布参数系统，建立了参数激励悬臂梁的镇定方法。电机驱动的单摆使控制系统的自由度增加了1，即由于单摆的运动，控制系统的自由度比横梁的多。为了防止这种自由度的增加，我们提出了一种稳定控制，用压电陶瓷代替电机驱动的摆作为执行器。通过将实验结果与理论结果进行比较，验证了该方法的有效性。

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.