有限频域内线性系统的模型降阶与模型补偿

项目名称： 有限频域内线性系统的模型降阶与模型补偿

项目编号： No.61304143

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 自动化技术、计算机技术

项目作者： 杜鑫

作者单位： 上海大学

项目金额： 23万元

中文摘要： 许多实际系统的工作频率范围通常为已知的有限频域，故本项目拟在有限频域内研究线性系统的模型降阶和模型补偿问题。对有限频模型降阶问题，拟基于平衡截断理论，通过结合可分析线性系统有限频性能的广义KYP引理，设计出一套频率相关的有限频平衡截断法。同现有的全频平衡截断法可很好的解决全频模型降阶问题类似，拟开发的有限频平衡截断法将可以快速求解有限频模型降阶问题，且所得降阶模型可以保持原系统在给定频率范围内的物理特性，同时还可以给出一个合理的频率相关的有限频先验误差估计上界。对有限频模型补偿问题，拟首先给出一个基于系统哈密顿矩阵谱特征的有限频耗散性判据，进而开发出一套新的有限频矩阵摄动模型补偿方法，该方法可以在实现系统有限频耗散性补偿的同时，根据给定频率来选取实现补偿所需的最小摄动量，从而得到和频率区间匹配的补偿精度。本项目的开展对模型降阶和模型补偿理论的发展以及对实际系统的建模仿真等都具有重要的意义。

中文关键词： 模型降阶；有限频；线性系统；平衡截断；KYP引理

英文摘要： It is well known that the operating frequency of many practical systems is generally maintained in a pre-known finite frequency intervals. Therefore, this item is dedicated to cope with the finite-frequency model reduction and model compensation problems of linear systems. For finite-frequency model reduction problems, a totally new research methodology that combing the Genaralized KYP Lemma and blanced truncation theory will be adopted, and a new frequency-dependent balanced truncation method will be developed. It is expected that the new method possessing many desirable properties, such as finite-frequency physical properties of the original system can be preserved and an accurate and proper finite frequency approximation error bound can also be provided. For model compesation problems, new criteria for checking the finite frequency dissipativity will be established by further exploiting the spectrum of Hamiltonian matrices at first. Then, new finite frequency dissipativity enforcement algorithm will be designed based on the matrix perturbation theory. Adopting the new model compensation method, the samllest perturbation associated with the pre-specified frequency range can be derived and the frequency-dependent compensation accuracy can be obatined. This research item is of great importance form either the de

英文关键词： Model order reduction；Finite frequency；Linear systems；Balanced truncation；KYP Lemma