【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．更多还原

【Abstract】 The corresponding repeated mode system (RMS) of a closely spaced mode system (CSMS) is considered in the design of the state observer for the CSMS in this paper. The necessary condition of the observability of the RMS is that the output dimension is no less than the system degree of freedom, hence only two cases with displacement or speed measured are considered in the remainder of the paper. The polar allocated methods to design the state observers with various form of the observational matrix for the above RMS are proposed, in which the observational error of the state decays with the preassigned ratios and frequencies. For a closely spaced mode system (CSMS), the corresponding RMS is found at first and the observer of the original CSMS can be subsequently obtained by the following two methods: (1) to apply the observer of the corresponding RMS with the above method to the CSMS directly. By analyzing the relative error of the observer, it is shown that this method has high precision when the frequency dispersion of the CSMS is small enough. (2) to obtain the observational matrix of the corresponding AMS with the above polar allocated method at first and then to construct the state observer of the CSMS. It is also proved that the decayed ratios of the observer are very close to the preassigned values when the frequency dispersion is small enough and it isn’t affected by the original state variables directly. A numerical example at the end of this paper shows that such state observer combined with the state feedback controller~[6] could make the vibration of the CSMS vanish within the preassigned ratios range effectively. The foregoing results show that the corresponding RMS can be used to design the dynamical compensator of the CSMS directly when the frequency dispersion is small enough.更多还原