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研究生:張明新
研究生(外文):Ming-Hsing Chang
論文名稱:線性時變系統的範數模式和相關控制設計
論文名稱(外文):A Two-Norm Model of Linear Time-Varying System and Related Control Designs
指導教授:陳明新陳明新引用關係
指導教授(外文):Min-Shin Chen
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:53
中文關鍵詞:division control線性時變系統least squarecontrollability grammianforward Riccati equation
外文關鍵詞:controllability grammianleast squarelinear time-varying systemdivision controlforward Riccati equation
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在本篇論文中,我們要介紹一個非線性狀態轉換來將一個線性時變系統轉換到一個純量系統,並且探討該純量系統在控制輸入下的狀態變化。接著,利用不同的控制方法來針對這個純量模式加以控制,控制的方法包括forward Riccati equation control、controllability grammian control、least square control以及division control共四種。然而,在控制的過程中,即使線性時變系統是可控制的,該純量系統有可能會失去可控制性。因此,這是未來還需要研究的課題。
In this thesis, we introduce a nonlinear state transformation to transform a linear time-varying system into a scalar system, which describes how the two-norm of the system state changes with the control input. With this two-norm scalar model, different control designs can be constructed, including the forward Riccati equation control, controllability grammian control, least-squares control, and the division control. However, even if the linear time-varying system is controllable, the two-norm
scalar system may lose its controllability in the process of control. Hence, further research is required in the future.
Abstract-Chinese version I
Abstract-English version II

Chapter1. Introduction 1
Chapter2. Scalar Two-Norm Model for LTV System 3
2.1 Backward Riccati equation 3
2.2 Forward Riccati equation 4
2.3 Scalar two-norm model for LTV system 6
Chapter3. Forward Riccati Control 7
3.1 Example 8
Chapter4. Least Square Control 10
4.1 When A=0 10
4.2 When A≠0 11
4.3 Example 14
Chapter5. Controllability Grammian Control 16
5.1 When A=0 16
5.2 When A≠0 17
5.3 Example 20
Chapter6. Division Control 22
6.1 When A=0 22
6.1.1 Smooth division controller 22
6.1.2 Division controller + dead zone 23
6.2 When A≠0 23
6.2.1 Smooth division controller 23
6.2.2 Division controller + dead zone 24
6.3 Example 25
Chapter7. Conclusion 28
References 29
Figures 30
Figure 3.1 Time history of system states 30
Figure 3.2 Norm of states with time 30
Figure 3.3 Lyapunov function with time 31
Figure 3.4 Solution q of forward Riccati equation with time 31
Figure 3.5 Scalar b of the transformed system with time 32
Figure 3.6 Control input u with time 32
Figure 3.7 Time history of system states 33
Figure 3.8 Norm of states with time 33
Figure 3.9 Lyapunov function with time 34
Figure 3.10 Solution q of forward Riccati equation with time 34
Figure 3.11 Scalar b of the transformed system with time 35
Figure 3.12 Control input u with time 35
Figure 4.1 Time history of system states 36
Figure 4.2 Norm of states with time 36
Figure 4.3 Control input u with time 37
Figure 4.4 Converge rate with time 37
Figure 4.5 Time history of system states 38
Figure 4.6 Norm of states with time 38
Figure 4.7 Control input u with time 39
Figure 4.8 Converge rate with time 39
Figure 4.9 Time history of system states 40
Figure 4.10 Norm of states with time 40
Figure 4.11 Control input u with time 41
Figure 4.12 Converge rate with time 41
Figure 5.1 Time history of system states 42
Figure 5.2 Control input u with time 42
Figure 5.3 Time history of Lyapunov function 43
Figure 5.4 Time history of controllability grammain p 43
Figure 5.5 Time history of system states 44
Figure 5.6 Control input u with time 44
Figure 5.7 Time history of Lyapunov function 45
Figure 5.8 Time history of controllability grammain p 45
Figure 6.1 Time history of system states 46
Figure 6.2 Norm of states with time 46
Figure 6.3 Control input u with time 47
Figure 6.4 Time history of system states 47
Figure 6.5 Norm of states with time 48
Figure 6.6 Control input u with time 48
Figure 6.7 Time history of system states 49
Figure 6.8 Norm of states with time 49
Figure 6.9 Control input u with time 50
Figure 6.10 Time history of system states 50
Figure 6.11 Norm of states with time 51
Figure 6.12 Control input u with time 51
Figure 6.13 Time history of system states 52
Figure 6.14 Norm of states with time 52
Figure 6.15 Control input u with time 53
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