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密频系统振动控制的状态估计
引用本文:徐博侯,鲍荣浩,张阿平.密频系统振动控制的状态估计[J].力学学报,2000,32(5):606-612.
作者姓名:徐博侯  鲍荣浩  张阿平
作者单位:浙江大学力学系, 杭州 310027
基金项目:国家自然科学基金(69391903),浙江省自然科学基金和曹光彪高科技基金(197017)资助项目.
摘    要:首先在研究了重频系统中状态可观察的必要条件基础上,给出了设计重频系统状态估计器的方法,使得状态估计的误差能以事先指定的速率衰减。随后给出两种方法将上述重频系统的估计器用到密频系统上去:一种是直接用重频系统估计器来估计密频系统状态,另一种是用按重频系统设计得到的估计矩阵构造密频系统的观察器,并分析由此引起的误差。分析表明,第一种方法简单易行,并且在频率分散度比较小时可以得到理想的结果;第二方法的精度较高,其误差与状态变量本身无直接关系。数值例子表明,用提出的状态估计器,并按相应的状态控制器,可以使密频系统的振动按事先给定的衰减程度趋向于零。

关 键 词:振动控制  密频系统  状态估计器  动态补偿器  大型空间结构
修稿时间:1998年10月28

STATE OBSERVER IN VIBRATION CONTROL OF CLOSELY SPACED MODE SYSTEMS
Xu Bohou,Bao Ronghao,Zhang Aping.STATE OBSERVER IN VIBRATION CONTROL OF CLOSELY SPACED MODE SYSTEMS[J].chinese journal of theoretical and applied mechanics,2000,32(5):606-612.
Authors:Xu Bohou  Bao Ronghao  Zhang Aping
Abstract:The corresponding repeated mode system (RMS) of a closely spaced modesystem (CSMS) is considered in the design of the state observer forthe CSMS in this paper. The necessary condition of the observability ofthe RMS is that the output dimension is no less than the systemdegree of freedom, hence only two cases with displacement or speedmeasured are considered in the remainder of the paper. The polarallocated methods to design the state observers with various form of theobservational matrix for the above RMS are proposed, in which theobservational error of the state decays with the preassigned ratiosand frequencies.   For a closely spaced mode system (CSMS), the corresponding RMS isfound at first and the observer of the original CSMS can be subsequentlyobtained by the following two methods: (1) to apply the observerof the corresponding RMS with the above method to the CSMS directly.By analyzing the relative error of the observer, it is shownthat this method has high precision when the frequency dispersion of theCSMS is small enough. (2) to obtain the observationalmatrix of the corresponding RMS with the above polar allocated method atfirst and then to construct the state observer of the CSMS. Itis also proved that the decayed ratios of the observer are very close tothe preassigned values when the frequency dispersion is small enoughand it isn't affected by the original state variables directly.   A numerical example at the end of this paper shows that suchstate observer combined with the state feedback controller[6] couldmake the vibration of the CSMS vanish within the preassigned ratiosrangeeffectively.   The foregoing results show that the corresponding RMS can beused to design the dynamical compensator of the CSMS directly when thefrequency dispersion is small enough.
Keywords:vibration control  CSMS  RMS  state observer  dynamical compensator
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