Title: 含高階微分插值條件限制的靈敏度最小化
Sensitivity Minimization with High Order Derivative Interpolation Constraints
Authors: 吳卓諭
Wu, Jwo-Yuh
林清安
Lin Ching-An
電控工程研究所
Keywords: 高階微分插值條件;靈敏度;Sensitivity Minimization;Interpolation
Issue Date: 1997
Abstract: 本論文探討當系統包含重數大於一之非最小相位零點的靈敏度最小化
問題。在此情況下為了使閉環系統穩定,靈敏度函數必須在非最小相位零
點滿足一系列高階微分的插值條件。此類系統在實際上雖不常見,但對於
研究此類零點對控制系統設計上的限制以及性能的影響,本論文提供一個
定量描述問題的方法。從插值理論的觀點我們推導出系統權重靈敏度函數
最小 範數的解析公式,並且提出ㄧ個從線性非時變系統之輸入-輸出的關
係來解釋數學上的插值問題。我們發現兩者得到的結果是相同的。我們嘗
試去探討此範數之最小值與系統非最小相位零點重數的關係,希望未來能
根據這個解析的結果來進一步研究當非最小相位零點的重數增加時,對控
制系統設計上有何限制。
In this thesis we consider sensitivity minimization problem
for plants containing a nonminimum phase zero with multiplicity
. Stability requirement in this case imposes high order
derivative interpolation constraints on the sensitivity
function. Based on an interpretation of Pick*s Theorem, we
proposed two methods to compute a lower bound on the achievable
weighted sensitivity. We show that the lower bound is tight by
using the result of the Carathe*odory problem. We extend the
result to plants containing a real unstable pole. The analytic
nature of our results allow a future study on how the minimal
weighted sensitivity increases as the multiplicity of nonminimum
phase zero increases.
URI: http://140.113.39.130/cdrfb3/record/nctu/#NT860591002
http://hdl.handle.net/11536/63176
Appears in Collections:Thesis