H_∞分散控制系统范数计算的模态综合法(Ⅱ)  

Modal Synthesis Method for Norm Computation of H_∞ Decentralized Control Systems (Ⅰ)

作　　者：钟万勰[1] 吴志刚[1] 高强[1] 梁以德[2] F.W.威廉姆斯 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116023 [2]香港城市大学建筑系

出　　处：《应用数学和力学》2004年第2期111-120,共10页Applied Mathematics and Mechanics

基　　金：国家重点基础研究发展规划资助项目(G1999032805);国家自然科学基金资助项目(19732020;10202004);英国工程与物理科学研究理事会资助项目(GR/R05437/01)

摘　　要：　在大系统控制中,H∞分散控制方法将整个系统划分成一系列子系统分别研究,然后综合设计大系统的分散控制器,这与结构力学中的子结构分析技术类似·　本着这一思想建立了分散H∞控制与子结构振动分析的模拟关系、分散控制系统的最优H∞范数与整体结构一阶本征值之间的对应关系,进而利用结构力学中的模态综合法和扩展Wittrick＿Williams算法计算这一参数·　论文的第(Ⅰ)部分主要介绍系统H∞控制及其本征函数的正交性和展开定理;第(Ⅱ)When using H_∞ techniques to design decentralized controllers for large systems, the whole system is divided into subsystems, which are analysed using H_∞ control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which H_∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H_∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure. Hence, modal synthesis methodology and the extended Wittrick_Williams algorithm were transplanted from structural mechanics to compute the optimal H_∞ norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems H_∞ control are presented in part (Ⅰ) of the paper. The modal synthesis method for computation of the optimal H_∞ norm of decentralized control systems and numerical examples are presented in part (Ⅱ).

关 键 词：H∞控制 分散控制 模态综合 广义Rayleigh商 扩展Wittrick-Williams算法 

分 类 号：O32[理学—一般力学与力学基础] TP273[理学—力学]