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研究生:廖志傑
研究生(外文):Jeih-Jang Liou
論文名稱:模糊系統的輸出追蹤控制及應用
論文名稱(外文):Output Tracking Control for Fuzzy Systems and Its Applications
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:2006
畢業學年度:94
語文別:英文
論文頁數:103
中文關鍵詞:控制應用輸出追蹤模糊系統
外文關鍵詞:fuzzy systemsOutput trackingControl application
相關次數:
  • 被引用被引用:3
  • 點閱點閱:163
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  • 下載下載:3
  • 收藏至我的研究室書目清單書目收藏:0
這篇論文主要探討模糊系統的輸出追蹤控制。採用此設計方法分成以下兩個獨立的步驟︰i)根據追蹤目標之輸出方程式和廣義動態的限制條件,求取其虛擬設計變數。ii)採用線性矩陣不等式(LMIs)的方法計算控制器增益,文中採用方法之線性矩陣不等式與一般穩定問題的方程式相同。接著針對前述的方法延伸一些系統模式和控制的問題。首先,將非線性系統表示成T-S模糊的模式,依據這類系統模式,模糊的估測器被設計來處理輸出追蹤問題。然而,有些物理系統對參數變化敏感,例如混沌系統。為此,針對混沌系統採用精確的模式(exact model)。在控制混沌系統時,提出以混合式控制器來降低控制力。當混合式控制器應用於非線性系統以致形成混合系統。進一步,討論如何將混合系統轉化成模糊系統,然後,以脈波寬度調整(PWM)的手法來實現控制混合系統。但採用脈波寬度調整手法容易產生控制輸入飽和的問題,因此,引進具有控制輸入之限制條件之模型預測控制來處理此問題。最後,模糊模型預測控制器用以處理輸出追蹤和含有輸入控制之限制條件。在數值模擬方面,我們使用非線性彈簧質量系統、直流對直流降壓型轉換器、感應電動機、Chua電路、跳躍機器人和Henon map為例,進一步證實理論的結果。
This thesis presents the issue of developing output tracking control for fuzzy systems.
Our design procedure is split into two independent steps: i) to determine the virtual
desired variables from the desired output equation and the generalized kinematic constraint;
ii) to determine the control feedback gains by solving a set of LMIs, which is the
same type LMIs for stabilization problem. Then, the modelling and the controlling are
discussed. First, a general nonlinear system is expressed by the T-S fuzzy model. Based
on this model, fuzzy observer-based control design is proposed to deal with the output
tracking problem. However, some physical systems are sensitive to parameter variation,
for instance, chaotic system. Hence, the chaotic systems are adopted as the exact models.
For controlling chaotic systems, a hybrid-type of controllers to arrive at a low e ort is designed.
Hybrid systems are considered as the hybrid controllers are utilized for nonlinear
systems. So that, it is discussed how to obtain the fuzzy models from hybrid systems.
Then, PWM scheme control for hybrid systems are presented. The PWM scheme usually
imposes some constraints on the control input. Therefore, model predictive control is introduced
to cope with input constraints. Finally, output tracking control via fuzzy model
predictive control with input constraints is designed. For numerical simulations, we use
mass-spring systems, DC-DC buck converter, induction motor, Chua's circuit, a hopping
robot and the H enon map as examples to further verify the theoretical derivations.
Contents
1 Introductory Chapter 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Output Tracking Control for Fuzzy Systems 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Output Tracking Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Constraint of Generalized Kinematics . . . . . . . . . . . . . . . . . . . . . 14
2.4 Observer-based Output Tracking Control . . . . . . . . . . . . . . . . . . . 21
2.5 Design Based on Separation Principle . . . . . . . . . . . . . . . . . . . . . 23
2.6 Numerical simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3 Low E ort Control for Chaotic Systems via a Fuzzy Model-Based Ap-
proach 33
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Exactly Fuzzy Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3 Output Tracking Using Fuzzy Chaos Hybrid Controller . . . . . . . . . . . 41
3.3.1 Fuzzy Chaos Hybrid Controller . . . . . . . . . . . . . . . . . . . . 41
3.3.2 Analysis of Attraction Region . . . . . . . . . . . . . . . . . . . . . 43
3.3.3 Prede ned Attraction Region by Minimizing Ellipsoid Volume . . . 44
3.4 Numerical simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.1 Chua's Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
i
3.4.2 Mass-spring System . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4 Fuzzy Model and Control for Hybrid Systems Using Averaging Tech-
niques 52
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2 Fuzzy Model of Hybrid Systems . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3 LMI-based PWM Scheme Approach Output Tracking Control . . . . . . . 61
4.4 Integral Fuzzy Output Regulation Control . . . . . . . . . . . . . . . . . . 64
4.5 Output Tracking via feasible Fuzzy control . . . . . . . . . . . . . . . . . . 67
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5 Output Tracking Control for Fuzzy Model Predictive Controller 76
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2 Discrete-Time Fuzzy Model . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.3 Fuzzy Control for Discrete-Time Fuzzy Model . . . . . . . . . . . . . . . . 80
5.3.1 Output Tracking Control . . . . . . . . . . . . . . . . . . . . . . . . 80
5.3.2 Constraint of Generalized Kinematics . . . . . . . . . . . . . . . . . 81
5.4 Output Tracking for Fuzzy Model Predictive Control . . . . . . . . . . . . 82
5.4.1 Input Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.5 Updating Grade Functions via Neural Networks[57] . . . . . . . . . . . . . 86
5.6 Numerical simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6 Conclusions and Future Works 93
References 97
1.1 Flow chart depicting layout of the overall thesis . . . . . . . . . . . . . . . 8
2.1 Mass-spring mechanical system . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Equivalent circuit of a buck converter . . . . . . . . . . . . . . . . . . . . . 17
2.3 Response of x1; x1d; x2; x2d and control input u for mass-spring system. . . 29
2.4 Responses of x1; x1d; ^x1; x2; x2d and control input u for buck converter. . . . 30
2.5 Responses of ia; ida; a; da; T and Td for induction motor. . . . . . . . . . . 32
3.1 The universe of discourse is chosen . . . . . . . . . . . . . . . . . . . . . . 35
3.2 The bounding of (x) by d1 and d2 for exact representation of nonlinear
term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 The Lyapunov functions are used to estimate the domain of attraction . . 43
3.4 Ellipsoid algorithm can be used to estimate the domain of attraction for
tracking control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.5 Chua's circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.6 Purely T-S fuzzy model-based control of Chua's circuit . . . . . . . . . . . 48
3.7 Fuzzy chaos hybrid control of Chua's circuit . . . . . . . . . . . . . . . . . 49
3.8 Purely T-S fuzzy model-based controller . . . . . . . . . . . . . . . . . . . 50
3.9 Fuzzy chaos hybrid control . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1 The concept is the averaging techniques . . . . . . . . . . . . . . . . . . . . 56
4.2 Hybrid systems controlled by switching signals . . . . . . . . . . . . . . . . 56
4.3 hopping robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4 A typical PWM scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.5 Each period of the PWM consists of third stages . . . . . . . . . . . . . . . 63
4.6 Response of output voltage for buck converter . . . . . . . . . . . . . . . . 64
4.7 Response of output voltage for buck converter by integral fuzzy output
regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.8 The response of robot angle and leg angle for the hopping robot . . . . . . 73
4.9 The response of leg length, linear and angular velocities of leg for the
hopping robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.10 The PWM scheme for the hopping robot . . . . . . . . . . . . . . . . . . . 75
5.1 Internal structure of the controller. . . . . . . . . . . . . . . . . . . . . . . 87
5.2 An orbit of the H enon map . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3 The control gains of the LMI-based FMPC. . . . . . . . . . . . . . . . . . 91
5.4 Control results of Scenario 2: state responses for the FMPC-type controller
(dashed curves) and the proposed controller (dotted curves). . . . . . . . . 92
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