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研究生:謝正雄
研究生(外文):Shieh, Cheng-Shion
論文名稱:不確定性系統的模式轉換與強健數位重新設計
論文名稱(外文):Model Conversion and Robust Digital Redesign of Uncertain Linear Systems
指導教授:蔡聖鴻, 孫育義
指導教授(外文):Jason Sheng-Hong Tsai, York-Yih Sun
學位類別:博士
校院名稱:國立成功大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:1998
畢業學年度:86
語文別:中文
論文頁數:1
中文關鍵詞:數位重新設計區間可調式雙線性近似包含式區間模式遺傳基因演算法則區間運算法則均值法則
外文關鍵詞:digital redesigninterval tuning bilinear approximationenclosing interval modelgenetic algorithminterval operation arithmeticlaw of mean
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本文提出一些新方法混合區間運算法則與遺傳基因演算法則來解決以
下問題: 1)不確定線性系統的模式轉換,2)具有輸入時延之採樣不確定性
系統的強健數位重新設計 ,3)較不保守之個別特徵根的範圍與不確定性線
性系統的線性二次調節器範圍. 基於線性近似方法,吾人引入一個參
數來調整精確系統矩陣與近似系統矩陣間的誤差範圍,透過本文提出的區
間可調二次線性近似法,區間系統矩陣的範圍比現今存在的區間二次線性
近似法與區間佩得近似法來得更窄.而且此區間模式(圍繞區間模式)能緊
密地包含住精確不確定性系統模式,同樣地,近似數位狀態區間解也能緊密
地包含住不確定性連續狀態的精確區間解. 基於均值定律,可調二次線
性法與區間運算法,吾人提出二種方法來求連續不確定性時延系統的強健
數位控制器,使得數位控制採樣不確定性系統的動態狀態能緊密地吻合原
始設計良好的不確定性連續系統狀態.然而,由於區間運算法則的保守性,
吾人再提出一種新的方法混合遺傳基因演算法則來解決此保守性的問題.
但若系統狀態無法獲得,那麼就須要從原始的連續時延系統觀測器和預測
器來建立一個數位觀測器使得數位重新設計觀測器的狀態估測值和原始時
延連續觀測器的狀態在採樣瞬間上吻合.吾人也運用遺傳基因演算法則的
全域搜索特性來計算不確定性連續系統的個別特徵根範圍與線性二次調節
器的控制器範圍. 本文提出的方法將有助於1)不確定性系統的分析與
設計,2)具有輸入時延之採樣不確定性系統混合控制的實現,3)改良直接數
位控制器設計只考慮系統週期點上的狀態反應.此外,並舉出一些例子來說
明本文所推演出方法的有效性.
In this dissertaion , some new method together with interval
operation arithmetic and genetic algorithms(GAs) are proposed to
solve the problems:1) model conversion of uncertain linear
systems, 2) robust digital redesign of sampled-data uncertain
systems with input time delay and 3) non-conservativeindividual
bound and controller bound of linear quadratic (LQ) regulator of
uncertain linear systems. Based on the bilinear approximation
method, we induct one parameter for tuning the error bound
between the exact and approximate uncertain system matrices. The
bounds of the interval system matrices via the proposed
intervaltuning bilinear approximation method are narrower than
those of the existing interval bilinear and the interval pade
approximation methods. The resulting interval models (the
enclosing interval models) are able to tightly enclose the exact
uncertain models. Also the approcximate discrete-time interval
solution is able to tightly enclose the exact interval solution
of the continuous-time uncertain state-space equation. Based
on the law of mean, the tuning bilinear method and the interval
arithmetic operation, we propose two methods for determining the
robust digital control law from the continuous-time uncertain
system with input time delay so that the resulting dynamic
states of the digitally controlledsampled-data uncertain system
are able to closely match those of the originalcontinuous-time
well-designed uncertain system. Whereas, due to the nature of
the interval arithmetic and the inherent conservativeness of
interval arithmetic operations, we present a new method together
with genetic algorithmsto solve the conservativeness problem.
Meanwhile, when the system state is notavailable, a discrete-
time observer is built based on the original continuous-time
observer with input time delay and predictor such that the
estimated states of the redesigned discrete-time observer match
those of the originalcontinuous-time observer with input time
delay at the sampling instants. We also use the property of
global search of genetic algorithm to calculate theindividual
eigenvalue bound and controller bound of the LQ regulator for
uncertain linear systems. The proposed methods will be helpful
for 1)analysis and synthesis of uncertain systems,
2)implememtation of hybrid control of sampled-data uncertain
systems with input time delay and 3) improving the direct
digitalcontroller design which only considers the system
behavior at sampling instants(not inter-sampling behavior). Some
illustrative examples are included to demonstate the
effectiveness of the proposed methods
Cover
ABSTRACT
ACKNOWLEDGMENT
CONTENTS
GLOSSARY OF SYMBOLS
LIST OF FIGURES AND TABLES
CHAPTER 1 INTRODUCTION
1.1 Definition of the problem of hybrid control system with input time delay
1.2 The reasons for the need of digital redesign
1.3 Eigenvalue problem
1.4 Objective on the adaptive controller bound of linear quadratic regulator(LQR) of the uncertain system
1.5 Organization of this dissertation
CHAPTER 2 MATHEMATICAL PRELIMINARIES
2.1 Interval analysis preliminaries
2.2 Overview of genetic algorithms
2.3 The solution ofRiccati equation via matrix sign function method
CHAPTER 3
3.1 Introduction
3.2 Digital interval model conversion
3.3 Analog interval model conversion
3.4 Illustrative example
3.5 Summary
CHAPTER 4 DIGITAL MODELLING AND ROBUST DIGITAL REDESIGN OF SAMPLED-DATA UNCERTAIN SYSTEMS VIA THE INTERVLA TUNING BILINEAR APPROXIMATION METHOD
4.1 Introduction
4.2 Problem formulation
4.3 Discrete-time modeling of continuous-time uncertain systems
4.4 Digital redesign of sampled-data uncertain system via tuning bilinear approximation method
4.5 Illustrative example
4.6 Summary
CHAPTER 5
5.1 Introduction
5.2 Problem formulation
5.3 Discrete-time model conversion of uncertain systems
5.4 A new method for digital redesign of uncertain systems with input time delay
5.5 Illustrative example
5.6 Summary
CHAPTER 6 DIGITAL MODELING AND HYBRID CONTOL OF SAMPLED-DATA UNCERTAIN SYSTEM WITH INPUT TIME DELAY USING THE LAW OF MEAN
6.1 Introduction
6.2 Problem formulation
6.3 Discrete-time model conversion of analogue uncertain systems with input time delay
6.4 Digital redesign of analogue uncertain systems with input time delay
6.5 Illustrative example
6.6 Summary
CHAPTER 7 DIGITAL MODELING AND HYBRID CONTROL OF SAMPLED-DATA UNCERTAIN SYSTEM WITH INPUT TIME DELAY USING GENETIC ALGORITHMS
7.1 Introduction
7.2 Problem formulation
7.2.1 Discrete-time conversion of analogue uncertain system with input time delay
7.2.2 New method for digital redesign of an analogue uncertain system with input time delay
7.3 Digital modeling of analogue uncertain system with input time delay via GAs
7.4 Digital redesign of analogue uncertain system with input time delay via GAs
7.5 Illustrative example
7.6 Summary
CHAPTER 8 HYBRID CONTROL OF SAMPLED-DATA UNCERTAINSYSTEM WITH INPUT TIME DELAY USING DIGITALLY REDESIGNED OBSERVER-BASED CONTROLLER
8.1 Introduction
8.2 Problem formulation
8.3 Discrete-time model of uncertain system with input time delay using GAs
8.4 New method for digital redesign of an analogue uncertain system with input time delay
8.5 New method for digital redesign of discrete-time observer
8.6 Illustrative example
8.7 Summary
CHAPTER 9 NON-CONSERVATIVE INDIVIDUAL EIGENVALUE BOUND AND CONTROLLER BOUND OF LQ REGULATOR FOR THE UNCERTAIN LINEAR SYSTEM
9.1 Introduction
9.2 Non-conservative individual eigenvalue bound of an interval system matrix via GAs
9.3 Non-conservative controller bounds ofLQ regulator for uncertain linear systems via GAs
9.4 Illustrative examples
9.5 Summary
CHAPTER 10 CONCLUSIONS
10.1 Conclusions
10.2 Further research directions
APPENDIX A
APPENDIX B
APPENDIX C
REFERENCES
BIOGRAPHY
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