Hinf控制設計為一種系統化的控制器設計方法，只需建立對應的標準控制架構，再代入滿足成本函數最小化的不等式，即可求解出一組控制器。本論文是將多軸軌跡輪廓控制、力量和位置之切換控制及伺服動態剛性之設計等問題，利用混合靈敏度加權方法設計強健控制器，並經由特別建構的外加權函數選擇，使得混合靈敏度設計具有部分極點移位(pole placement)之功能。
多軸同動之輪廓控制的重點是著重在設計軸控制器，使得在操作頻率內滿足鬆弛性能準則，即增益為1、匹配之線性相位移，且各軸控制器之間為解耦合之控制架構。而軸控制器之設計是採用Hinf極點移位，使得整個閉迴路近似於二階之Bessel系統，以符合鬆弛性能準則(relaxed performance measure)之要求。
伺服系統之動態剛性設計是轉化為Hinf範數的最小化問題，利用工業上常用的PDFF控制架構，轉化為Hinf控制之標準控制架構，採用Hinf靈敏度設計法則，求得高等PDFF控制架構中所需之控制器。並以一設計實例說明高等PDFF控制器比不具動態的PDFF控制器有較好的動態剛性。
第三個主題是探討力量與位置控制器之切換問題，其非線性現象發生於力量與位置控制器之切換，及控制訊號受限制所發生的飽和現象。本研究採用兩步驟設計策略，即在不考慮飽和與切換的情況下，分別先設計對應的速度、力量與位置等之線性控制器，其中控制器設計是採用Hinf迴路整型法則。接著採用Hanus調整技術分別設計速度、力量與位置之AWCT補償器，使得整個閉伺服系統在飽和與控制器切換發生時，其訊號仍可維持較為平滑之特性。

The H¥ design provides a systematic procedure where a set of controllers can be derived by substituting the formulation of standard control configurations into cost functions. In this thesis, multi-axis contouring control, servo dynamic stiffness design and switching control between force and position controllers are handled based on the H¥ mixed sensitivity design, where a particular external weighting function is used as a mechanism for partial pole placement.
Contouring control of multi-axis coordination is to independently design the axial controller satisfying the requirement of the relaxed performance measure, i.e., unity gain and phase-matching over a bounded operating frequency range. Using the H¥ pole placement design, the transfer function of the closed-loop system is approximately equal to a second order Bessel system.
Design of dynamic stiffness can be treated as a problem of H¥ -norm minimization for transfer functions from load torque to position. The advanced PDFF control configuration, which has been implemented in industrial servo systems, can be translated into the standard H¥ control structure. The H¥ mixed sensitivity design procedure, based on the coprime factorization, is employed for deriving advanced PDFF controllers.
The third topic was concerned with the switching problem between position and force controllers. The non-linearities are encountered due to switching between position and force controllers, and the constraint on the torque signal to a motor drive. The so-called two-step design paradigm is employed, where the velocity, position and force controllers are first designed by ignoring control input non-linearities, followed by adding anti-windup conditioned transfer compensators using the Hanus conditioning technique to diminish the adverse effects from windup and switching.

摘要I
英文摘要II
誌謝III
目錄IV
圖目錄.VII
表目錄X
符號說明XI
第一章 前言1
1.1 研究動機1
1.2 文獻回顧3
1.3 研究目的6
1.4 論文架構8
第二章 H¥控制理論10
2.1 數學基礎10
2.2 Hinf控制器之解14
2.3 混合靈敏度設計22
第三章 兩軸輪廓控制27
3.1 鬆弛性能準則27
3.2 Hinf混合靈敏度設計31
3.3 軸控制器之設計36
3.4 模擬及實驗結果43
第四章 伺服動態剛性之設計48
4.1 二維自由度系統48
4.2 伺服動態剛性之設計52
4.2.1 混合靈敏度設計52
4.2.2 PDFF與混合靈敏度設計58
4.3 設計應用實例63
第五章 切換控制73
5.1 Hanus調整技術73
5.2 位置及力量AWCT控制器78
5.3 控制器設計83
5.3.1 速度控制器85
5.3.2 力量控制器與位置控制器86
5.4 實驗89
第六章 結論與建議96
6.1 結論96
6.2 建議98
參考文獻99

[1] Alter, D. M. and Tsao,T. C., 1996, “Control of linear motors for machine tool feed drives：design and implementation of H¥ optimal feedback control,” ASME J. of Dynamic Systems, Measurement, and Control, Vol. 118, pp. 649-656.
[2] Åström, K. J. and Wittenmark, B., 1984, Computer controlled systems－theory and design, Prentice-Hall, New Jersey.
[3] Balas, G. J., Doyle, J. C., GLover, K., Packard, A., and Smith, R., 1993, m-Analysis and Synthesis Toolbox－User’s Guide, the Math Works Inc..
[4] Banerjee, J.R., 1997, “Dynamic stiffness formulation for strucual elements: a general approach”, Computers & Structures, Vol. 63, No.1, pp. 101-103.
[5] Chang, J.Y. and Tsai, M.C., 1994, “Relationships between weighting functions and the central controllers in H¥ mixed sensitivity design, ” National Symposium on Automatic Control, Tao Yuan, pp. 320-325.
[6] Chuang, H. Y., Cross-coupled adaptive feedrate control for multi-axis machine tools, D. Phil. Thesis, College of National Taiwan Institute Technology, 1991.
[7] Dewilde, P. and Dym, H., 1981, “Schur recursions, error formulas, and convergence of rational estimators for stationary stochastic sequences,” IEEE Trans. on Information Theory, Vol. 27, pp. 446-461.
[8] Doyle, J.C. and Stein, G., 1981, “Multivariable feedback design: concepts for a classical/modern synthesis,” IEEE Trans. on AC, Vol. 26, No.1, pp. 4-16.
[9] Edwards, C. and Postlethwaite, I., 1998, “Anti-windup and bumpless-transfer schemes,” Automatica, Vol. 34, pp. 199-210.
[10] Francis, B.A., 1987, A course in H¥ control theory, Spring-Verlag, Berlin.
[11] Francis, B.A. and Wonham, W.M., 1975, “The internal model principle for linear multi-variable regulators,” Appl. Math. Opt., Vol. 2, pp. 170-194.
[12] Franklin, G. F., Powell, J. D., and Emani-Naeini, A., 1991, Feedback control of Dynamic Systems, Addison-Wesley,
[13] Glover, K., and Doyle, J.C., 1988, “State-space formulae for all stabilizing controllers that satisfy an H¥-norm bounded and relations to risk sensitivity,” Syst. Contr. Lett., Vol. 15, pp.167-172.
[14] Graebe, S. F., and Ahlén, A. L. B., 1996, “Dynamic transfer among alternative controllers and its relation to antiwindup controller design,” IEEE Trans. on Control SystemTechnology, Vol. 4, No.1, pp. 92-99.
[15] Hanselmann, H., 1987, “Implementation of digit controllers — a survey,” Automatica, , Vol. 23, pp. 7-32.
[16] Hanus, R., 1988, “Antiwindup and bumpless transfer: A survey,” Proc. 12th World Congress on Scientific Computa., IMACS, Paris, France, pp. 59-65.
[17] Hanus, R., Kinnaert, M. and Henrotte, J. L., 1987, “Conditioning technique, a general anti-windup and bumpless transfer method,” Automatica, Vol. 23, pp. 729-739.
[18] Hewlett Packard, 1990, HP3563A Operating Manual－Control System Analyzer.
[19] Hogan, N., 1987, ”Stable execution of contact tasks using impedance control,” Proc. IEEE Int. Conf. Robot. Auto, pp. 1047-1053,.
[20] Houshangi, N., and Koivo, A., 1987,”Eigenvalue assignment and performance index based force position control with self-tuning for robotics manipulators,” Proc. IEEE Int. Conf. Robot. Auto, pp. 1386-1391.
[21] Hyde, R. A., 1995, H¥ Aerospace Control Design , Springer-Verlag, Berlin.
[22] Kothare, M. V., Campo, P. J., Morari, M. M. and Nett, C. N., 1994, “A unified framework for the study of anti-windup design,”Automatica, Vol. 30, pp. 1869-1883.
[23] Kuo, B. C. , 1991, Automatic control systems, Prentice-Hall, Englewood Cliffs, New Jersey.
[24] Kwakernaak, H., 1986, “A polynomial approach to minimax frequency domain optimization of multivariable systems, ” Int. J. Control, Vol. 44, pp. 117-156.
[25] Koren, Y., 1980,“Cross-coupled control of biaxial feed drive servomechanism,” ASME. J. of Dynamic Systems, Measurement and Control, Vol.102, No.4, pp. 265-272.
[26] Koren, Y., and Lo, C.C., 1992,“Advanced controller for feed drivers,” Annals of the CIRP, Vol.41, pp. 689-698.
[27] Lee, M.Y., 1991, Kinematic/Kinetic, and Dynamic Performance Synthesis for Multi-DOF Mechanisms, Ph. D. Thesis, University of Minnesota, USA.
[28] Lee, M. Y., Holt, T., and Strum, JR. A.J., 1991, “A Contribution to multi-axis robot contouring accuracy analysis: modeling, simulation, and evaluation,” ASME J. of Mechanical Design, Vol. 113, pp. 526 —535.
[29] Lo, C.C., 1999, “Real-time generation and control of cutter path for 5-Axis CNC machining,” International Journal of Machine Tools & Manufacture, Vol.39, pp. 471-488.
[30] Loughborough Sound Images Ltd., 1990, TMS320C30 System Board User’s Manual, Loughborough, England.
[31] McFarlane, D. and Glover, K., 1990, Robust controller design using normalized coprime factor plant descriptions, Lecture notes in control and information sciences, Springer-Verlag.
[32] McFarlane, D., and Glover, K., 1992, “A loop shaping design procedure using H¥ synthesis, ” IEEE Trans. on AC, Vol. 37, No.6, pp. 759-769.
[33] McFarlane, D. and Glover, K., 1992, “Robust stabilization of normalized coprime factor plant descriptions with H¥- bounded uncertainty, ” IEEE Trans. on AC, Vol. 34, No.8, pp. 821-830.
[34] Mei, X., Tsutsumi, M., Yamazaki, T., and Sun, N., 2001, “Study of the friction eoor for a high-speed high precision table,” Int. J. Mach. Tools Manufact., Vol. 41, pp. 1405-1415.
[35] Patarinski, S. P. and Botev, R. G., 1993, “Robot force control : a review,” Mechatronics, Vol. 3, pp. 377-398.
[36] Peng, Y., Vrancic, D., and Hanus, R., 1996, “Anti-windup, bumpless, and conditioned transfer techniques for PID controllers,” IEEE Control Systems, Vol. 16, pp. 48-57.
[37] Raibert, M, and Craig , J., 1981,”Hybrid position/force control of manipulators,” Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 102, pp. 126-133.
[38] Tsai, M.C., Geddes, E.J.M., and Postlethwaite, I., 1992 ,“Pole-zero cancellations and closed-loop properties of an H¥ mixed sensitivity design problem, ” Automatica, Vol. 28, pp. 519-530.
[39] Tsai, M. C. and Tsai, C.S., 1993, “A chain scattering-matrix description approach to H¥ control,” IEEE Trans. on AC, Vol. 38, No. 9, pp. 1416-1421.
[40] Tung, E. D., Anwar, G. and Tomizuka, M., 1993, “An algorithm for high-speed control of machine tools,” Proc. of the 1993 ACC, San Francisco, CA, Vol. 2, pp. 1966-1970.
[41] Walgama, K. S. and Sternby, J., 1990, “Inherent observer property in a class of anti-windup compensators,” Int. J. Control, Vol. 52, pp. 705-724.
[42] Younkin, G.W., 1991, “Considerations for low-inertia ac drives in machine tool axis servo applications,” IEEE. Trans. on IA, Vol. 27, No. 2, pp. 262-267.
[43] Zhou, K., and Doyle, J. C., 1998, Essentials of Robust Control, Prentice-Hall, Englewood Cliffs, New Jersey.