Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/8385
標題: 雙曲線型偏微分方程式之取樣資料控制型式推導
A Sampled-Data Formulation for Boundary Control of a Hyperbolic Partial Differential Equation System
作者: 李權育
李權育, Quan-Yu Li
關鍵字: Sampled-Data;雙曲線型;Hyperbolic Partial Differerntial;偏微分;取樣資料控制
出版社: 電機工程學系所
摘要: 
本論文主要針對一個雙曲線型偏微分方程式系統,明顯地,偏微分方程式系統之研究困難度遠高於常微分系統。故因此,本論文提出一個取樣資料型式來解決邊界控制問題之分析方法。藉由邊界條件滿足司徒姆-呂維耳問題(Str-umLiouville Problem)之規則形式,並利用特徵函數展開法,使得雙曲線型偏微分方程式轉化成一無窮級數之離散時間控制問題。並利用傅立葉級數最小平方差定理取得有限維度離散時間系統的近似解,
本論文為了驗證分析推導之結果,則採用了兩種數值模擬方法,一種是利用有限差分法來直接解出雙曲線型偏微分方程式系統,另一則是本論文所提出的之取樣資料型式之有限維度離散系統控制,最後並將兩種方法來比較驗證出本論文所提出的方法的可行性。

This thesis presents an analytic solution to the hyperbolic partial differential equation systems. Obvious, the partial differential equations are more difficult than the ordinary differential equations system for study. Therefore, this thesis proposed a sample-data formulation to analytic solution to the boundary hyperbolic partial differential equation systems. With boundary conditions satisfying the regular form of Strum-Liouville problem, and used the eigenfunctions expansion method to making hyperbolic partial differential equation into an infinite sequence of discrete-time control problems. The finite-dimensional approximation of the discrete-time system is obtained by the minimum square error theorem of Fourier series.
And this thesis for verification to the proposed analysis derivation of the equation result. Therefore, to introduce two numerical analysis simulation methods, ones are direct to used finite difference approximate method to solve hyperbolic partial differential equation systems, and the other ones are use proposed sampled-data formulation of finite-dimensional discrete-time system control. In the end, to compare our proposed method with finite difference approximate method for to verification this proposed method feasibility.
URI: http://hdl.handle.net/11455/8385
Appears in Collections:電機工程學系所

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