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狀態時滯多采樣率線性離散廣義因果系統的最優輸出調節器設計

Design of optimal output regulators for multirate linear discrete-time descriptor causal system with time delay

  • 摘要: 研究了帶有狀態時滯的多采樣率線性離散時間廣義因果系統的最優輸出調節器的設計問題.首先利用離散提升技術將原系統轉化為形式上無時滯的系統.再通過等價變換,利用系統的因果性特點將其化為一個正常系統.繼續對系統進行離散提升,導出一個形式上簡單的單采樣率系統.然后將原系統的二次性能指標函數修正為單采樣率系統的二次性能指標函數,進而利用最優調節原理,得到其最優調節器.再經過變換,得到多采樣率系統的最優輸出調節器.同時對導出的單采樣率系統的能穩定性和能檢測性進行了討論,給出了嚴格的數學證明.最后的數值仿真表明,本文所設計的最優調節器是有效的.

     

    Abstract: This paper introduces the design problem of optimal output regulators for multirate linear discrete-time descriptor causal systems. At first, by making use of the discrete lifting technique the original system is transformed into no state time-delay system in form. Then thought the equivalent transformation, taking advantage of the causal characteristics of the system, it is changed into a normal system. Continuing to apply discrete lifting into the system, a simple single-rate system in form is exported. The performance index function of the original system is modified to that of the single-rate system, and then an optimal output regulator is obtained by using the optimal regulator theory. Through transformation an optimal output regulator for the original system is finally derived. At meantime, the stabilizability and detectability of the exported single-rate system were discussed, and their rigorous mathematical proofs were given. Numerical simulations proved the effectiveness of the preview controller designed in this paper.

     

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