權重靈敏度函數最小化問題之降階控制器設計

Design of Reduced-order Controllers for Weighted Sensitivity Minimization Problem

褚永誠(Yong-Cheng Chu)

指導教授 ： 周永山

淡江大學/工學院/電機工程學系碩士班/碩士(2006年)

https://doi.org/10.6846/TKU.2006.00647

摘要

控制器的階數越高，硬體實現的成本及複雜度就越高，所以，長久以來，研究人員不斷尋求較低階控制器的設計方法，但目前仍缺乏有效的方法。我們改良Souza等人的想法，提出新型的 暨 降階輸出迴授動態控制器以及追踨控制器之設計。首先將原動態控制器的設計問題轉換為靜態輸出迴授增益的設計問題，再藉由控制靜態輸出迴授增益向量的個數以達到降階的目的。我們利用類似的技巧推導得到降階控制器存在的充要以及充分條件。另外，我們也提出植基於等價條件的疊代式演算法，將可以得到性能更佳的降階控制器。我們推導得到的條件皆為線性矩陣不等式(Linear Matrix Inequality,LMI)的形式，因此可以用現有軟體Matlab所提供的LMI Control Toolbox有效求解。

關鍵字

降階控制器 ； Hinfinity ； H2 ； 線性矩陣不等式 ； 遞迴法線性矩陣不等式

並列摘要

As the order of a controller becomes higher, the complexity of its hardware implementation becomes higher and the cost is more expensive. Therefore, much work has been done for the design of low-order controllers. However, it still lacks an efficient way to solve the problem in practice. We extend the idea of Souza et al to propose a novel design of the reduced-order Hinfinity or H2 output feedback controllers and tracking controllers. First, we convert the problem of designing dynamic controllers into the problem of designing static output feedback gain. Necessary and sufficient conditions for the existence of the reduced-order controllers are derived in a unified manner. Then we reach the goal of obtaining lower order controllers via controlling the number of variables of the feedback gain vector. Only sufficient conditions are obtained. In addition, we also present two iterative algorithms which can yield reduced-order controllers with better performance. The conditions we obtained are all in LMI form which can be efficiently solved via the LMI Control Toolbox in Matlab.

並列關鍵字

reduced-order ； Hinfinity ； H2 ； Linear Matrix Inequality(LMI) ； Iterative Linear Matrix Inequality (ILMI)

參考文獻

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