臺灣博碩士論文加值系統

在研究與設計撓性結構時，機械的結構振動是一個重要的研究主題。本文之目的在於應用線性二次調節器的最佳化性能指數於移動在一有或無初始撓度樑的運動質量之暫態與動態控制，並分析以三個分散式制動器所建構之閉迴路回授控制模式於運動質量與樑系統之動態響應與動態控制情形。
基於尤拉-柏努力樑理論與牛頓力學，得到一個結合閉迴路回授控制的非線性耦合運動方程式。由電腦模擬結果顯示，雖然變動某些物理參數，如質量比、質量的初始速度和樑的初始撓度…等，但若有適當的調節器設計就可以使加入的控制器之控制效能還是能有效的維持系統的穩定。所以在本文中雖然使用一個簡單的控制方法，但是對於系統的振動卻能達到良好的抑制效果。

關鍵字： 運動質量與樑系統，撓性結構體，主動式最佳化控制

Mechanical vibration is an important topic in the study and design of flexible structures. The objective of this thesis is to study the dynamics and control of an attached mass rolling on with or without initially curved beam based on a simplified control model. The transient dynamics of system and the optimization of the performance index of linear quadratic regulator (LQR) are considered. Three discrete actuators are placed along the beam that provides the necessary forces to control the response of the beam-mass system.
Based on Euler-Bernoulli beam theory and Newtonian mechanics, the coupled non-linear equations of motion combining with a simple closed-loop feedback control are obtained.
Results of computer simulation show that with appropriate regulator design, although the variation of certain physical parameters, such as the mass ratio, the initial speed of mass and initially curved of beam, excellent control performance of the introduced control system is still maintained. Therefore, the vibration of the system can be suppressed significantly even if a simplified control model is applied.

Keyword： beam-mass system, flexible structures, active optimal control

Abstract (Chinese) I
Abstract (English) II
Acknowledge III
Contents IV
Figure Contents VII
Index Notation XI

Chapter 1 Introduction 1
1-1 Background and Motivation 1
1-2 Literature Survey 3
1-3 Organization 5
Chapter 2 Equation of Motion of Beam-Mass System 7
2-1 Basic Formulas of A Beam-Mass System without initial curvature 7
2-1-1 Boundary-Value and Control Forces Problem of A Beam-Mass System 11
2-1-2 The Approximate Solution of A Beam-Mass System 12
2-2 Basic Formulas of A Beam-Mass System with initial curvature 16
2-2-1 Boundary-Value and Control Forces Problem of A Beam-Mass System 20
2-2-2 The Approximate Solution of A Beam-Mass System 22
Chapter 3 Control Law Design 27
3-1 A Review of The Linear Quadratic Control 27
3-2 The Linear Quadratic Regulator Vibration Control Design 29
3-3 The Number of Actuators and the Placement of Actuators 34
Chapter 4 Numerical Results and Discussions 36
4-1 The Transient Dynamics of A Beam-Mass System 36
4-1-1 The Dynamic Responses of The System without Initial Curvature 36
4-1-2 The Dynamic Responses of The System with Initial Curvature 47
4-2 The Optimal LQR Vibration Control with A Beam-Mass System 51
4-2-1 The Control Responses of The System without Initial Curvature 51
4-2-2 The Control Responses of The System with Initial Curvature 59
Chapter 5 Conclusions 63
5-1 Summary 63
5-2 Recommendations for Future Work 63
Bibliography 64
Publications 68

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