基于压电换能器的柔性梁动力学建模及主动振动控制

Dynamic Model and Active Vibration Control of Flexible Manipulator Based on PZT Transducers

本文以Euler-Bernoulli柔性梁为研究对象,在铰接-自由的边界条件下,运用哈密尔顿原理以及变分和积分的数学方法建立了柔性梁系统的动力学模型。采用假设模态法离散柔性梁的弹性变形,通过数值求解得到柔性梁弹性变形的振型函数。为了能够快速抑制柔性梁的弹性振动,基于压电换能器对其进行主动振动控制。结合压电换能器的传感器和作动器的动力学模型,推导了压电换能器主动控制力作用下柔性梁系统的整体动力学方程。利用MATLAB/Simulink对所建立的动力学模型进行仿真实验研究,发现在施加外界主动控制力的作用下,柔性梁系统的弹性振动得到了有效的抑制。

Under the hinged-free boundary condition,Euler-Bernoulli flexible beam was researched in this paper.The dynamics model of flexible beam system was established using Hamilton′s principle,calculus of variations and integral equations.The assumed modes method was applied to discretize the elastic deformation of the flexible beam,and the mode functions were obtained by numerical calculation.In order to suppress elastic vibration of the flexible beam rapidly,an active vibration control based on piezoelectric transducers was performed.Combined with the dynamics models of piezoelectric transducers,the overall dynamics equation of the flexible beam system under the active control force by the piezoelectric transducers was derived.Using MATLAB/Simulink to conduct simulation experiments on the established dynamics model,it was found that under the action of external active control force,the elastic vibration of the flexible beam system was effectively suppressed.