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。

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.

Machines with Friction,” Automatica, Vol. 30, No. 7, pp. 1083-1138.
[2]. Swevers J., Al-Bender F., Ganseman C. G. and Prajogo T., 2000, "An
Integrated Friction Model Structure with Improved Presliding Behavior for
Accurate Friction Compensation," IEEE Trans. on Automatic Control, Vol. 45,
No. 4, pp. 675-686.
[3]. Canudas de Wit C. and Lischinsky P., 1997, “Adaptive Friction Compensation
with Partially Known Dynamic Friction Model,” International Journal of
Adaptive Control and Signal Processing, Vol. II, pp. 65-80.
[4]. Chen, Y. Y., Huang, P. Y. and Yen, J. Y., 2002, “Frequency-Domain
Identification Algorithms for Servo Systems With Friction,” IEEE Transactions
on Control Systems Technology, Vol. 10, No. 5, pp. 654-665.
[5]. Tung, Pi-Cheng., and Cheng, S. C., 1993, “Experimental and Analytical Studies of the Sinusoidal Dither Signal in a DC Motor System,” Dynamics and Control, Vol. 3, pp. 53-69.
[6]. Canudas de Wit, C., Olsson H., Åström K. and Lischinsky, P., 1995, "A New
Model for Control of Systems with Friction," IEEE Trans. on Automatic Control, Vol. 40, No. 3, pp. 419-425.
[7]. Bliman, P. A., and Sorine, M., 1995, “Easy-to-use realistic dry friction models for automatic control,” Proceedings of 3rd European Control Conference, Rome, Italy, pp 3788-3794.
[8]. Threlfall, D. C., “The Inclusion of Coulomb Friction in Mechanisms Programs with Particular Reference to DRAM,” Mechanism and Machine Theory, Vol.
13, No. 4 (1978), pp475-483.
[9]. Rooney, G. T. and Deravi, P., “Coulomb Friction in Mechanism Sliding
Joints,” Mechanism and Machine Theory, Vol. 17, No. 3 (1982), pp. 207-211.
[10]. Begley, C. J. and Virgin, L. N., “A Detailed Study of the Low-Frequency
Periodic Behavior of a Dry Friction Oscillator,” ASME J. of Dynamic Systems,
Measurement and Control, Vol. 119 (1997), pp. 491-497.
[11]. Karnopp, D., 1985, “Computer Simulation of Slip-Stick Friction in Mechanical Dynamic Systems,” ASME J. of Dynamic Systems, Measurement and Control, Vol. 107, pp. 100-103.
[12]. Cheok, K. C., Hu, H. and Loh, N. K., 1988, “Modeling and Identification of a Class of Servomechanism Systems With Stick-Slip Friction,” ASME J. of
Dynamic Systems, Measurement and Control, Vol. 110, pp. 324-328.
[13]. Younkin, G. W., 1991, “Modeling Machine Tool Feed Servo Drivers Using
Simulation Techniques to Predict Performance,” IEEE Trans. on Industry
Applications, Vol. 27, No. 2, pp. 268-274.
[14]. Johnson, C. T. and Lorenz, R. D., 1992, “Experimental Identification of
Friction and Its Compensation in Precise, Position Controlled Mechanisms,”
IEEE Trans. on Industry Applications, Vol. 28, No. 6, pp. 1392-1398.
[15]. Sepehri, N., Sassani, F., Lawrence, P. D., and Ghasempoor, A., 1996,
“Simulation and Experimental Studies of Gear Backlash and Stick-Slip Friction
in Hydraulic Excavator Swing Motion,” ASME J. of Dynamic Systems, Measurement and Control, Vol. 118, pp. 463-467.
[16]. Tan, X. and Rogers, R. J., 1998, “Simulation of Friction in
Multi-Degree-of-Freedom Vibration Systems,” ASME J. of Dynamic Systems,
Measurement and Control, Vol. 120, pp. 144-146.
[17]. Huang, S. J., Yen, J. Y., and Lu, S. S., 1999, “Dual Mode control of a System with Friction,” IEEE Trans. on Control Systems Technology, Vol. 7, No. 3, pp. 306-314.
[18]. Haessig, D. A. and Friedland, B., 1991, “On the Modeling and Simulation of Friction,” ASME J. of Dynamic Systems, Measurement and Control, Vol. 113,
pp. 345-362.
[19]. Dahl, P. R., 1977, “Measurement of Solid Friction Parameters of Ball
Bearings,” Proc. of 6th Annual Symp. On Incremental Motion, Control Systems
and Devices, University of Illinois, ILO.
[20]. Bonsignore A., Ferretti G. and Magnani G., 1999, “Analytical Formulation of the Classical Friction Model for Motion Analysis and Simulation,”
Mathematical and Computer Modelling of Dynamical Systems, Vol. 5, No. 1,
pp. 43-54.
[21]. Bo, L. C. and Pavelescu, D., 1982, “The Friction-Speed Relation and Its
Influence on the Critical Velocity of Stick-Slip Motion,” Wear, Vol. 82, pp.
277-289.
[22]. Armstrong-Hélouvry, B., 1993, Control of Machines with Friction. Norwell,
MA: Kluwer.
[23]. Yang, S., and Tomizuka, M., 1988, “Adaptive Pulse Width Control for Precise Pointing Under the Influence of Stiction and Coulomb Friction,” ASME J. of Dynamic Systems, Measurement and Control, Vol. 110, pp. 221-227.
[24]. Du, H., and Nair, S. S., 1999, “Modeling and Compensation of Low-Velocity
Friction with Bounds,” IEEE Trans. on Control Systems Technology, Vol. 7,
No. 1, pp. 110-121.
[25]. Klamecki, B. E., 1985, “A Catastrophe Theory Description of Slip-Stick
Motion in Sliding,” Wear, Vol. 101, pp. 325-332.
[26]. Futami, S., Furutani, A. and Yoshida, S., 1990, “Nanometer Positioning and Its Micro-Dynamics,” Nanotechnology, Vol. 1, No. 1, pp. 31-37.
[27]. Ro, P. I. and Hubbel, P. I., 1993, “Model Reference Adaptive Control of
Dual-Mode Micro/Macro Dynamics of Ball Screws for Nanometer Motion,”
ASME J. of Dynamic Systems, Measurement and Control, Vol. 115, pp.
103-108.
[28]. Yang, Y. P. and Chu, J. S., 1993, “Adaptive Velocity Control of DC Motors
With Coulomb Friction Identification,” ASME J. of Dynamic Systems, Measurement and Control, Vol. 115, pp. 95-102.
[29]. Radcliffe, C. J. and Southward, S. C., 1990, “A Property of Stick-Slip Friction Models Which Promotes Limit Cycle Generation,” Proc. 1990 American
Control Conference, ACC, San Diego, CA, pp. 1198-1203.
[30]. Brandenburg, G. and Schäfer, U., 1991, “Influence and Compensation of
Coulomb Friction in Industrial Pointing and Tracking Systems,” Proc. of the
Indus. App. Soc. Annual Meeting, IEEE, Dearborn, MI, pp. 1407-1413.
[31]. Osborn, N. A. and Rittenhouse, D. L., 1974, “The Modeling of Friction and Its Effects on Fine Pointing Control,” AIAA Mechanics and Control of Flight
Conference, Paper 74-875, Aug. 1974.
[32]. Merritt, H. E., 1966, Hydraulic Control Systems, John Wiley & Sons, Inc.
[33]. Johnson, K. L., 1987, Contact Mechanics. Cambridge University Press,
Cambridge.
[34]. Olsson, H., Åström, K. J., and Canudas de Wit, C., Gafvert, M., and Lischinsky, P., 1998, “Friction models and friction compensation,” European Journal on Control, Dec. 1998, No.4, pp.176-195
[35]. Lin, Ting-Yung, 2000, Fast Precision-Limit Positioning Compensation of the
Creep Motion in Presliding Phase, PhD thesis, Department of Aeronautics and
Astronautics, National Cheng Kung University, Taiwan, R.O.C.
[36]. Dupont, P., Hayward, V., Armstrong, B. and Altpeter, F., 2002, “Single State Elasto-Plastic Friction Models,” IEEE Trans. on Automatic Control, Vol. 47, No. 5, pp. 787-792.
[37]. Canudas de Wit, C., Noël, P., Aubin, A., and Brogliato, B., 1991, “Adaptive Friction Compensation in Robot Manipulators: Low Velocities,” The Inter. J. of Robotics Research, Vol. 10, No. 3, pp189-199.
[38]. Canudas de Wit, C., Astrom, K. J., and Braun, K., 1987, “Adaptive Friction Compensation in DC-Motor Drives,” IEEE J. of Robotics and Automation,
RA-3, No. 6, pp681-685.
[39]. Southward, S. C., Radcliffe, C. J. and MacCluer, C. R., 1991, “Robust
Nonlinear Stick-Slip Friction Compensation,” ASME J. of Dynamic Systems,
Measurement and Control, Vol. 113, pp. 639-645.
[40]. Guzzella, L. and Glattfelder, A. H., 1992, “Pointing of Stick-Slip Systems Comparison of a Conventional and a Variable-Structure Controller Design,” Proc. 1992 American Control Conference, Vol. Wp13, pp. 1277-1281.
[41]. Kim, J. H., Chae, H. K., Jeon, J. Y. and Lee, S. W., 1996, “Identification and Control of Systems with Friction Using Accelerated Evolutionary Programming,” IEEE Trans. on Control Systems, Vol. 16, No. 4, pp. 38-47.
[42]. Popovic, M. R., Gorinevsky, D. M., and Goldenberg, A. A., 1995, “Fuzzy
Logic Controller for Accurate Pointing of Direct-Drive Mechanism Using
Force Pulses,” IEEE International Conference on Robotics and Automation, pp.
1166-1171.
[43]. De Weerth, S. P., Nielsen, L, Mead, C. A., and Åström, K. J., 1991, “A simple neuron servo,” IEEE Trans. on Neural Networks, Vol. 2, No. 2, pp. 248-251.
[44]. Hojjat, Y. and Higuchi, T., 1991, “Application of Electromagnetic Impulsive Force to Precise Positioning,” International Journal of Japan Society, Precision Engineering, Vol. 25, No. 1, pp39-44.
[45]. Ruh-Hua Wu and Tung, Pi-Cheng, 2002, “Studies of Stick-Slip Friction,
Presliding Displacement and Hunting,” ASME J. of Dynamic Systems, Measurement and Control, Vol. 124, pp. 111-117.
[46]. Lin, Kwan-Chen, 2002, Sliding Mode Controller of High Precision Positioning Control, Master thesis, Department of Aeronautics and Astronautics, National Cheng Kung University, Taiwan, R.O.C.
[47]. Polycarpou, A. and Soom, A., 1992, “Transitions between Sticking and
Slipping, in Friction-Induced Vibration, Chatter, Squeal, and Chaos,” Proc.
ASME Winter Annual Meeting, New York: ASME, Volume DE-Vol. 49, pp.
139-148.