CAJ | 학술논문

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;第二种方法的精度较高,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速度趋向于零.
수선재연구료중빈계통중상태가관찰적필요조건기출상,급출료설계중빈계통상태고계기적방법,사득상태고계적오차능이사선지정적속솔쇠감.수후급출량충방법장상술중빈계통적고계기용도밀빈계통상거:일충시직접용중빈계통고계기래고계밀빈계통상태,령일충시용안중빈계통설계득도적고계구진구조밀빈계통적관찰기,병분석유차인기적오차.분석표명,제일충방법간단역행,병차재빈솔분산도비교소시가이득도이상적결과;제이충방법적정도교고,기오차여상태변량본신무직접관계.수치례자표명,용제출적상태고계기,병안상응적상태공제기,가이사밀빈계통적진동안사선급정적쇠감속도추향우령.
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.