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姓名 吳日華(Ruh-Hua Wu)  查詢紙本館藏   畢業系所 機械工程學系
論文名稱 摩擦力作用下的控制系統研究
(Studies on Control Systems with Friction)
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摘要(中) 摩擦為一般機構中普遍存在的非線性現象,本文研究控制系統受摩擦影響下的動態行為。本文首先研究此類系統在摩擦影響下的參數鑑別問題,提出對於轉動慣量、阻尼係數,以及動靜摩擦力等重要參數的估測方式。接著研究摩擦的數學模型,分析連續與不連續模型間的差異,並針對不連續模型提出創新的雙階段積分法,解決此模型在零速度時的數值問題,去除在Karnopp 方法中的零速度區間限
制。此外,利用雙階段式積分法,本文修正傳統庫倫摩擦模型,並依據修正模型探討摩擦對系統定位性能的影響。此研究發現,接觸面間因靜摩擦造成的順預滑位移(presliding displacement)會改變自激性抖動(hunting)的穩定性,並會在使用積分控制的系統中產生特有的慢動態行為,影響精密定位系統的性能甚巨。據此,本文提出三段式(比例、脈波,以及斜坡,PPR)控制器,其中斜坡控制為本文提出之獨特創新方式。PPR 控制器主要依據與摩擦相關的兩項數據設計:最大靜摩擦力與順預滑位移。此二者均無須精確估測,前者甚至容許達200%的變化。實驗證實,PPR 控制器僅以位置回授,可在0.3-0.7 秒間完成精度1 微米的定位控制,而一最佳調測的PID 控制器至少需3 秒以上。本文末以Lyapunov 理論證明PPR
控制器的穩定性。
摘要(英) Friction is inherent in mechanisms. In this dissertation we study the dynamics of
pointing systems involving conspicuous friction. First we develop a general method
for the identification of systems with friction. Then an analytic algorithm for
simulation of discontinuous friction model is presented. In the proposed algorithm we
remove the requirement of the zero-velocity region in the Karnopp-like method and
develop a two-stage integration algorithm to solve the differential equations involving
a discontinuity at zero velocity. A procedure to estimate the Stribeck velocity, which
specifies how the friction force decreases in the range of very low velocities, is also
presented. Next we study the influence of presliding displacement on hunting.
Through experimental and numerical evaluations, we found that presliding
displacement could affect the stability of hunting. Such displacement is also crucial
to the performance of high-accuracy pointing applications. With this observation, we
propose a modified Coulomb friction model to increase its accuracy in the sticking
regime. Finally a controller consisting of three schemes, proportional gain, pulse, and
ramp (PPR), is proposed to achieve precise and fast pointing control under the presence
of friction. Design of the PPR controller is based on two distinctive features of
friction, the varying sticking force and presliding displacement of contacts. The latter
is the main idea behind the ramp scheme to replace integration control, which induces
slow dynamics in the sticking state. Experimental results demonstrate the robustness
and effectiveness of the proposed controller. Stability investigated by the Lyapunov
theorem is given in this dissertation.
關鍵字(中) ★ 摩擦力
★ 非線性系統
★ 定位控制
★ 滯滑現象
★ 電腦模擬
★ 數學模型
★ 系統鑑別
關鍵字(英) ★ pointing control
★ stick-slip
★ simulation
★ nonlinear systems
★ friction
論文目次 摘要........................................................................ i
Abstract .................................................................. ii
Acknowledgement........................................................... iii
List of Figures ........................................................... iv
List of Tables............................................................ vii
Nomenclature ............................................................ viii
Chapter 1. Introduction .................................................... 1
1.1. Background and Motivation.............................................. 1
1.2. Objective of This Dissertation......................................... 2
1.3. Organization of This Dissertation ............................................................... 3
1.4. Contribution of Studies in This Dissertation................................................................ 4
Chapter 2. Identification of Systems with Friction.................................................................... 5
2.1. Outline of This Chapter................................................ 5
2.2. Setup of the Experimental System ...................................... 5
2.3. Identification of System Parameters ................................................................. 7
2.4. Estimate of Friction.................................................. 10
2.5. Backlash of the Mechanism............................................. 13
Chapter 3. An Analytic Algorithm for Simulation of Friction ............... 15
3.1. Outline of This Chapter............................................... 15
3.2. Introduction ..........................................................15
3.3. The Two-Stage Integrating Algorithm................................... 18
3.4. Friction Models in Simulation ........................................ 23
3.5. Simulation and Experimental Results .................................. 24
3.6. Conclusions of This Chapter........................................... 30
Chapter 4. Studies on Friction, Presliding Displacement, and Hunting ...... 31
4.1. Outline of This Chapter............................................... 31
4.2. Introduction ..........................................................31
4.3. Dead Zone, Hunting, and Presliding Displacement ...................... 33
4.4. Modification of the Coulomb Friction Model............................ 38
4.5. Experimental and Simulation Results .................................. 43
4.6. Conclusions of This Chapter........................................... 45
Chapter 5. Fast Pointing Control for Systems with Stick-Slip Friction...... 50
5.1. Outline of This Chapter............................................... 50
5.2. Introduction ..........................................................50
5.3. The PPR Controller ................................................... 52
5.3.1. Principle of the Proposed Controller................................ 52
5.3.2. Distinguish Between Sliding and Sticking Modes...................... 53
5.3.3. Region 0: The Proportional-Gain Scheme ............................. 55
5.3.4. Region I: The Pulse Control Scheme ................................. 56
5.3.5. Region II: The Ramp Control Scheme.................................. 59
5.3.5.1. Presliding Displacement............................................60
5.3.5.2. The Slope of the Ramp............................................. 62
5.3.6. Region III: The Target Region....................................... 63
5.4. Stability Issues of the PPR Controller................................ 64
5.4.1. Stability Investigation via an Engineering Viewpoint ............... 65
5.4.2. Stability Proof of Region 0......................................... 65
5.4.3. Stability Proof of Region I ........................................ 66
5.4.4. Stability Proof of Region II........................................ 68
5.4.5. Stability Proof of Region III....................................... 70
5.5. Experimental and Simulation Results .................................. 70
5.6. Conclusions of This Chapter........................................... 78
Chapter 6. Conclusions and Discussions .................................... 79
References ................................................................ 81
List of Publications............................................................... 85
Journal Paper Published in 2002-2004....................................... 85
Earlier Journal Paper ..................................................................... 85
Journal Paper Under Consideration.............................................................. 85
Conference Paper ..................................................................... 86
Book Chapter.................................................................... 86
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指導教授 董必正(Pi-Cheng Tung) 審核日期 2004-3-17
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