本論文旨在研究輕巧的可撓性連桿機構的強健控制器設計。考慮連桿機構在高速運轉下會引發慣性力的干擾，再加上系統參數模式化誤差、捨去誤差、以及結構控制中有限維建模之殘餘模態所引起的過溢控制與過溢估測等不確定問題，這些因素都會造成系統不穩定。本論文基於LQ、最佳模式追蹤、頻率整型等設計原理分別提出強健控制的穩定充份條件之設計準則，它能保證系統參數在有界的各種參數不確定量干擾和建模捨去誤差下，系統仍然是維持穩定的。另外研究以田口法與基因演算法尋找致動器與感測器的最佳位置。
本論文以有限單元法(FEM)進行系統之模式化工作，取有限維低頻模態做為控制器及估測器設計。先以LQ設計一個含有估測器的強健控制器; 另以最佳模式追蹤原理設計強健控制器，使受控系統具有時域所指定的最佳模式性能; 又利用頻率整型原理從頻域的觀點設計強健控制器，對高維模態加以抑制，以避免系統受到高維模態激發所引發的不穩定; 最後探討致動器與感測器對系統穩定的影響，此等研究係以田口法結合基因演算法等兩項技術去尋找最佳致動器與感測器位置。
由電腦模擬得知本論文所提出的諸項強健控制穩定準則，均能主動且有效地抑制連桿中點之變形，且避開以過溢和時變參數擾動所誘發之不穩定。

The purpose of this dissertation is to study the robust control for the smart flexible linkage mechanism. The control of flexible linkage induced inertia force under high-speed rotation is taken into consideration with the system parameter uncertainties such as modeling error, truncation error, and both of control spillover and observation spillover due to the residual modes of structural control problem. Based on the principles of LQ, optimal model following (OMF) and frequency shaping, this study proposes some sufficient conditions of stability criteria for the design of robust controller, respectively. These techniques guarantee that the controlled plant, under both bounded parameter perturbations and model truncation, could remain stable. Meanwhile, searching for the optimal locating positions of sensor and actuator by applying Taguchi method and genetic algorithm (GA) combined technique is further studied.
The system is modeled through employing finite element method (FEM), and the limited lower frequency part modes are separated into controlled modes and residual modes. In time domain, at first we design a Luenberger-observer-based robust controller for the finite-dimensional mode plant keeping stability in a specified region. And then, a robust controller with the OMF is designed for the controlled system to achieve the performance as those of the specified optimum model. From the view of frequency domain, the robust controller could also be deigned according to the frequency shaping principle to suppress the exciting effect of higher frequency residual modes, and similarly avoid that the system might be destabilized. Finally, the combination of Taguchi method and GA technique to search the optimal locations for placing actuator and sensor to coincide with the stability and performance requirement is also done.
From the computer simulation, the middle point movement of the linkage is obviously well controlled; hence, the designed robust controllers can certainly suppress the affection of parameter uncertainties and the spillover stimulation of residual modes, and can produce satisfactory results.

目錄 i
圖表索引 iv
符號說明 vi
摘要(中) ix
摘要(英) x
第一章 緒 論 1
1.1 研究動機 1
1.2 文獻回顧 7
1.2.1 可撓性連桿強健控制 7
1.2.2 LQR強健控制 10
1.2.3 最佳模態追蹤之強健控制 10
1.2.4 頻率整型之強健控制 11
1.2.5 最佳化致動器與感測器之位置 13
1.3 章節與組織 14
第二章 系統模式化與基本數學定理 16
2.1 前言 16
2.2 可撓性連桿機構 16
2.3 運動學分析 16
2.4 壓電片致動器與感測器的數學模式 18
2.5 可撓性連桿的動態方程式 19
2.5.1 簡介 19
2.5.2 平面架之有限單元法模式化 20
2.5.3 模態轉換 22
2.6 輔助定理 24
第三章 可撓性連桿之LQ強健控制 28
3.1 前言 28
3.2 問題描述 29
3.3 強健控制定理 36
3.4 範例說明 38
3.5 結果研討 41
3.6 附錄：定理3.1之證明 42
第四章 最佳模式追蹤之強健控制 48
4.1 前言 48
4.2 問題描述 49
4.3 強健控制器定理 54
4.4 範例說明 57
4.5 結果研討 59
4.6 附錄：定理4.1之證明 60
第五章 頻率整型之強健控制 64
5.1 前言 64
5.2 問題描述 65
5.3 強健控制定理 74
5.4 範例說明 76
5.5 結果研討 79
5.6 附錄：定理5.1之證明 80
第六章　致動器和感測器之最佳位置設計 85
6.1 前言 85
6.2 問題描述 87
6.2.1 LQ觀測器基的強健控制器 87
6.2.2 基因演算法 89
6.2.3 田口實驗法 90
6.3 範例說明 95
6.4 結果討論 97
第七章 結 論 105
7.1 總結 105
7.2 未來展望 106
參考文獻 108

1. Abdul-Wahab, A.-A.A., 1988, "Robustness Measure Bounds for Optimal Model Matching Control Designs," IEEE Trans. on Automatic Control, Vol. 33, No. 12 , pp. 1178 –1180.
2. Aldrainhem, O. J., T. Singh and R. C. Wetherhold, 1997, "Realistic Determination of the Optimal Size and Location of Piezoelectric Actuators/Sensors," Proceedings of the 1997 IEEE International Conference on Control Applications, Hartford, CT, October 5-7, pp. 435-440.
3. Anderson, B. D. O. and D. L. Mingori, 1985, "Use of Frequency Dependence in Linear Quadratic Control Problems to Frequency-Shape Robustness,” Journal of Guidance, Control, and Dynamics, Vol. 8, pp. 397-401.
4. Anderson, B. D. O. and J. B. Moore, 1971, Linear Optimal Control, Prentice-Hall, Englewood Cliffs, New Jersey.
5. Andrzej, M., Jan H. S. and Francisco L. A., 1996, "Optimal Sensor Location in Active Control of Flexible Structures,” AIAA Journal, Vol. 34, No. 4, pp. 857-859.
6. Bailey, T. and J. E. Hubbard, 1985, "Distributed Piezoelectric Polymer Active Vibration Control of a Cantilevered Beam,” J. of Guidance, Control and Dynamics, Vol. 8, No. 5, pp. 605-611.
7. Balas, M. J., 1978, "Feedback Control of Flexible Systems,” IEEE Trans. on Automatic Control, Vol. 23, No. 4, pp. 673-679.
8. Bernnan, M. J., and M. J. Day, 1994, "Piezoelectric Actuators and Sensors,” IUTAM Symposium on The Active Control of Vibration, Published by Mechanical Engineer Pub. Ltd, London, pp. 263-274.
9. Borowiec, J. and A. Tzes, 1997, "Linear Quadratic Frequency-Shaped Implicit Force Control of Flexible Link Manipulators,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 119, pp. 405-411.
10. Chandrupatla, T. R. and Belegundu, A.D., 1985, Introduction to Finite Elements in Engineering, Prentice Hall, New Jersey.
11. Chen, C. I. and C. W. Yang, 1995, "Active Control of Flexible Mechanism and Piezoelectric Actuator Dynamic System,” Proc. of the Third National Conference on the Society of Sound and Vibration, Taipei, Taiwan, Republic of China, pp. 77-85.
12. Chen, C. Q. and Y. P. Shen, 1997, "Optimal Control of Active Structures with Piezoelectric Modal Sensors and Actuators,” Smart Materials and Structures, Vol. 6, pp. 403-409.
13. Chen, K. H., 1989, "Robust Analysis and Design of Multiloop Control System,” Ph.D. Dissertation, National Tsing-Hua University, Taiwan, Republic of China.
14. Chen, S. H., 1996, "Robust LQG Control for Mechanical Systems,” Dissertation for Ph. D., Institute of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC.
15. Choe, K and H. Baruh, 1992, "Actuator Placement in Structural Control,” Journal of Guidance, Control, Vol. 15, No. 1, pp. 40-48.
16. Choi, S. B., C. C. Cheong, B. S. Thompson and M. V. Gandhi, 1994, "Vibration Control of Flexible Linkage Mechanisms Using Piezoelectric Films,” Mechanism and Machine Theory, Vol. 29, No. 4, pp. 535-546.
17. Chou, J. H., 1990, "Structured Perturbations for a Class of Multivariable Nonlinear Systems with Actuator Saturation,” Proc. of the 14th National Symposium on Automatic Control, Taiwan, Republic of China, pp. 249-254.
18. Chou, J. H. 1994, "Robust Stability Bounds on Structured Time-Varying Independent Perturbations for Linear State-Space Models,” JSME International Journal, Series C, Vol. 37, No. 4, pp. 733-738.
19. Chou, J. H. and I. R. Horng, 1987, "On sufficient conditions for the Stability of Interval Matrices,” Proc. of the 4th CSME Annual Conference, Taiwan, Republic of China, pp. 1377-1381.
20. Chou, J. H., I. R. Horng and W. H. Liao, 1998, "Robust Observer-Based OMF Vibration Control of Flexible Linkage Mechanisms Using Piezoelectric Films,” International Journal of Mechanical Science, Vol. 40, No. 8, pp. 749-759.
21. Crawley, E. F. and J. deLuis, 1987, "Use of Piezoelectric Actuators as Element of Intelligent Structures,” AIAA Journal, Vol. 25, No. 10, pp. 1373-1385.
22. Desoer, C. A. and M. Vidyasagar, 1975, "Feedback Systems: Input-Output Properties,” Academic Press, New York.
23. Devasia, S., T. Meressi, B. Paden and E. Bayo, 1993, "Piezoelectric Actuator Design for Vibration Suppression: Placement and Sizing,” Journal of Guidance, Control, Vol. 16, No. 5, pp. 859-864.
24. Ding, C., C. Zhang and G. Liu, 1997, "Configure the Control Parameters of Genetic Algorithms Using Orthogonal Experimental Method,” Journal of Xi’An Jiao-Tong University, Vol. 31, No. 9, pp. 81-86.
25. Fanson, J. L., T. K. Canghey and J. C. Chen, 1985, "Stiffness Control of Large Space Structures,” Proceedings of the Workshop on Identification and Control Flexible Space Structures, Vol. 2, pp. 351-364.
26. Fox, R. L., 1971, Optimization Method for Engineering Design, Addison-Wesley, New York.
27. Gen, M. and Cheng, R. 1997, Genetic Algorithms and Engineering Design, John Wiley & Sons, Inc.
28. Georges, D., 1995, "The Use of Observability and Controllablility Gramians or Functions for Optimal Sensor and Actuator Location in Finite-Dimensional Systems,” Proceedings of the 34th Conf. On Decision and Control, New Orleans, LA-December, pp. 3319-3324.
29. G'eradin, M. and Riexen, D., 1994, Mechanical Vibrations Theory and Application to Structural Dynamics, Willey.
30. Goldberg, D. E., 1989, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley.
31. Grace, A., 1990, Optimization Toolbox for use with MATLAB-User’s Guide, The Math Works, Inc.
32. Gupta, N. K., 1980, "Frequency-Shaped Cost Functionals: Extension of Linear-Quadratic-Gaussian Design Methods,” Journal of Guidance, Control, Vol. 3, No. 6, pp. 529-535.
33. Han, J. H. and I. Lee, 1999, "Optimal Placement of Piezoelectric Sensors and Actuators for Vibration Control of a Composite Plate Using Genetic Algorithm,” Smart Materials and Structures, Vol. 8, pp. 257-267.
34. Hsu, Yen-Ting, Te-Ping Tsai and Yau-Tarng Juang, 1994, "Equivalence of Model-Following Systems Designed in the Time Domain and Frequency Domain,” IEEE Transactions on Automatic Control, Vol. 39, No. 8, pp. 1722-1726.
35. Hwang, W. S. and H. C. Park, 1993, "Finite Element Modeling of Piezoelectric Sensors and Actuators,” AIAA Journal, Vol. 31, No. 5, pp. 930-611.
36. IEEE Standard on Piezoelectricity, 1987, ANSI-IEEE Std 176-1987.
37. Inman, D. J., 1989, Vibration With Control, Measurement and Stability, Prentice-Hall, Englewood Cliffs, New Jersey.
38. James, M. L., G. M. Smith, J. C. Wolford and P. W. Whaley, 1994, Vibration of Mechanical and Structural Systems with Microcomputer Applications, (2nd Edition), New York: HarperCollins College Publishers.
39. Joshi, S. M., 1989, Control of Large Flexible Space Structures, Berlin: Spriger.
40. Kahn, S. P. and K. W. Wang, 1994, "Structural Vibration Control via Piezoelectric Materials with Active-Passive Hybrid Networks,” ASME, Active Control of Vibration and Noise, DE-Vol. 75, pp. 187-194.
41. Kang, Y. K., H. C. Park, W. Hwang and K. S. Han, 1996, "Optimum Placement of Piezoelectric Sensor/Actuator for Vibration Control of Laminated Beams,” AIAA Journal, Vol. 34, No. 9, pp. 1921-1926.
42. Khot, N. S. and S. A. Heise, 1994, "Consideration of Plant Uncertainties in the Optimum Structural-Control Design,” AIAA Journal, Vol. 32, No. 3, pp. 610-615.
43. Kim, Y. and J. L. Junkins, 1991, "Measure of Controllability for Actuator Placement,” Journal of Guidance, Control, Vol. 14, No. 5, pp. 895-902.
44. Kirk, D. E., 1970, Optimal Control Theory, Prentice-Hall, Englewood Cliffs, New Jersey.
45. Kouvaritakis, B., R. F. Harrison and H. A. Latchman, 1987, "Stability and Dynamic Performance Bounds for Nonlinear Multivariable Systems,” IEE Proceedings, Part D, Vol. 134, No. 2, pp. 115-123.
46. Krishnakumar, K. and D. E. Goldberg, 1992, "Control System Optimization Using Genetic Algorithm,” Journal of Guidance, Control, Vol. 15, No. 3, pp. 735-740.
47. Lee, A. C. and S. T. Chen, 1994, "Collocated Sensor / Actuator Positioning and Feedback Design in the Control of Flexible Structure System,” ASME Journal of Vibration and Acoustics, Vol. 116, pp. 146-154.
48. Lee, A. Y. and M. A. Salman, 1989, "On the Design of Active Suspension Incorporation Human Sensitivity to Vibration,” Optimal Control Applications & Methods, Vol. 10, pp. 189-195.
49. Leo, D. J. and D. J. Inman, 1993, "Modeling and Control Simulations of a Slewing Frame Containing Active Members,” Smart Materials and Structures, Vol. 2, No. 1, pp. 82-95.
50. Liao, C. Y. and C. K. Sung, 1993, "An Elastodynamic Analysis and Control of Flexible Linkages Using Piezoceramic Sensors and Actuators,” ASME J. of Mechanical Design, Vol. 115, No. 3, pp. 658-665.
51. Liao, W. H., J. H. Chou and I. R. Horng, 1997, "Robust Vibration Control of Flexible Linkage Mechanisms Using Piezoelectric Films,” Smart Materials and Structures, Vol. 6, pp. 457-463.
52. Liao, W. H., J. H. Chou and I. R. Horng, 1997, "Frequency-Shaping Optimal Vibration Control of Uncertain Flexible Linkage Mechanisms Using Piezoelectric Films,” Proc. of the Fifth National Conference on the Society of Sound and Vibration, Taiwan, pp. 475-484.
53. Lim, K. B., 1992, "Method for Optimal Actuator and Sensor Placement for Large Flexible Structures,” Journal of Guidance, Control, and Dynamics, Vol. 15, No. 1, pp. 49-57.
54. Lim, K. B., 1997, "Disturbance Rejection Approach to Actuator and Sensor Placement,” Journal of Guidance, Control, and Dynamics, Vol. 20, No. 1, pp. 202-204.
55. Lin, C. L., 1993, "Robust Control of Flexible Structures Using Residual Mode Filters,” Journal of Guidance, Control, and Dynamics, Vol. 16, No. 5, pp. 973-977.
56. Lin, C. L. and B. S. Chen, 1994, "Robust Observer-Based Control of Large Flexible Structures,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 116, pp. 713-722.
57. Liu, S. W. and T. Singh, 1997, "Robust Time-Optimal Control of Flexible Structures With Parametric Uncertainty,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 119, pp. 743-748.
58. Maghami, P. G. and S. M. Joshi, 1993, "Sensor/Actuator Placement for Flexible Space Structures,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 29, No. 2, pp. 345-351.
59. Matsuzaki, Y., 1997, "Smart Structures Research in Japan,” Smart Materials and Structures, Vol. 6, pp. R1-R10.
60. Meirovitch, L. 1997, Principles and Techniques of Vibrations, Englewood Cliffs, NJ: Prentice-Hall.
61. Meckl, P. H. and R. Kinceler, 1994, "Robust Motion Control of Flexible Systems Using Feedforward Forcing Functions,” IEEE Transactions on Control Systems Technology, Vol. 2, No. 3, pp. 245-254.
62. Meressi, T. and B. Paden, 1993, "Buckling Control of a Flexible Beam Using Piezoelectric Actuators,” Journal of Guidance, Control, and Dynamics, Vol. 16, No. 5, pp. 977-980.
63. Moore, J. B. and D. L. Mingori, 1987, "Robust Frequency-Shaped LQ Control,” Automatica, Vol. 23, No. 5, pp. 641-646.
64. Moura, J. M., R. G. Roy and N. Olgac, 1997, "Sliding Mode Control With Perturbation Estimation (SMCPE) and Frequency Shaped Sliding Surfaces,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 119, pp. 584-588.
65. Nonami, K. and S. Hirasawa, 1999, "Sliding Mode Positioning Control of Single Link Flexible Arm Using H-Infinity Control Hyperplane with Q-Parametrization,” JSME International Journal Serial C - Mechanical Systems Machine Elements and Manufacturing, Vol. 42, No. 2, pp. 350-356.
66. Onoda, J. and Y. Hanawa, 1993, "Actuator Placement Optimization by Genetic and Improved Simulated Annealing Algorithm,” AIAA Journal, Vol. 31, No. 6, pp. 1167-1169.
67. Ortega, J. M. and W. C. Rheinboldt, 1970, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York.
68. Oshima, K., T. Takigami and Y. Hayakawa, 1997, "Robust Vibration Control of a Cantilever Beam Using Self-Sensing Actuator,” JSME International Journal Serial C - Mechanical Systems Machine Elements and Manufacturing, Vol. 40, No. 4, pp. 681-687.
69. Papadopoulos, M. and E. Garcia, 1998, "Sensor Placement Methodologies for Dynamic Testing,” AIAA Journal, Vol. 36, No. 2, pp. 256-263.
70. Park, S. H., 1996, Robust Design and Analysis for Quality Engineering, Chapman & Hall.
71. Pieper, J. K., S. Bailli and K. R. Goheen, 1994, "Linear-Quadratic Optimal Model-Following Control of a Helicopter in Hover,” Proceedings of the American Control Conference, Baltimore, Maryland, June 1994, pp. 3470-3474.
72. Preiswerk, M. and A. Venkatesh, 1994, “An Analysis of Vibration Control Using Piezoceramics in Planar Flexible-Linkage Mechanisms”, Smart Materials and Structures, Vol.3, No.2, pp.190-200.
73. Rana, R., H. Gupta and T. Singh, 1997, "Application of Controllability Measure for Actuator Placement in a Civil Engineering Structure,” Proceedings of the 1997 IEEE International Conference on Control Applications, Hartford, CT, October 5-7, pp. 553-558.
74. Rao, S. S., T. S. Pan and V. B. Venkayya, 1990, "Modeling, Control, and Design of Flexible Structures: A Survey,” Applied Mechanical Review, Vol. 43, No. 5, pp. 99-117.
75. Rehbock, V., C. C. Lim and K. L. Teo, 1994, "Stable Constrained Optimal Model Following Controller for Discrete-Time Nonlinear Systems Affine in the Control," Control-Theory and Advanced Technology, Vol. 10, No. 4, pp. 793-814.
76. Roy, R. K., 1990, A Primer on the Taguchi Method, Van Nostrand ReinHold, New York.
77. Shaw, J., 1987, "Improving Control System Performances Via A Genetic Algorithm,” Hau Fan Annual Journal, Taiwan, ROC, Vol. 4, No. 1, pp. 153-164.
78. Shen, Y. and A. Homaifar, 1999, "Active Control of Flexible Structure Using Genetic Algorithms and LQG/LTR Approaches,” Proceedings of the American Control Conference, San Diego, California, June 1999, pp. 4398-4402.
79. Sheu G. J., 1996, "Vibration Control of Rotor Systems by Experimental Design,” Dissertation for Ph. D., Institute of Aeronautics and Astronautics, National Chang Kung University, Tainan, Taiwan, ROC.
80. Soni, A. H., 1974, Mechanism Synthesis and Analysis, McGraw-Hill Book Company, New York.
81. Sung, C. K. and B. S. Thompson, 1987, “A Variational Principle for the Hygrothermoelastodynamic Analysis of Mechanism Systems,” Transactions of the ASME, Journal Mechanisms, Transmissions, and Automation in Design, Vol. 109, pp. 297-300.
82. Sung, C. K. and Y. C. Chen, 1991, “Vibration Control of the Elastodynamic Response of High-Speed Flexible Linkage Mechanisms,” Transactions of the ASME, Journal Vibration and Acoustics, Vol. 113, pp. 14-21.
83. Taguchi, G., 1976, Experimental Designs, 3d ed, Vol. 1 and 2, Tokyo: Maruzen Publishing Company. (Japanese)
84. Taguchi, G., 1988, Quality Engineering Series 3, Japanese Standards Association.
85. Teo, C. L., 1988, "Frequency-Shaped Linear Quadratic Regulator with Application to the Controls of a Flexible Arm,” Ph. D. Dissertation, Berkeley, University of California.
86. Teo, C. L. and M. Tomizuka, 1989, " Frequency-Shaped Cost Functionals: Output or Input Weighting,” Proc. of the IEEE 28th Conference on Decision and Control, Tampa, Florida, pp. 2389-2390.
87. Thompson, B. S. and C. K. Sung, 1984, “A Variational Formulation for the Dynamic Viscoelastic Finite Element Analysis of Robotic Manipulators Constructed from Composite Materials,” Transactions of the ASME, Journal Mechanisms, Transmissions, and Automation in Design, Vol. 106, pp. 183-190.
88. Tirupathi, R. C. and D. B. Ashok, 1991, Introduction to Finite Elements in Engineering, Prentice Hall, Englewood Cliffs, New Jersey.
89. Weinmann, A., 1992, Uncertain Models and Robust Control, Springer-Verlag Wien, New York.
90. Yang, B., 1994, "Model Controllability and Observability of General Mechanical Systems,” ASME, Active Control of Vibration and Noise, DE-Vol. 75, pp. 363-370.
91. Yang, C. D., H. C. Tai and F. B. Yeh, 1997, "Synthesis of Robust-Performance Controllers Using Matrix Experiments and Analysis of Variance,” Int. J. Control, Vol. 68, No. 6, pp. 1475-1498.
92. Yang, C. D., H. S. Ju and S. W. Liu, 1994, "Experimental Design of H∞ Weighting Function for Flight Control Systems,” Journal of Guidance, Control, and Dynamics, Vol. 17, No. 3, pp. 544-552.
93. Yang, S. M. and Y. J. Lee, 1993, "Vibration Suppression with Optimal Sensor/Actuator Location and Feedback Gain,” Smart Materials and Structures, Vol. 2, pp. 232-239.
94. Yao, L., W. A. Sethares and D. C. Kammer, 1993, "Sensor Placement for On-Orbit Modal Identification via a Genetic Algorithm,” AIAA Journal, Vol. 31, No. 10, pp. 1922-1928.
95. Young, K. D. and U. Ozguner, 1993, "Frequency Shaping Compensator Design for Sliding Mode,” Int. J. Control, Vol. 57, No. 5, pp. 1005-1019.
96. Zhou, K. and J. C. Doyle, 1998, Essentials of robust control, Prentice Hall.
97. Zohdy, M. A., N. K. Loh and A. A. A. Abdul-Wahab, 1987, "A Robust Optimal Model Matching Control,” IEEE Trans. on Automatic Control, Vol. 32, No. 5, pp. 410-414.