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

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陳震武(Cheng-Wu Chen) 查詢紙本館藏

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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)

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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

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指導教授

蕭鳳翔、蔣偉寧
(Feng-Hsiag Hsiao、Wei-Ling Chiang)

審核日期

2004-6-10

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