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研究生:杜慧雯
研究生(外文):Hui-Wen Tu
論文名稱:隨機嚴格反饋系統之LMI方法的適應性控制
論文名稱(外文):LMI-Based Adaptive Control of Stochastic Strict-Feedback Systems
指導教授:練光祐
指導教授(外文):Kuang-Yow Lian
學位類別:博士
校院名稱:中原大學
系所名稱:電機工程研究所
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:2007
畢業學年度:95
語文別:英文
論文頁數:95
中文關鍵詞:隨機模糊控制輸出追蹤T-S 模糊模型直流對直流轉換器線性矩陣不等式
外文關鍵詞:DC-DC convertersStochastic fuzzy controlLinear matrix inequalities (LMIs)T-S fuzzy modelOutput tracking
相關次數:
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本篇論文主要是針對以T-S 模糊模型來探討隨機嚴格反饋系統之適應性追
蹤控制。其設計方法主要分成兩個獨立步驟:i) 根據追蹤目標之輸出方程
式及廣義動態限制條件,求其虛擬之設計變數;ii) 採用線性矩陣不等式
(LMIs) 之方法,計算控制器之增益,其所對應之線性矩陣不等式的型式與
處理一般穩定化之問題一樣。本論文首先將非線性嚴格反饋系統以T-S 模
糊模型來表示,在討論其穩定化問題後,再延伸至輸出追蹤控制之探討。
為了助益於吾人之追蹤設計,而提出虛擬設計變數與廣義運動方程之觀

念,並將追蹤設計之控制問題轉換為穩定化問題之處理。若所探討的系統
為嚴格反饋之模式,其對應於廣義運動方程之虛擬設計變數皆可經由本論
文中所定義之遞迴程序完整推導而出,則系統之控制器亦可因應而生。之
後,將前述之討論延伸至參數未知的嚴格反饋系統,因而提出LMI-based
適應性追蹤控制,並將此控制方法擴展至多輸入系統。然而,當LMIs 中
之正定矩陣P 的結構須有所限定時,易使LMIs 無解,故吾人提出balance
technique 來解決此一問題。隨後,因考慮高頻切換脈波在PWM 直流對直
流降壓型轉換器之穩壓控制所產生的電磁波干擾現象,則對以Itô 微分式
表示之非線性系統進行隨機控制探討,因而提出兩種控制器:其一為隨機
積分型控制器,另一個為隨機輸出追蹤型控制器,此兩種控制器分別以數
位訊號處理器及類比電路來呈現。最後,在融合了前述之LMI-based 適應
性追蹤控制及非線性系統隨機控制,將吾人之研究拓展到以T-S 模糊模型
來表示之參數型的隨機嚴格反饋系統上。而由數值模擬呈現令人滿意的結
果得知:本論文所提出之控制方法是可實行的。
This dissertation presents the issue of developing adaptive output tracking control
for fuzzy stochastic parametric strict-feedback systems. Our design procedure is in two
independent steps: i) to determine the virtual desired variables from the desired output
equations and the generalized kinematic constraints; ii) to determine the control feedback
gains by solving a set of LMIs, which is in the same type of stabilization problem. First, an
LMI-based scheme is proposed for output tracking control after discussing the stabilization
of nonlinear strict-feedback systems with T-S fuzzy model. To bene t the tracking design,
the concepts of virtual desired variables and, in turn the so-called generalized kinematics
are introduced to convert the design procedure into stabilization problem. All the virtual
desired variables can be determined without fail from the generalized kinematics via a
newly de ned recursive procedure if the system is in strict-feedback form and, the practical
controller of the system can be obtained naturally. Subsequently, the LMI-based adaptive
scheme is developed for the systems with unknown parameters. It is also investigated
the adaptive tracking control for parametric multi-input strict-feedback systems. The
balance technique is proposed to deal with the restriction on the speci ed structure of
the symmetric positive de nite matrix P in LMIs. Then, the new stochastic integral
and the stochastic output tracking controllers for nonlinear It^o di erential systems are
developed. This is motivated by the output regulation problem of PWM DC-DC buck
converters when the electromagnetic interference due to high-frequency switching pulses is
considered. These two proposed controllers are implemented by DSP and analog circuits
as well. Finally, we extend our work to the fuzzy stochastic parametric strict-feedback
systems with integrating the achievements which have been obtained in nonlinear strictfeedback
and stochastic systems, respectively. From the numerical simulations, it is found
that the proposed schemes are feasible and the performance is satisfactory.
Contents
1 Introductory Chapter 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Organization of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Output Tracking Control of Fuzzy Systems in Strict-Feedback Form 10
2.1 Stabilization of Strict-Feedback Systems . . . . . . . . . . . . . . . . . . . 10
2.2 Output Tracking Control of Strict-Feedback Systems . . . . . . . . . . . . 13
2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Adaptive Tracking Control of Fuzzy Strict-Feedback Systems 19
3.1 Adaptive Tracking Control with Fuzzy Model in Basic Design . . . . . . . 19
3.2 Adaptive Tracking Control with Fuzzy Model for General Cases . . . . . . 27
3.3 Balance Technique Between Feasibility and Simplicity . . . . . . . . . . . . 29
3.4 Multi-Input Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Nonlinear Stochastic Fuzzy Control 48
4.1 Problem Formulation And Design Concepts . . . . . . . . . . . . . . . . . 48
4.2 Regulation Control of Buck Converters . . . . . . . . . . . . . . . . . . . . 54
4.3 Stochastic Tracking Fuzzy Control . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 Simulation and Experiment Results . . . . . . . . . . . . . . . . . . . . . . 61
4.5 Conlusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5 Adaptive Tracking Control of Stochastic Fuzzy Strict-Feedback Systems 69
5.1 The Basic Design of Adaptive Tracking Control for Stochastic Fuzzy Systems 69
5.2 Extending to the General Cases . . . . . . . . . . . . . . . . . . . . . . . . 76
5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6 Conclusions and Future Works 87
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
References 89
List of Figures
1.1 Flow chart depicting layout of the overall dissertation. . . . . . . . . . . . 9
2.1 Block diagram of a strict-feedback system with (x) = 1. . . . . . . . . . . 11
2.2 State responses of Example 2.1 . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1 Block diagram of a parametric strict-feedback system with (x) = 1. . . . . 20
3.2 State responses of Example 3.1 . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 State responses of Example 3.2 . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 State responses of Example 3.3 . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5 State responses of Example 3.3 by approximation technique . . . . . . . . 38
3.6 State responses of Example 3.4 . . . . . . . . . . . . . . . . . . . . . . . . 40
3.7 State responses of Example 3.5 . . . . . . . . . . . . . . . . . . . . . . . . 44
3.8 State responses of Example 3.5 . . . . . . . . . . . . . . . . . . . . . . . . 45
3.9 State responses of Example 3.5 . . . . . . . . . . . . . . . . . . . . . . . . 46
4.1 Equivalent circuit of buck converter with actual components. . . . . . . . . 55
4.2 Inductance contaminated by noise. . . . . . . . . . . . . . . . . . . . . . . 56
4.3 PWM sawtooth waves contaminated by noise. . . . . . . . . . . . . . . . . 60
4.4 (a) The response of inductor current; (b) The response of output voltage;
(c) The transient response of integral error. . . . . . . . . . . . . . . . . . . 62
4.5 Output voltage response with analog circuits using stochastic integral fuzzy
controller for the load R changed from 6
to 15
. . . . . . . . . . . . . . . 63
4.6 Output voltage response with analog circuits using stochastic integral fuzzy
controller for the load R changed from 15
to 6
. . . . . . . . . . . . . . . 64
4.7 Output voltage response with DS1103 using stochastic integral fuzzy controller
for the load R changed from 6
to 15
. . . . . . . . . . . . . . . . . 65
4.8 Output voltage response with DS1103 using stochastic integral fuzzy controller
for the load R changed from 15
to 6
. . . . . . . . . . . . . . . . . 65
4.9 (a) The response of inductor current; (b) The response of capacitor voltage;
(c) The transient response of integral error. . . . . . . . . . . . . . . . . . . 66
4.10 Output voltage response with analog circuits using stochastic output tracking
fuzzy controller for the load R changed from 6
to 15
. . . . . . . . . 66
4.11 Output voltage response with analog circuits using stochastic output tracking
fuzzy controller for the load R changed from 15
to 6
. . . . . . . . . 67
4.12 Output voltage response with DS1103 using stochastic output tracking
fuzzy controller for the load R changed from 6
to 15
. . . . . . . . . . . 67
4.13 Output voltage response with DS1103 using stochastic output tracking
fuzzy controller for the load R changed from 15
to 6
. . . . . . . . . . . 68
5.1 The state responses of Example 5.1. . . . . . . . . . . . . . . . . . . . . . . 75
5.2 The noises of states in Example 5.1. . . . . . . . . . . . . . . . . . . . . . . 76
5.3 The state responses of Example 5.2. . . . . . . . . . . . . . . . . . . . . . . 81
5.4 The noises of states in Example 5.2. . . . . . . . . . . . . . . . . . . . . . . 82
5.5 The state responses of Example 5.3. . . . . . . . . . . . . . . . . . . . . . . 84
5.6 The noises of states in Example 5.3. . . . . . . . . . . . . . . . . . . . . . . 85
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