Modal Synthesis Method for Norm Computation of H∞ Decentralized Control Systems (Ⅱ)
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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)部分介绍分散控制系统最优H∞范数计算的模态综合法及数值算例．
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关键词:
- H∞控制 /
- 分散控制 /
- 模态综合 /
- 广义Rayleigh商 /
- 扩展Wittrick-Williams 算法
Abstract: 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). -
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