基于扩展内外分解的多变量系统解析设计及其应用

项目名称： 基于扩展内外分解的多变量系统解析设计及其应用

项目编号： No.60874005

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 张卫东

作者单位： 上海交通大学

项目金额： 30万元

中文摘要： 内外分解问题在系统与控制领域具有重要意义. 原始的内外分解定义是针对稳定对象提出的,只能用数值方法进行计算. 本项目将内外分解的定义推广到了一般情形(即对象可以包含不稳定极点,非最小相位零点和虚轴极点), 通过分析对象逆的特征, 给出了扩展内外分解的解析解. 基于该解析解, 应用最优控制理论研究了多变量控制系统的设计问题. 重要的问题包括推导控制器参数化,证明最优控制器和系统性能极限,发展定量的设p计过程. 研究新设计方法的原因在于目前发展起来的高级设计方法在控制实践中难以应用. 这些方法需要根据经验选择权函数,存在数值稳定性和计算复杂性问题,控制器无法按定量的工程性能指标进行设计. 本项目提出的无权函数的、解析的、定量的设计方法克服了这些问题,大大简化了多变量控制系统的设计工作, 有助于促进先进控制理论在工业实践中的应用.项目执行期间,在国际著名出版社出版了一本英文专著,在国内外刊物和会议上发表了2篇论文(其中1篇被SCI收录),有9项国家发明专利获得授权. 除此之外,项目负责人获得了国家杰出青年科学基金,项目组申请到了国家自然科学基金重点项目,一位博士生荣获上海市优秀博士学位论文.

中文关键词： 内外分解;多变量控制;解析设计;最优控制;PID

英文摘要： The inner-outer factorization problem plays a pivotal role in system and control theory. The original inner-outer factorization is defined for stable plants and only numerical computing methods are available. In this project, the inner-outer facotrization is defined for general plants (the plant can be unstable, NMP, or have imaginary axis poles). By analyzing the feature of the plant inverse, an analytical solution to the extended inner-outer factorization is given. Using this solution, we discuss the multivariable system design problem with the optimal design theory. The important problems in the design include deriving the controller parameterization, proving the optimal controller and the performance limit, and developing quantitative design procedure. The reason of developing this new design method is that it is not easy to use those existing advanced design methods in control practice. In these methods, one has to choose weighting functions empirically solving the controller with high complexity numerical procedure, and the controller cannot be design for quantitative engineering performance indices. The proposed method overcomes these problems with a no-weight, analytical and quantitative design provedure and the design task can be significantly simplified, which will boost the application of advanced design methods. During the study, 1 English book was published by an international publisher, 22 refereed papers (9 papers are included by SCI) were published in domestic and international journals ans conferences, and 9 invention patents were granted. In addition, the principal investigator won the National Science Fund for Distinguished Young Scholars of China, the research group won one key project of NSFC and two enterprise projects of 1400k RMB, and one PhD student won the Excellent PhD Thesis of Shanghai.

英文关键词： Inner-outer factorization; multivariable design; analytical design; optimal control;PID