【作者】 钟万勰； 吴志刚； 高强； 梁以德；

【Author】 ZHONG Wan-xie, WU Zhi-gang, GAO Qiang, LEUNG A. Y. T. ( State Key Laboratory of Structural Analysis for Industrial Equipment , Dalian University of Technology, Dalian 116023; Department of Building and Construction , City University of Hong Kong, Hong Kong Kowloon)

【机构】 大连理工大学工业装备结构分析国家重点实验室； 香港城市大学建筑系；

【摘要】 根据结构力学与最优控制的模拟关系,H∞状态反馈控制的最优参数γcr2与柱形结构的稳定性分析或振动中的Rayleigh商一阶本征值相对应。在大系统控制中,分散控制方法通过将整个系统划分成一系列子系统来研究系统的控制问题,这一点与结构力学中的子结构分析技术类似。本文由此建立了H∞分散控制与子结构振动问题之间的对应关系,并指出大系统的最优参数对应于整体结构的一阶本征值,进而介绍了基于模态综合方法计算H∞分散控制问题中的最优参数γcr2的详细过程,并给出了算例。更多还原

【Abstract】 Based on the analogy between structural mechanics and optimal control, the optimal parameter γcr2 of state feedback H∞ control has been shown corresponding to the fundamental Rayleigh quotient eigen-value in structural stability or in structural vibration problems formulated in the prismatic domain. For control problems of large-scale system, the de-centralized control theory is developed, for which the whole system is subdivided into a number of sub-systems. The de-centralized system control theory is similarly shown to be analogous to sub-structural analysis in structural mechanics. The H∞ de-centralized control theory is shown corresponding to the sub-structural vibration, and the global parameter γcr2 of the whole system corresponds to the fundamental natural vibration frequency of the whole structure. The modal synthesis methodology is therefore transplanted to find the optimal parameter γcr2 in H∞ de-centralized control. The detailed derivation is given in the paper. Numerical examples are provided to demonstrate the analogy.更多还原