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研究生：	王彥博 Wang, Yen-Po
論文名稱：	多軸運動之耦合效應補償：以定位平台之追蹤與水平校準為例 The Compensation for Coupling-effect in Multi-axis Motion: a Tracking and Levelling Example with Positioning Stages
指導教授：	田思齊 Tien, Szu-Chi
學位類別：	碩士 Master
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
論文出版年：	2012
畢業學年度：	100
語文別：	英文
論文頁數：	86
中文關鍵詞：	耦合效應補償、前饋控制、H∞回授控制、疊代控制
外文關鍵詞：	Coupling-effect compensation, Feedforward control, H∞ feedback control, Iterative control
相關次數：	點閱：116 下載：2
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本論文的主要研究目的在於補償多軸運動平台之耦合效應。由於多軸運動平台包含了耦合效應，各個自由度的運動會互相干涉與影響，此現象造成了多軸運動平台之定位誤差。因此，本論文以三軸定位平台為例，提出控制方法補償耦合效應並達到x-y平面之運動追蹤與z軸平面之水平校準。除了利用逆向Preisach模
型前饋控制改善x-y平面運動之非線性遲滯效應，最佳化前饋控制與H∞回授控制更用來補償因x-y平面運動之耦合效應造成之振動問題；此外，基於逆向運動學之疊代控制用於克服定位平台之z軸運動耦合效應並達到z軸平面之水平校準。實驗結果證明，逆向Preisach模型前饋控制、最佳化前饋控制與H∞回授控制及基於
逆向運動學之疊代控制能有效補償耦合效應並達到此三軸定位平台之精密追蹤與水平校準。

The purpose of this thesis is to compensate for the coupling-effect in multi-axis motion. Coupling-effect typically exists in multi-axis positioning stages, and motion of each degree-of-freedom will affect each other and results in positioning errors by the proposed control methods. Therefore, this thesis demonstrates x-y plane tracking and z-axis levelling with a three-axis positioning stage. In particular, the inverse Preisach model feedforward control is used to reduce nonlinearity of hysteresis effect in x- and y-axis axes. Moreover, optimal inversion-based feedforward control and H1 feedback control are used to compensate for the vibration resulted from the coupling-effect. Furthermore, inverse-kinematics based iterative control is implemented to compensate for the coupling-effect in z-axis motion and the parallelism control is achieved. Experiment results show that the proposed control methods can compensate for the coupling-effect and improve the tracking and levelling performance.

TABLE OF CONTENTS
Page
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Challenges of Precision Positioning Control on Piezo-based Positioning
Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Bad Effects of Piezo-actuators on Precision Positioning . . . . . . 2
1.2 Dynamic Coupling-effect in Multi-axis Motion . . . . . . . . . . . . . . . . 3
1.3 Parallelism Issue of Two Platforms . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Control Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4.1 Compensation for Bad Effects of Piezo-actuators . . . . . . . . . . 4
1.4.2 Compensation for Dynamic Coupling-effect in Multi-axis Motion . 5
1.4.3 Parallelism Control of Two Platforms . . . . . . . . . . . . . . . . 6
1.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Chapter 2: Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Coupling-effects in Dual-axis Piezo-stage . . . . . . . . . . . . . . . . . . . 7
2.2 Parallelism between Two Platforms . . . . . . . . . . . . . . . . . . . . . . 7
Chapter 3: Mechanical Design of Positioning Stages . . . . . . . . . . . . . . . 10
3.1 Dual-axis Piezo-stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Levelling System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Chapter 4: Control Scheme and Simulation Results . . . . . . . . . . . . . . . 17
4.1 Modeling of the Dual-axis Piezo-stage . . . . . . . . . . . . . . . . . . . . 18
4.2 Compensation for Hysteresis of Piezo-actuators . . . . . . . . . . . . . . . 20
4.3 Compensation for the Dynamic Coupling-effect in the Dual-axis Piezo-stage 20
4.3.1 Optimal Inversion-based Feedforward Control . . . . . . . . . . . . 22
4.3.2 H∞ Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4 Parallelism Control of Two Platforms . . . . . . . . . . . . . . . . . . . . 44
4.4.1 Kinematics and Inverse Kinematics . . . . . . . . . . . . . . . . . . 44
4.4.2 Iterative Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
i
Chapter 5: Experiment Results and Discussions . . . . . . . . . . . . . . . . . 50
5.1 Experiment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2 Experiment Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.1 Hysteresis Effect Compensation . . . . . . . . . . . . . . . . . . . . 54
5.2.2 Dynamic Coupling-effect Compensation . . . . . . . . . . . . . . . 54
5.2.3 Parallelism Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3.1 Coupling-effect in Dual-axis Piezo-stage . . . . . . . . . . . . . . . 64
5.3.2 Coupling-effect in Parallelism Control . . . . . . . . . . . . . . . . 64
Chapter 6: Conclusion and Further work . . . . . . . . . . . . . . . . . . . . . 68
6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.1.1 Tracking with dual-axis piezo-stage . . . . . . . . . . . . . . . . . . 68
6.1.2 Parallelism control with levelling system . . . . . . . . . . . . . . . 68
6.2 Further work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Appendix A: Circuit diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
A.1 Signal conditioner for sensors . . . . . . . . . . . . . . . . . . . . . . . . . 73
A.2 Signal conditioner for controllers . . . . . . . . . . . . . . . . . . . . . . . 78
Appendix B: Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Appendix C: Engineering Drawing . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Appendix D: H∞ controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

                                    

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校內：2014-07-09公開
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