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姓名陳震武(Cheng-Wu Chen) 查詢紙本館藏 畢業系所土木工程學系 論文名稱結合模糊控制與類神經網路探討非線性結構控制的穩定性

(Stability of Nonlinear Structural Control via Fuzzy Control and Neural Network)相關論文檔案[Endnote RIS 格式] [Bibtex 格式] [相關文章] [文章引用] [完整記錄] [館藏目錄] 至系統瀏覽論文 ( 永不開放) 摘要(英)In this dissertation, several new stability analysis techniques and systematic design procedures for the Takagi-Sugeno (T-S) model-based fuzzy control and neural-network-based approach are proposed.

This paper also investigates the effectiveness of a passive Tuned Mass Damper (TMD) and fuzzy controllers in reducing the structural responses under the external force. In general, TMD is good for linear system. We proposed here an approach of Takagi-Sugeno (T-S) fuzzy controller to deal with the nonlinear system. In this dissertation, the nonlinear part is concerned with the nonlinear stiffness but not the field of nonlinear plastic behavior of the structural response.

To overcome the effect of modeling error between nonlinear systems and T-S fuzzy models, a robustness design of fuzzy control via model-based approach is proposed in this work. A stability criterion in terms of Lyapunov’’s direct method is derived to guarantee the stability of nonlinear interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear interconnected system and the control performance is achieved at the same time. Also, several asymptotically stability conditions via linear matrix inequalities (LMI) approaches are derived for multiple time-delay nonlinear systems.

In this dissertation, neural network (NN) model is employed to approximate the nonlinear systems. Then, the dynamics of each NN model is converted into LDI (linear differential inclusion) representation. Next, a robustness design of fuzzy control via NN-based approach is proposed to overcome the effect of modeling error between nonlinear systems and NN models. Meanwhile, NN model approach is better than T-S fuzzy model to approximate the nonlinear systems.

Finally, the developed theory is illustrated by an example of a nonlinear TMD system throughout this paper. Several illustrative examples and simulations are used to demonstrate that the proposed approaches are effective. However, in chapter 6, the practical application in structural system does not discuss the influence of the time delay. Besides, the designing procedures for the T-S fuzzy model and NN model are systematic and simplified.關鍵字(中)★ 結構系統

★ 非線性系統

★ 迷糊神經關鍵字(英)★ structural system

★ nonlinear system

★ fuzzy neural論文目次Chapter 1 Introduction

1.1 Background and Motivation 1

1.2 Review of Previous Works 11

1.2.1 Fuzzy Control 11

1.2.1.1 Themes in Design 11

1.2.1.2 Themes in Analysis 13

1.2.2 Neural Network 17

1.2.3 Controller Design via T-S Fuzzy Model and NN 19

1.3 Organization of This Dissertation 25

Chapter 2 Lyapunov Theory

2.1 Introduction 27

2.2 Nonlinear Systems and Equilibrium Points 28

2.2.1 Nonlinear Systems 28

2.2.2 Equilibrium Points 30

2.3 Concepts of Stability 31

2.3.1 Stability and Instability 32

2.3.2 Asymptotic Stability and Exponential Stability 32

2.3.3 Local and Global Stability 34

2.4 Lyapunov Direct Method 34

2.5 Positive Definite Function and Lyapunov Functions 35

Chapter 3 Problem Formulations

3.1 Introduction 40

3.2 T-S Fuzzy Model and The Stability Conditions 41

3.2.1 T-S Fuzzy Continuous Model and PDC Control 41

3.2.2 T-S Fuzzy Discrete Model 45

3.3 Example 47

3.4 Conclusion 49

Chapter 4 Robustness Design of T-S Fuzzy Controllers for Nonlinear multiple Time-Delay Interconnected TMD Systems

4.1 Introduction 52

4.2 Large Scale System and Chaotic Vibration 53

4.2.1 Large Scale System 53

4.2.1.1 Formulation of Large Scale System 54

4.2.1.2 Weakly Connected and Strongly Connected 55

4.2.2 Chaotic Vibration 55

4.2.2.1 Some Characteristics of Chaotic Vibrations 56

4.2.2.2 Nonlinear Vibration Theory 58

4.3 System Description 59

4.4 Parallel Distributed Compensation 61

4.5 H Infinity Control Design via Fuzzy Control 62

4.6 Robustness Design of Fuzzy Control 63

4.6.1 Modeling Error 63

4.6.2 Stability in The Presence of Modeling Error 67

4.7 Algorithm 69

4.8 Example 69

4.9 Conclusions 77

Chapter 5 Stability Analysis via Neural Network

5.1 Back Propagation Network 99

5.1.1 Introduction 99

5.1.2 BPN Operation 99

5.2 Stability Analysis of Neural Network for Nonlinear Systems 101

5.3 System Description and Stability Analysis 101

5.4 Example 106

5.4.1 Example 1 107

5.4.2 Example 2 107

5.5 Conclusions 116

Chapter 6 Model-Based Fuzzy Control for Structural Systems

6.1 Summary 126

6.2 Introduction 127

6.3 Fuzzy System Modeling 130

6.3.1 Two Representative Fuzzy Model Structures 131

6.3.2 Fuzzy Modeling of Structural System 134

6.3.3 Stable Controllers Design via Linear Matrix Inequalities 140

6.4 Neural Network Modeling 141

6.5 Numerical Examples 146

6.6 Conclusions 156

Chapter 7 Conclusions

7.1 Summary of Research 172

7.2 Future Research 174

Reference 175

Appendix 193

List of Figures and Tables

Fig. 1.1 Functional Diagram of a Fuzzy Controller 26

Fig. 1.2 Basic architecture of a fuzzy logic controller (FLC). 26

Fig. 2.1 Concepts of stability 38

Fig. 2.2 Interpreting positive definite functions using contour curves 38

Fig. 2.3 Illustrating Definition 2.7 for n=2 39

Fig. 3.1 The block diagram of T-S fuzzy model-based control system 50

Fig. 3.2 Parallel-distributed-compensation (PDC) design 50

Fig. 3.3 The state response of fuzzy system. 51

Fig. 3.4 The control force of fuzzy system. 51

Fig. 4.1 The jth subsystem of the nonlinear large-scale system. 85

Fig. 4.2 Structure of the composite system. 85

Fig. 4.3 The jth subsystem of the fuzzy large-scale system. 86

Fig. 4.4a Period-2 motion for forced motion of a buckled beam in the phase planes. 86

Fig. 4.4b Chaotic trajectory for forced motion of a buckled beam. 87

Fig. 4.5 (a) Frequency spectrum of buckled elastic beam for low-amplitude

excitation-linear periodic response. 87

Fig. 4.5 (b) Frequency spectrum of buckled elastic beam for larger

excitation-broad-band response of beam due to chaotic vibration. 87

Fig. 4.6 Experimental bifurcation diagram for a periodically forced nonlinear

circuit systems. 88

Fig. 4.7 Introduction the complete design procedure 88

Fig. 4.8 Two-DOF structure-TMD system. 89

Fig. 4.9 The effectiveness of a TMD system. 89

Fig. 4.10 The effectiveness of a TMD system with linear stiffness k(x). 90

Fig. 4.11 Dynamic magnification factor of a TMD system with nonlinear

stiffness k(x). 90

Fig. 4.12 Dynamic magnification factor of a TMD system with nonlinear

stiffness k(x). 91

Fig. 4.13 Dynamic magnification factor of a TMD system with nonlinear

stiffness k(x). 91

Fig. 4.14 Phase-plane trajectory of the chaotic system. 92

Fig. 4.15 Chaotic behavior of a nonlinear system with no control force. 92

Fig. 4.16 The plots of

(dashed line) and (solid line). 93

Fig. 4.17 The plots of

(dashed line) and (solid line). 93

Fig. 4.18 The plots of

(dashed line) and (solid line). 94

Fig. 4.19 The plots of

(dashed line) and (solid line). 94

Fig. 4.20 The plots of

(dashed line) and (solid line). 95

Fig. 4.21 The plots of

(dashed line) and (solid line). 95

Fig. 4.22 The plots of

(dashed line) and (solid line). 96

Fig. 4.23 The plots of

(dashed line) and (solid line). 96

Fig. 4.24 The state response of system 1. 97

Fig. 4.25 The state response of system 2. 97

Fig. 4.26 The control force of system 1. 98

Fig. 4.27 The control force of system 2. 98

Fig. 5.1 Neural Network of Back propagation. 121

Fig. 5.2 The jth isolated NN subsystem. 121

Fig. 5.3 Original function. 122

Fig. 5.4 2-2-1 Neural network. 122

Fig. 5.5 2-5-1 neural network. 123

Fig. 5.6 The first isolated NN subsystem. 123

Fig. 5.7 The second isolated NN subsystem. 123

Fig. 5.8 The third isolated NN subsystem. 124

Fig. 5.9 The state of subsystem 1. 124

Fig. 5.10 The state of subsystem 2. 125

Fig. 5.11 The state of subsystem 3. 125

Fig. 6.1 The Chi Chi earthquake. 148

Table. 6.1 Maximum response with and without input control. 148

Fig. 6.2 Time histories of response quantities of the first floor. 148

Fig. 6.3 Time histories of response quantities of the second floor. 149

Fig. 6.4 Time histories of response quantities of the third floor. 149

Fig. 6.5 Time histories of response quantities of the fourth floor. 149

Figs. 6.6-6.9 Time histories of response quantities of the first-fourth floor via decentralized

control. 150-151

Figs. 6.10-6.13 Time histories of control force of the first-fourth floor via decentralized

control. 151-152

Table. 6.2 Maximum response via T-S fuzzy model and NN model. 152

Figs. 6.14-6.17 Time histories of response quantities of the first-fourth floor.153-154

Fig. 6.18 The model error of the overall subsystems without decentralized control. 154

Figs. 6.19-22 The model error of the first-fourth subsystem with decentralized control. 154-155

Fig. 6.23 The model error of the overall subsystems via NN model. 156參考文獻1. Barnard, E. “Optimization for training neural nets,” IEEE Trans. Neural Networks, vol. 3, pp. 232-240, 1992.

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(Feng-Hsiag Hsiao、Wei-Ling Chiang)審核日期2004-6-10 推文facebook plurk twitter funp google live udn HD myshare reddit netvibes friend youpush delicious baidu 網路書籤Google bookmarks del.icio.us hemidemi myshare