多個不穩定線性系統存在使系統穩定之切換律以及線性控制系統在致動器出現故障時存在共同穩定器之研究

國

立

交

通

大

學

電機與控制工程學系

碩士論文

多個不穩定線性系統存在使系統穩定之切換律以及

線性控制系統在致動器出現故障時

存在共同穩定器之研究

On Existence and Construction of Stabilizing Switching Laws

Between Unstable Linear Systems and the Existence of

Common Stabilizer for a Class of Linear Control Systems

Experience Actuator’s Outage

研 究 生：張嘉良

指導教授：梁耀文 博士

中 華 民 國 九 十 四年 七 月

多個不穩定線性系統存在使系統穩定之切換律以及

線性控制系統在致動器出現故障時

存在共同穩定器之研究

On Existence and Construction of Stabilizing Switching Laws Between

Unstable Linear Systems and the Existence of

Common Stabilizer for a Class of Linear Control Systems

Experience Actuator’s Outage

研 究 生：張嘉良

Student: Jia-Liang Chang

指導教授：梁耀文 博士 Advisor: Dr. Yew-Wen Liang

國立交通大學電機與控制工程學系

碩士論文

A Thesis

Submitted to Department of Electrical and Control Engineering

College of Electrical Engineering and Computer Science

National Chiao Tung University

In Partial Fulfillment of the Requirements

For the Degree of Master

In

Electrical and Control Engineering

June 2005

Hsinchu, Taiwan, Republic of China

I

多個不穩定線性系統存在使系統穩定之切換律以及

線性控制系統在致動器出現故障時

存在共同穩定器之研究

研究生：張嘉良

指導教授：梁耀文 博士

國立交通大學電機與控制工程學系

摘要

本篇論文主要在探討兩個關於多個不穩定系統間是否存在有穩

定切換律之判斷條件的對等關係，並且利用此對等關係來判斷線性控

制系統在致動器發生故障時是否存在有共同穩定器。更進一步，我們

針對二階系統來瞭解這些判斷條件對應於幾何上的意義為何，並提供

一個利用特徵值與特徵向量來判斷是否存在有使系統穩定之切換律

的對等條件。根據這兩個條件的對等關係，我們將其應用於判斷多個

不可穩定化線性控制系統是否存在適當的控制器及穩定切換律。這些

控制律及穩定切換律在本論文中也被完整且明確的提出。最後，我們

也整理出一個演算法則來判斷線性控制系統是否存在有共同穩定器

並且提出完整的建構方法。

II

On Existence and Construction of Stabilizing Switching Laws

Between Unstable Linear Systems and the Existence of

Common Stabilizer for a Class of Linear Control Systems

Experience Actuator’s Outage

Student: Jia-Liang Chang

Advisor: Dr. Yew-Wen Liang

Department of Electrical and Control Engineering

National Chiao Tung University

ABSTRACT

This thesis investigates the equivalence of two sufficient conditions

for the existence of stabilizing switching laws between unstable linear

systems, and then employs the equivalence to the existence of common

stabilizers of a linear control system in the presence of actuator’s outage.

To further understand the geometrical insight of these conditions, an

equivalent condition involving the information of eigenvalues and

eigenvectors of system dynamics is presented for planar systems. With

the help of the equivalent relation, a condition for the existence of

controllers and stabilizing switching laws between N unstabilizable linear

control systems is presented, too. Finally, an algorithm for checking and

constructing the existence of common stabilizer for a class of linear

control system of experiencing actuator’s outage is also explicitly

presented.









  

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