臺灣博碩士論文加值系統

本文研究如何精密控制一個受摩擦非線性影響下的直線馬達驅動運動系統。此系統受摩擦力以及 cogging force 的影響。摩擦力採用具動態之 LuGre 模型來預估，而cogging force 以數個弦波函數的組合來表示。
研究中發現 LuGre 模型需要局部修改才能符合摩擦力在起動區與換向區之不同。摩擦力模型中的參數以各種的實驗求出。而比較特別的是，在摩擦力與 cogging force 之干擾下，重要的系統參數如慣量、阻尼係數、庫倫摩擦力以及 cogging force 之模型參數等均可以用簡單的實驗來鑑別。最後的控制器設計可以使系統達到精密的追蹤與定位，模擬與實驗均得到一致的結論。以實驗來說，啟動區之誤差可小於4微米，而最後的定位精度在0.02微米。

This paper studies how to control a linear-motor-driven motion system under the effect of nonlinear friction. In addition, the cogging force is another disturbance source to this system. The friction is compensated by the estimated force from the LuGre friction model; while the cogging force is compensated by the model formed by several sinusoidal functions.
The LuGre model is needed to be modified so as to match both the friction phenomena in the motion-start region and the motion-reverse region. The friction phenomena between these two regions are different. Various parameters of the friction model are obtained by several different experiments. Specially, although the friction and cogging force exist in the same time while the table is in motion, those important system parameters, such as the inertia, the damping ratio, the Coulomb friction, and the parameters of cogging force model are obtained by very simple experiments. Finally, the controller proposed in this paper can let the system achieve precision control both in tracking and positioning. Simulations and experiments show the same conclusion. We can see from the experiment results that the maximum error occurs at the motion-start region is less then 4 micrometer, and the final positioning error is 0.02 micrometer.

TABLE OF CONTENTS
LIST OF FIGURES vi
LIST OF TABLES xii
CHAPTER 1 GENERAL INTRODUCTION 1
CHAPTER 2 SURVEY ON IDENTIFICATION OF FRICTION MODEL AND CONTROL
METHODS 5
2.1 Introduction 5
2.2 Static Models 7
2.3 Dynamic Models 8
2.4 Parameter Estimation 12
2.5 Friction Compensation 17
2.5.1 Stiff PD Control 18
2.5.2 Integral Control 19
2.5.3 Dither Signal 20
2.5.4 Joint Torque Control 20
2.5.5 Impulse Control 22
2.5.6 Disturbance observer (DOB) 22
2.5.7 Repetitive Control 23
2.5.8 Extended Kalman-Bucy filter (EKBF) 23
2.5.9 Learning Feed-forward/Feedback Compensation 25
2.6 Model-based Compensation for Friction 26
2.6.1 Direct Feed-forward/Feedback Compensation 27
2.6.2 Friction Observers 30
2.6.3 Adaptive Control 32
2.6.4 Dual Mode Control 34
2.7 Future Trends 36
CHAPTER 3 SETUP OF EXPERIMENTAL SYSTEM 39
3.1 Hardware setup 39
3.2 Calibration of fiber optic laser encoder (RLE10) 39
3.3 Modeling of the linear-motor-driven system 42
CHAPTER 4 PARAMETER ESTIMATION OF FRICTION MODEL 45
4.1 The Dynamic LuGre model 45
4.2 Estimating the Coulomb and viscous friction parameters 46
4.3 Estimating the Stribeck velocity and maximum stick force 50
4.4 Estimating maximum stick force by break-away test 50
4.5 Iterative estimation of inertia, viscous coefficient and Coulomb friction 51
4.6 Estimating the bristle stiffness and damping coefficients 69
4.7 Comparison of Simulated and Experimental Results 71
4.8 Conclusions 77
CHAPTER 5 PARAMETER ESTIMATION OF THE COGGING FORCE MODEL 79
5.1 The cogging force model 79
5.2 The parameter estimation of cogging force model 81
5.3 Experiments study for the identification of cogging force and
system models 90
5.4 Validation of the identification method for system plant model 95
CHAPTER 6 CONTROLLER DESIGN 97
6.1 Disturbance observer design 98
6.2 Feedforward control 103
6.3 Velocity loop design 104
6.4 Position loop design 106
6.5 Comparison of the feedforward structures 108
6.6 Simulations of controlled system 112
6.6.1 Test commands 112
6.6.2 Control structures under testing and comparison 114
6.7 Experiments of various control structures 125
CHAPTER 7 CONCLUSIONS AND FUTURE WORKS 133
7.1 Conclusions 133
7.2 Future works 134
REFERENCE 135

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