二维系统的有限频设计方法研究

项目名称： 二维系统的有限频设计方法研究

项目编号： No.61473032

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 丁大伟

作者单位： 北京科技大学

项目金额： 82万元

中文摘要： 二维系统在过程控制、图像与信号处理、重复过程等诸多领域有着广泛应用，同时二维系统的很多问题需要在有限频域内加以考虑，如模型降阶问题、故障检测问题、扰动抑制问题等。本项目将针对二维系统的以上问题，提出一套有限频设计方法，该方法将避免频率加权法带来的计算复杂性和不准确性，同时可降低现有全频方法的保守性。具体如下：针对模型降阶问题，在相关的有限频域内，结合二维广义KYP引理和凸优化技术，提出有限频模型降阶方法；针对故障检测问题，在故障发生的频率范围内设计故障检测滤波器，借助于二维广义KYP引理准确刻画故障和干扰的有限频特性，进而给出数值上易于求解的设计条件；针对不确定二维系统，在有限频域内设计鲁棒H∞控制器，使闭环系统的有限频H∞性能得到优化，并给出凸的或数值上可行的设计条件；最后，推导出新的适用于复杂频率范围的二维广义KYP引理，从而完善二维系统的有限频理论，拓展有限频设计方法的应用范围。

中文关键词： 二维系统；有限频域；模型降阶；鲁棒控制

英文摘要： Two-dimensional(2-D) systems have vast applications in process control, image and signal processing, repetitive processes,etc. On the other hand, many problems of 2-D systems need to be considered in finite frequency domain, e.g.,model reduction, fault detection, disturbance attenuation,etc. This project will develop finite frequency design methodologies for these problems of 2-D systems. The proposed methodologies can avoid computational complexity and inaccuracy of the weighting method, and reduce conservatism of the existing full frequency methods. The details are as follows: The model reduction problem is considered in finite frequency domain. Combined the 2-D generalized KYP lemma and convex optimization techniques, a finite frequency model reduction method will be proposed for 2-D systems. For the fault detection problem, fault detection filters are designed over the frequency ranges of faults. The finite frequency characteristics of faults and disturbances are described by the aid of the 2-D generalized KYP lemma. Convex or numerically tractable design conditions will be derived. For uncertain 2-D systems, robust H∞ controllers are designed in finite frequency domain such that the finite frequency H∞ performance is optimized. Convex or numerically tractable design conditions will be given. Finally, novel 2-D generalized KYP lemmas for complex frequency ranges will be developed to complete the finite frequency theory and enlarge the application ranges of the finite frequency design methodologies.

英文关键词： 2-D;Finite frequency domain;Model reduction;Robust control