多維系統的模式化及最佳控制

陳嘉偉* 蔡聖鴻**
國立成功大學電機工程學系

摘要

本文主要探討多維系統的模式化及最佳控制。首先，文中敘述如何將一個用二階偏微分方程式表示的變係數多輸入多輸出系統，模式化為一個變係數的羅莎模型。而此法在其實際應用上有一重要問題，即如何選擇微分運算子的差分近似和積分範圍，使其能獲得羅莎模型。且此法在文獻上扮演著未來研究領域的起始點。然後，在本論文中亦新近提出二維輸入延遲系統模型。此模型主要是用於設計和分析具不可避免的內在延遲和計算延遲的系統。再者，二維系統/二維輸入延遲系統/二維連續-數位系統/三維系統的模式轉換在文中亦被提出。這些被提出的模式轉換允許我們能間接分析和設計混合系統。而且，連續三維系統的離散化最佳/次最佳追蹤器設計法(一種新穎且具連續品質函數的數位再設計法)也在文中被提出。其中所提出的次最佳追蹤器可減少大量記憶體的需求。最後，在文中提出具連續品質指標函數的非線性連續二維系統的離散化次最佳追蹤器設計法，且其中包含了以下幾種特色：(i)非線性連續羅莎模型的最佳線性化，(ii)連續二維系統的離散化最佳/次最佳追蹤器設計，(iii)非線性連續二維系統的離散化次最佳追蹤器的設計。

* 研究生
** 指導教授

Modeling and Optimal Control of Multi-Dimensional Systems

Chia-Wei Chen* and Jason Sheng-Hong Tsai**

Department of Electrical Engineering
National Cheng Kung University, Tainan, Taiwan, R.O.C.

Abstract

Modeling and optimal control of multi-dimensional systems have been investigated in this dissertation. Firstly, this dissertation addresses how a variable coefficient two-dimensional (2-D) multi-input multi-output system described by second-order partial differential equations can be converted to a discrete variable coefficient Roesser model (RM). The important problem for its practical application is how the choice of the finite difference operators for each differential operator and the respective integral intervals determine a formulation of RM. The proposed methodology serves as a starting point for the future research in literature. Then, the model of the 2-D input-delay system is newly presented in this dissertation. The presented model significantly facilitates analysis and design of a system when it faces the unavoidable inherent delay and the computation delay. The model conversions of 2-D/ 2-D input-delay/ continuous-discrete/ three-dimensional (3-D) systems are also proposed in our research works. The proposed model conversions allow us to indirectly carry out analysis and design of hybrid composite systems. Furthermore, the discretized quadratic optimal/sub-optimal tracker for linear continuous 3-D systems, a novel methodology for indirect digital redesign with a continuous cost function, is proposed. The proposed sub-optimal tracker decreases the overall memory size requirements of the optimal tracker. Finally, the discretized quadratic sub-optimal tracker for nonlinear continuous two-dimensional 2-D systems is presented in this dissertation. This includes the following features: (i) the 2-D optimal-linearization approach of nonlinear 2-D RM, (ii) the discretized quadratic optimal/sub-optimal tracker for linear continuous 2-D systems, and (iii) the discretized quadratic sub-optimal tracker for nonlinear continuous 2-D systems.

* the student
** the advisor

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