- 學位論文
受性能條件限制之正規強健濾波器設計
Normal Robust Filter Design with Performance Constraints
摘要
本論文主要討論受性能條件限制之強健H∞ 濾波器問題。針對濾波器設計，不僅考慮H∞ 性能指標，也針對不同類型系統討論不同的濾波器性能限制條件。在訊號處理及通訊系統中，濾波器問題中一種常見的性能規格，是濾波器輸出端在時域上的響應封套限制，尤其對於具有不確定因素之多輸入多輸出系統更具有理論與實際應用上的重要性，因為它可以處理耦合效應的影響。另一個常見而受矚目的性能規格是濾波系統的極點位置。不像時域封套限制條件，設定濾波器極點位置的條件是一種間接的性能規格設定方式，因其必須依賴對系統響應與極點位置關係的知識，但廣受有經驗之系統設計者採用。和控制系統設計問題相比，在濾波問題上，可以只考慮濾波器極點位置的選擇，而非整個系統之極點位置。另外當系統本身具有不穩定極點的情況時，則需要分開討論。在本論文中所考慮的系統包含正規狀態空間模式與奇異狀態空間模式兩類。這是需要的，因為在一些情況下正規狀態空間模式無法如奇異狀態空間模式般可以表現脈衝式的特性，尤其是當系統受到擾動時。 本論文首先考慮具有時域封套條件之濾波問題，並提出直接的方法以允許設計者能針對多輸入多輸出系統，設計具有消除通道耦合效應能力之濾波器。然後，考慮濾波器的D-穩定度條件，這將使濾波器設計者能彈性地調整濾波器的特性。接著針對具有不確定性之奇異系統，比較所設計之正規濾波器與奇異濾波器的性能表現。在討論的過程中將提出一個正規的轉換方式，以轉換具有不確定性之奇異系統成為正規系統。最後，針對奇異系統模式所有系統矩陣皆包含不確定性的情況，與系統具有不穩定極點的情況，進行更深入的研究。本論文的研究特色之一，是在分析與合成的問題上，皆利用線性矩陣不等式的技巧，所以發展出來的方法很容易便能加以實現，而且具計算上的效率優勢。
並列摘要
This dissertation studies the robust H∞ filtering problems with performance constraints. Not only the H∞ performance index is considered for filter design, but also various constraints with respect to other filtering performance requirements are posed for different systems. A general performance specification of filtering problems in signal processing and communication systems is the filter output time-domain response envelope constraints. It is especially of theoretical interest and practical importance for MIMO systems with uncertainties, since coupling effects can be accommodated. Another general performance specification often concerned is about the pole locations of filter systems. Unlike the time-domain envelope constraints, setting pole location constraints is an indirect approach based on the knowledge of system responses and pole locations, but it is widely adopted by experienced system designers. In contrast to control system design problems, in filtering problems only the filter, not the overall system, pole locations may be selected, and systems with unstable poles need to be treated separately. Here both systems described by normal state-space models as well as singular state-space models are considered. This is mandatory because in some cases normal state-space models can not express the impulsive characteristic as the singular systems, especially when systems are perturbed. This dissertation begins by considering filtering problems with the time-domain envelope constraints, and proposes direct methods allowing one to design filters with the channel coupling cancellation capability for the MIMO systems. Then, the D-stability constraint for the filter is considered, enabling filter designers to shape the filter characteristics in a flexible fashion. Subsequently, filtering problems for singular systems with uncertainties are studied to compare the performance with normal and singular filters. In the development process a normal transformation that transfers singular system models with uncertainty to normal system models is proposed. Finally, a deeper exploration is made by letting all system matrices to contain uncertainties in the singular system models, as well as letting systems to have unstable poles. A feature of this research is the use of LMI techniques in both analysis and synthesis problems, so all derived method are easy to implement and computationally efficient.
參考文獻
延伸閱讀
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