悬臂梁智能结构主共振响应的最优化控制

Optimal Control of Primary Resonance of Smart Structures of Cantilever Beams

应用最优化控制方法研究悬臂梁主共振响应的减振控制。由主共振振动定常解的稳定条件得到反馈控制增益的参数范围。以主共振有控制振动峰值与无控制振动峰值的比值为减振的衰减率,以该衰减率为目标函数,反馈控制增益参数范围为约束条件,利用最优化方法计算得到衰减率最小的速度反馈控制参数。计算发现速度反馈控制参数数值越大,衰减率越小,控制效果越好。以非线性振动系统的能量函数为目标函数,计算得到能量函数值最小的位移反馈控制参数,实现智能结构体主共振响应的控制器设计。由悬臂梁主共振振动实验实测数据计算出最优化控制参数,设计非线性主共振振动实验控制系统,进行减振控制实验研究。

A piezoelectric optimal feedback control methodology was provided to mitigate the pri- mary resonance of a cantilever beam. The regions of the feedback gains were obtained by using the sta- bility conditions of eigenvalue equation. Attenuation rate was used to evaluate the performance of vi- bration control by taking the proportion of peak amplitude of the vibration for the suspension system with and without control. Taking the attenuation rate as objective function and the stable regions of the feedback gain as constraint conditions, the control parameter of velocity feedback gain was worked out by using optimal method. It is found that a big feedback gain can lead to a small attenuation rate and has a good control performance. Taking the energy function as objective function, the control pa- rameter of displacement feedback gain can be calculated. The controller was designed to control the amplitude of primary resonance of smart structures. The optimal feedback gains were worked out by using the datum of primary resonance experimental test. An experimental control system was designed and control experiments were carried out.