有限行程下的線性致動器參數估測與快速定位控制之穩定性研究

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姓名

李永瑤(Yun-Yao Lee) 查詢紙本館藏

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電機工程學系

論文名稱

有限行程下的線性致動器參數估測與快速定位控制之穩定性研究
(Identification of Linear Actuators within Limited Stroke and Stability Analysis on Fast-Pointing Systems)

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摘要(中)

本論文主要研究致動器在不同負載下的動態行為。首先推導致動器外接不同負載時的運動方程式，本文發展出獨特的模組式架構，將負載與致動器分離，使致動器在外接不同負載時完全不需要修改致動器本身的運動方程式，而以負載抗力作為致動器與負載之間的連結。所得到的運動方程式簡潔，極易轉換成系統或模擬所需的方塊圖，但最大的好處為，致動器或負載本身所含的非線性可個別鑑別，不需面對複雜而有行程限制的致動器與負載系統。
繼而提出致動器在無外加負載下的鑑別程序。本文提出一種新的鑑別方式，可在有限行程中鑑別致動器的阻尼、庫倫摩擦，以及系統轉動慣量等三大參數，其中轉動慣量的鑑別特別考慮到庫倫摩擦影響，並提出模擬與實驗結果，證實本方法的有效與正確性。
在建立制動器之參數鑑別後，繼續討論致動器與負載連結時，系統整體機械效率(hm)的鑑別方式。本文將與外力成正比的摩擦以機械效率來建模，詳細推導hm對系統運動方程式的影響，並提出hm 與致動器內部庫倫摩擦的鑑別方式。並提出實驗結果與理論模型比較，理論分析的正確性。
另外針對線性致動器中常見的非線性元素，特別是摩擦引起的死域(dead zone)非線性以及任意的非線性增益(nonlinear gain)，再提出一種補償方式。本文利用非線性增益調整(nonlinear gain compensation)方式，針對非線性的特性曲線，設計一前置補償器，先行調整依照線性模型設計的控制器產生的控制量，此調整過的控
制量經功率放大器放大後驅動致動器，雖同樣受致動器非線性影響而減損部分訊號強度，但因已經事先做過適當放大補償，致動器實際輸出結果會如線性模型所預期。
最後以一個針對線性致動器精密定位系統的三階段非線性PPR (Proportional,Pulse, Ramp)控制器的穩定性提出證明。此PPR 控制器於2004 年提出，以簡單的控制法則，克服致動器的摩擦、背隙、死域等非線性，快速達成精度1 μm 的定位控制。此控制器性能雖優異，但其穩定性證明尚未於期刊中正式提出。本文除以Lyapunov 方法證明PPR 的穩定性之外，並深入分析斜坡控制的穩定性。

摘要(英)

In this Dissertation, studies on actuators connected to various types of load are investigated, particularly on the topics of modeling, identification, compensation, controller design, and stability analysis. First we present a systematic approach to construct the equations of motion for various load types driven by a linear actuator. In this approach, the equations of motion for the actuator and the load are separated which enables the reader to derive the equations of motion of various types of load without being coupled with those of the linear actuator.
Next, we present a novel method for estimating the parameters of electro-mechanical systems, or known as actuators, within limited stroke. A sequence of pulses with various levels is designed to estimate the viscous damping coefficient and the Coulomb friction torque within the limited stroke of the actuator. Then an optimal algorithm based on the interior-reflective Newton method is applied to search the moment of inertia of the overall system.
We also examine the effect of mechanical efficiency on the performance of the actuator. In our research, we derive the equations of motion involving the mechanical efficiency hm and describe the procedure to estimate this important parameter of the actuator when connected to various types of load. To the best of the authors’knowledge, this topic has not been published in current research.
As regards the compensation for nonlinear elements inherent in the linear actuator,a novel approach to linearize such nonlinearities is proposed. This approach solves the inverse of the nonlinearity without requiring its I/O relations as a one-on-one map, which is necessary for the current inverse-model method.
Finally, we investigate the stability of a newly proposed ultra precise fasting pointing controller. This research investigates the sufficient stability condition of a
three-phase (proportional gain, pulse, and ramp, PPR) controller for pointing systems under the influence of friction. With the ramp and pulse schemes integrated, the PPR controller has been demonstrated to be an effective control strategy for fast and precise pointing applications. The Lyapunov direct method is applied to prove the stability of the PPR controller.

關鍵字(中)

★ 運動方程式
★ 非線性
★ 摩擦
★ 可動噴嘴
★ 倒單擺
★ 致動器
★ 系統鑑別

關鍵字(英)

★ friction
★ nonlinear systems
★ pointing control
★ stick-slip
★ simulation
★ modeling
★ identification

論文目次

Contents
摘要 i
Abstract ii
List of Figures vii
List of Tables x
List of Symbols xi
Chapter 1. Introduction 1
1.1. Background and Motivation 1
1.2. Objectives of This Dissertation 2
1.3. Organization of This Dissertation 2
1.4. Contribution of Studies in This Dissertation 4
Chapter 2. Modeling of Actuators with Various Load Types 5
2.1. Introduction 5
2.2. Schematic Diagram of the Linear Actuator 5
2.3. Equations of Motion for the Linear Actuator 6
2.3.1. Definition of the Gear Reduction Ratio 6
2.3.2. Equations from Motor to Ball Screw 8
2.3.3. Equations from Load to Motor 10
2.4. Reactance FL from Various Load Types 11
2.4.1. Rigid Linear Load 1: Spring 11
2.4.2. Rigid Linear Load 2: Ball-Screw-Driven Table 13
2.4.3. Rigid Rotational Load 1: Nozzle 14
2.4.4. Rigid Rotational Load 2: Gear Rotor 18
2.4.5. Rigid Rotational Load 3: Fork Rotor 19
2.4.6. Nozzle with Flexible Bolt Connection 24
2.4.7. Nozzle with Flexible Vertical Structure 26
2.5. Conclusions for This Chapter 33
Chapter 3. Identification of Actuators within Limited Stroke 34
3.1. Introduction 34
3.2. System Model and Experimental Setup 36
3.3. Procedure for Identifying Dmeq and Tf 37
3.4. Identifying Jmeq by ARX Model 41
3.5. Identifying Jmeq by Optimal Searching Algorithm 43
3.6. Simulation and Experimental Results 44
3.6.1. Friction Model for Simulation 44
3.6.2. Velocity Estimating Method 45
3.6.3. Simulation in Ideal Case 47
3.6.4. Simulation with Quantization Error 50
3.6.5. Simulation with Quantization Error and Random Noise 52
3.6.6. Experimental Evaluations 55
3.7. Conclusions of This Chapter 60
Chapter 4. Evaluation of Mechanical Efficiency of Actuators 62
4.1. Introduction 62
4.2. Friction and Mechanical Efficiency 62
4.2.1. Reactance FL and ηm 63
4.2.2. Internal Coulomb Friction and ηm 66
4.3. Equations of Motion Including ηm 70
4.4. Equations of Motion Including ηm and Fc 72
4.5. Equations of Motion for Servo Motors 73
4.6. Evaluation of ηm 74
4.6.1. Procedure for Evaluating ηm 75
4.6.2. Experiments for Evaluating ηm 78
4.7. Conclusions of This Chapter 80
Chapter 5. Compensation and Control for Dither Smoothed Nonlinearities 81
5.1. Introduction 81
5.2. The Dither-Smoothing Technology 82
5.3. The Proposed β-Compensation Algorithm 87
5.4. Numerical Examples 91
5.4.1. Arbitrary Gain Assignment 91
5.4.2. A Nonlinear Unstable System 94
5.5. Experimental Evaluations 98
5.6. Conclusions of This Chapter 102
Chapter 6. Ramp-Controlled Ultra Precise Pointing System 103
6.1. Introduction 103
6.2. Properties of Friction and Presliding 104
6.2.1. Some Explored Properties of Friction 104
6.2.2. Presliding Displacement of Static Friction 105
6.3. The PPR Controller 106
6.3.1. Principle of the PPR Controller 106
6.3.2. Region 0: Proportional Control 108
6.3.3. Region I: Pulse Control 109
6.3.4. Region II: Ramp Control 111
6.3.5. Design of Region III: the Target Region 115
6.3.6. PPR vs. PID, PI, and P Controllers 116
6.4. Stability Proof 118
6.4.1. Region 0: Proportional Control 118
6.4.2. Region I: Pulse Control 119
6.4.3. Region II: Ramp Control 121
6.4.4. Region III: the Target Region 123
6.5. Conclusions of This Chapter 123
Chapter 7. Discussions and Further Research 124
References 127
List of Publications 131
Journal Published in 2006-2009 131

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End of this Dissertation.

指導教授

徐國鎧(Kuo-Kai Shyu)

審核日期

2009-8-24

推文