悬臂梁结构振动系统的鲁棒主动控制优化  

Robust Active Vibration Control Optimization of Cantilever Beam Structure

作　　者：何丽丽[1] 郭庆林[1] 周小利 原冬霞[1] 

机构地区：[1]河北工程大学,河北邯郸056038

出　　处：《公路交通科技》2017年第8期145-151,共7页Journal of Highway and Transportation Research and Development

基　　金：国家自然科学基金项目(11302066;51508150);河北省自然科学基金项目(E2008000731);河北省高等学校青年拔尖人才计划项目(BJ2017034);邯郸市科学技术研究与发展计划项目(1621211041-1);材料力学课程案例式教学研究项目(16129011017)

摘　　要：基于模型降阶的控制器由于忽略了高频未建模动态的影响,有可能产生溢出问题从而导致闭环系统不稳定,难以保证振动控制的效果,考虑高频未建模动态等不确定性问题影响,克服传统控制策略在振动主动控制中的不足,研究了柔性悬臂梁结构振动系统的H_∞鲁棒主动控制策略。基于ANSYS软件数值模拟得到压电柔性悬臂梁结构的模态振型,避免了试验建模的繁琐性、复杂性及较高的成本投入,通过与理论结果的比较,验证了ANSYS软件分析结果的正确性。通过模态分析提取了压电柔性悬臂梁结构的前3阶模态振型,剩余模态作为模型的不确定性加以考虑,通过分析系统存在的模型不确定性以及选取适当的权函数,最终完成了柔性悬臂梁结构振动系统的鲁棒控制器设计。通过从频率域上分析闭环传递函数的奇异值,表明权函数有较强的抑制外部干扰的能力,通过从时域上分析开环和闭环振动系统的单位阶跃响应,表明闭环振动系统的振幅很快趋于稳定且在较长时间内没有出现溢出不稳定现象,仿真结果表明,基于H_∞控制理论的混合灵敏度分析方法的鲁棒控制器能有效抑制悬臂梁的振动,振动系统的动态性能及鲁棒性能均得到了极大改善。Due to the ignorance of the impact of high-frequency unmodeled dynamics of the controller based on model reduction,there may be an ＂overflow ＂problem that causes the closed loop system to become unstable which is difficult to ensure the effect of the vibration control. Considering the influence of high frequency unmodeled dynamics and other uncertainties,in order to overcome the weakness of the traditional control strategy in the active vibration control,the H_∞robust active control strategy of the vibration system of flexible cantilever beam structure is investigated. The mode shape of piezoelectric flexible cantilever beam structure is obtained from ANSYS numerical simulation,which avoids the triviality,complexity,and higher cost of real experimental modeling. The correctness of this analysis result is proved compared with theoretical result. The first 3 order mode shapes of the piezoelectric flexible cantilever beam are extracted by modal analysis,and the residual mode is taken as the uncertainty of the model. By analyzing the existing model uncertainty of the system and selecting the appropriate weight function,the robust controller for the flexible cantilever structure vibration system is designed finally. By analyzing the singular value of the closed-loop transfer function from frequency domain,it shows that the weight function has a strong ability to suppress external interference. By analyzing the unit step response of the opened-loop and closed-loop vibrationsystems from time domain,it shows that the amplitude of the closed-loop vibration system tends to be stable quickly and there is no ＂overflow＂instability in the long time,the simulation result shows that the robust controller for mixed sensitivity analysis method based on the H_∞control theory can effectively suppress the vibration of the cantilever beam,and both the dynamic performance and robust performance of the vibration system are greatly improved.

关 键 词：汽车工程 振动主动控制 数值模拟 H_∞鲁棒控制 柔性结构 混合灵敏度 

分 类 号：TB535[理学—物理]