H ∞ 分散控制系統範數計算的模態綜合法(Ⅰ)

Abstract

在大系統控制中, H ∞ 分散控制方法將整個系統劃分成一系列子系統分別研究, 然後綜合設計大系統的分散控制器, 這與結構力學中的子結構分析技術類似。本著這一思想建立了分散H∞控制與子結構振動分析的模擬關係、分散控制系統的最優H ∞ 範數與整體結構一階本征值之間的對應關係, 進而利用結構力學中的模態綜合法和擴展Wittrick-Williams算法計算這一參數。論文的第(Ⅰ)部分主要介紹系統H ∞ 控制及其本征函數的正交性和展開定理; 第(Ⅱ)部分介紹分散控制系統最優H ∞ 範數計算的模態綜合法及數值算例。

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).