悬臂梁智能结构主共振响应的最优化控制

中国机械工程 ›› 2013, Vol. 24 ›› Issue (12): 1600-1604,1670.

悬臂梁智能结构主共振响应的最优化控制

刘灿昌1,2;裘进浩1;孙慧玉1;季宏丽1;刘露1,2

1.南京航空航天大学机械结构力学及控制国家重点实验室,南京,210016
2.山东理工大学,淄博,255049

出版日期:2013-06-25 发布日期:2013-07-11
基金资助:
长江学者和创新团队发展计划资助项目（IRT0968）；中国博士后科学基金资助项目（2012M521082）；新教师类基金资助项目（20123218120035）
Supported by Program for Changjiang Scholars and Innovative Research Team in University（No. IRT0968）;
Supported by China Postdoctoral Science Foundation（No. 2012M521082）

Optimal Control of Primary Resonance of Smart Structures of Cantilever Beams

Liu Canchang1,2;Qiu Jinhao1;Sun Huiyu1;Ji Hongli1;Liu Lu1,2

1.State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing,210016
2.Shandong University of Technology,Zibo,Shandong,255049

Online:2013-06-25 Published:2013-07-11
Supported by:

Supported by Program for Changjiang Scholars and Innovative Research Team in University（No. IRT0968）;
Supported by China Postdoctoral Science Foundation（No. 2012M521082）

摘要/Abstract

摘要：

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。

关键词: 非线性振动, 压电, 悬臂梁, 主共振响应, 最优化控制

Abstract:

A piezoelectric optimal feedback control methodology was provided to mitigate the primary resonance of a cantilever beam.The regions of the feedback gains were obtained by using the stability conditions of eigenvalue equation.Attenuation rate
was used to evaluate the performance of vibration 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 parameter 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.

Key words: nonlinear vibration, piezoelectricity, cantilever beam, primary resonance response, optimal control

中图分类号:

O322
O328

刘灿昌1, 2, 裘进浩1, 孙慧玉1, 季宏丽1, 刘露1, 2. 悬臂梁智能结构主共振响应的最优化控制[J]. 中国机械工程, 2013, 24(12): 1600-1604,1670.

LIU Can-Chang-1, 2, QIU Jin-Gao-1, SUN Hui-Yu-1, JI Hong-Li-1, LIU Lou-1, 2. Optimal Control of Primary Resonance of Smart Structures of Cantilever Beams[J]. China Mechanical Engineering, 2013, 24(12): 1600-1604,1670.

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