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研究生：	林冠禎 Lin, Kuan-Chen
論文名稱：	具摩擦效應之二維平台輪廓控制 Contour Control of a Two-Dimensional Stage System with Friction
指導教授：	陳介力 Chen, Chieh-Li
學位類別：	博士 Doctor
系所名稱：	工學院 - 航空太空工程學系 Department of Aeronautics & Astronautics
論文出版年：	2006
畢業學年度：	94
語文別：	英文
論文頁數：	169
中文關鍵詞：	輪廓控制、摩擦力補償、滑動摩擦、預滑動摩擦、輸出回授
外文關鍵詞：	contour control, friction compensation, sliding friction regime, presliding friction regime, output feedback
相關次數：	點閱：152 下載：3
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　　輪廓控制問題實際上是由平台中各軸同時的運動行為所構成，本身即為一個相當活躍的研究領域。控制的目標在於對各種不同要求的輪廓形狀皆可有效地壓制系統軌跡與輪廓形狀之間的幾何誤差，統稱為輪廓誤差或輪廓精度。若考量實際平台系統的運動行為，即可發現存在於各軸的摩擦力不單單影響軸本身的運動精度表現，同時也會對整體的輪廓精度產生相當複雜的影響。因此本研究不僅只探討輪廓控制問題，同時還將摩擦力行為與其對應的控制補償問題一併納入討論。將輪廓誤差與摩擦力數學模型統整分析之後，包含摩擦力補償的輪廓控制器設計問題就被轉化成兩組完整的數學陳述。為了能讓所提出的設計結果切合實際的應用需求，本研究僅對輸出回授型的控制器設計問題進行討論。針對這兩組不同的數學陳述，透過理論分析架構，結果共提出了五種不同的新設計方法。透過固定追蹤圓形與直線這兩種不同幾何形狀的數值模擬結果，得到了與理論分析的一致性，進而展現了這五種設計在遭遇摩擦力下的輪廓控制問題的可行性。

　By the primitive definition, the contour error is a pure geometric quantity, which is not related to time, this makes the contour control design hard to proceed. The use of the contour error model entrusts a dynamic flavor to the contour control problem. Also, based on the varieties in frictional characteristics, the friction behaviour is divided into the sliding friction regime and the presliding friction regime. The contour control problem can be mathematically formulated for both regimes respectively. In this thesis, only output feedback type designs are considered. Five design approaches were proposed based on the different structures of models. Among these five approaches, one for the presliding friction model based design (PFMBD); three for the sliding friction model based designs (SFMBDs); and the other is dedicated for general multi-input multi-output linear systems. The last approach can also be applied to solve the problems of PFMBD and SFMBD. It is concluded that theoretical analysis and numerical results are consistent, which provides a feasible approaches to practical contour control problems.

ABSTRACT IN CHINESE                                                           i
ABSTRACT                                                                   viii
ACKNOWLEDGEMENTS                                                             ix
CONTENTS                                                                      x
LIST OF TABLES                                                              xiv
LIST OF FIGURES                                                              xv
NOMENCLATURE                                                                xix

CHAPTER
I. INTRODUCTION                                                               1
    1.1 Motivation                                                            1
    1.2 Literature Review                                                     2
        1.2.1 Review of Contour Control                                       2
        1.2.2 Review of Friction Modeling                                     5
    1.3 Thesis Outline                                                        7
II. MATHEMATICAL FORMULATIONS IN CONTOUR CONTROL AND FRICTION MODELING        9
    2.1 Contour Error Model for 2-D Case                                      9
    2.2 The Cross Coupled Control Approach                                   12
    2.3 The Task Coordinate Approach                                         15
        2.3.1 Derivation of Task Coordinate                                  15
        2.3.2 Application to Contour Control Problem                         18
    2.4 The Polar Coordinate Approach                                        21
        2.4.1 Derivation of Polar Coordinate                                 21
        2.4.2 Application to Contour Control Problem                         22
    2.5 Modeling Friction in the Sliding Regime                              26
        2.5.1 The Sliding Friction Model                                     26
        2.5.2 Parameter Identification                                       28
    2.6 Modeling Friction in the Presliding Regime                           31
        2.6.1 The Presliding Friction Model                                  31
        2.6.2 Rules of Reverse Points                                        35
        2.6.3 Parameter Identification                                       36
    2.7 Summary                                                              39
III. SLIDING FRICTION MODEL BASED CONTOUR CONTROLLER DESIGNS		    51
    3.1 Task Coordinate for 2-D Contours                                     51
    3.2 Stage System Dynamics in the Task Coordinate                         53
    3.3 Contour Controller Design Using Position Information Only            57
        3.3.1 The Design of State Observer                                   58
        3.3.2 Contour Controller Design Based on Observed States	    61
    3.4 Contour Controller Design Using Position and Velocity Information	    64
    3.5 Robust Design to Parametric Uncertainties                            68
    3.6 Numerical Examples and Numerical Simulations                         73
        3.6.1 Interpolations of the Test Contours                            73
        3.6.2 Simulation Results and Discussions                             76
IV. PRESLIDING FRICTION MODEL BASED CONTOUR CONTROLLER DESIGN               101
    4.1 Introduction                                                        101
    4.2 Derivation of the Output Dynamics from the Presliding Friction Model	                                                                   102
    4.3 Contour Controller Design Based on Output Dynamics                  104
    4.4 Robustness to Parametric Uncertainties                              108
    4.5 Design Examples and Numerical Simulations                           109

V. CHATTERING-FREE OUTPUT FEEDBACK SMC FOR MIMO LINEAR SYSTEM SUBJECTED TO INPUT DISTURBANCES                                                          122
    5.1 Introduction                                                        123
    5.2 Problem Formulation                                                 124
        5.2.1 Design Based on Output Dynamics                               125
        5.2.2 MIMO System Formulation                                       126
    5.3 Main Results                                                        129
        5.3.1 Design of Sliding Surface                                     130
        5.3.2 The Controller Synthesis                                      132
        5.3.3 Controller in Original Coordinate                             135
    5.4 Numerical Study                                                     136
    5.5 Application to the Sliding Friction Model Based Contour Control 
        Problem                                                             137
        5.5.1 Controller Design Procedure                                   138
        5.5.2 Simulation Results                                            141
    5.6 Application to the Presliding Friction Model Based Contour Control
        Problem                                                             142
        5.6.1 Controller Design Procedure                                   143
        5.6.2 Simulation Results                                            145
VI. Conclusions                                                             159
    6.1 Discussions and Conclusions                                         159
    6.2 Suggestions for Future Researches                                   161

REFERENCES                                                                  163
PUBLICATION LIST                                                            168
VITA                                                                        169
                                    

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