臺灣博碩士論文加值系統

本論文研究了具有時變不確定性的主動調諧質量阻尼器（ATMD）的建築物強健控制研究。 LQG最優控制方法和混合田口遺傳算法（HTGA）用於設計狀態反饋增益矩陣和估測器增益矩陣。 然後採用線性矩陣不等式（LMI）的穩定條件來確保在時變不確定性的情況下得到的控制系統是漸近穩定的。 最後，給出了一個仿真實例來演示使用設計方法。 結果表明，設計方法可以有效地獲得強健的控制器，以減少振動行為，保持ATMD的建築結構不受時變不確定性的不穩定性的影響。

This thesis studies the robust vibration control of a building with an active tuned mass damper (ATMD) subject to time-varying uncertainties. The LQG optimal control method and the the Hybrid Taguchi-Genetic Algorithm (HTGA) are used to design the state feedback gain matrix and observer gain matrix. And then, a sufficient condition in terms of linear matrix inequalities (LMIs) is employed to guarantee that the resulting control system in the presence of time-varying uncertainties is asymptotically stable. Finally, a simulation example is given to demonstrate the use of the design methods. The results show that the design method can efficiently obtain a robust controller to reduce vibration behavior and keep the building structure with an ATMD from the possibility of instability caused by time-varying uncertainties.

摘要..…………………………………………………………………………………iii
Abstract………………………………………………………………………………iv
目錄 …………………………………………………………………………………vi
表目錄 ……………………………………………………………………………….x
符號說明 .……………………………………………………………………………x
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 3
1.3 論文架構 8
第二章 數學模型與強健穩定分析 9
2.1 簡介 9
2.1.1 被動式諧調阻尼器(TMD) 9
2.1.2 主動式諧調阻尼器(ATMD) 11
2.1.3 主動式諧調阻尼器(ATMD)動態方程式模型 14
2.2 線性矩陣不等式之強健穩定性 17
第三章 最佳化控制器設計 19
3.1 LQR設計 20
3.1.1 濾波器設計 23
第四章 混合田口基因演算法 25
4.1 基因演算法介紹 25
4.2 基因演算法步驟 26
4.2.1 產生初始族群 27
4.2.2 計算適應函數值 27
4.2.3 複製及複製 27
4.2.4 交配 29
4.2.5 突變 30
4.2.6 滿足終止條件 31
4.3 田口實驗方法 31
4.3.1 田口法方法步驟 33
4.3.2 田口直交表選擇 33
4.3.3 訊號雜訊比(Signal-to-Noise Ratio, S/N) 36
4.4 混合田口基因演算法 37
4.4.1 混合田口基因演算法步驟 38
第五章 設計範例模擬 40
第六章 結論 44

[1] Frahm, H., 1911, “Device for damping vibrations of bodies”, U.S. Pantent No. 989958, October
[2] Ormondroy, J. d., J. P. Den Hartog, 1928, “The theory of the dynamic vibration absorber”, ASEM 50, A9-A22
[3] Hrova, D. t, P. Barak, and M. Rabins, 1983, “Semi-active versus passive or active tuned mass dampers for structural control“, Journal of Structural Engineering, Vol.109, No.3, June
[4] Samali B., J. N. Yang, and S. C. Liu, 1985, “Active control of seismic-excited buildings“, Journal of Structural Engineering, October
[5] Solari G., 1993, “Gust Buffeting. II: Dynamic Alongwind Response”, Journal of Structural Engineering, Vol.119, No.2, February
[6] Ankireddj S., and Henry T. Y. Yang, 1996, “SIMPLE ATMD CONTROL METHODOLOGY FOR TALL BUILDINGS SUBJECT TO WIND LOADS”, Journal of Structural Engineering, Vol.122, No.1, January
[7] Cao H., A. M. Reinhorn and T.T. Song, 1998, “Design of an active mass damper for a tall TV tower in Nanjing”, Engineering Structures, Vol.20, No.3
[8] Pinkaew T., Y. Fujino, 2001, “Effectiveness of semi-active tuned mass dampers under harmonic excitation”, Engineering Structures, August
[9] Zhou Y., T. Kijewski, S.M.ASCE and A. Kareem, 2002, “Along-Wind Load Effects on Tall Buildings: Comparative Study of Major International Codes and Standards”, Engineering Structures, June
[10] Jalili-Kharaajoo M., Y. Nikouseresht, A. Mohebbi, B. Moshiri and A. Esna Ashari, 2003, “Application of Linear Quadratic Regulator (LQR) in Displacement Control of an Active Mass Damper”, IEEE, Vol.30, No.8, April
[11] Law S.S., J.Q. Bu, X.Q. Zhu, 2005, “Time-varying wind load identification from structural responses”, Engineering Structures, Vol.27, No.10, May
[12] Körlin R., U. Starossek, 2007, “Wind tunnel test of an active mass damper for bridge decks”,　Journal of Wind Engineering and Industrial Aerodynamics, Vol. 95, 2007
[13] Ladipo I.,　A.G. A. Muthalif , A. Rozaime and A. Asyraf,2011, “DESIGN AND DEVELOPMENT OF AN ACTIVE MASS DAMPER FOR BROADBAND VIBRATION CONTROL”, Kulliyah of Engineering,May
[14] Branco F. A., J. Mohammadi, 2012, “OptimumDesign of TMD System for Tall Buildings”, ISRN Civil Engineering, April
[15] Lackner, G. S., Matthew, 2013, “Offshore Wind Turbine Load Reduction Employing Optimal Passive Tuned Mass Damping Systems”, IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, Vol. 21, No. 4, JULY
[16] J. H. Chou, S. H. Chen and L. A. Zheng, 2003, “LMI condition for robust stability of linear systems with both time-varying elemental and norm-bounded uncertainties”, Journal of the Chinese Institute of Engineers, Vol.26, pp.101-105.
[17] Alex,Y. T., G. Q. Shang,2014, “Vibration Control in a 101-Storey Building Using a Tuned Mass Damper”, Journal of Applied Science and Engineering, Vol. 17, No. 2,May
[18] Viet, L. D., N.B. Nghi, 2014, “On a nonlinear single-mass two-frequency pendulum tuned mass damper to reduce horizontal vibration”, Engineering Structures, Vol.81, October
[19] Ricciardelli, F., A. David Pizzimenti, Massimiliano Mattei, 2003, “Passive and active mass damper control of the response of tall buildings to wind gustiness”, Engineering Structures, Vol.25, March
[20] You,Ki-Pyo, Jang-Youl You, and Young-Moon Kim,2014, “LQG Control of Along-Wind Response of a Tall Building with an ATMD”, Mathematical Problems in Engineering, September, pp. 1-8
[21] Holland, J. H., 1975, “Adaptation in Natural and Artificial Systems”, Ann Arbor, MI：The University of Michigan Press.
[22] Back,T., and H. P., Schwefel, 1993, “An overview of evolutionary algorithms for parameter optimization”. Evolutionary Computation, Vol.1, pp.1-23.
[23] Sun,C. C., H. Y. Chung, and W. J. Chang, 2003, “GA-based robust H2 controller design approach for active suspension systems”, Proc. of the 2003 IEEE International Conference on Robotics and Automation, Taiwan, pp.2330-2335.
[24] Rana Rahul, T.T. soong, “Parametric study and simplified design of tuned mass dampers”, Engineering Structures, Vol. 20, NO.3, pp. 193-204, 1998
[25] Lin, C. C.,J.F. Wang, B.L. Chen, Train-Induced Vibration Control of Hign-speed Railway Bridge Equipped with Multiple Tuned Mass Dampers
[26] Krenk Steen, Jan Hogsberg, “Tuned mass absorber on flexible structure”, Journal of Sound and Vibration, pp. 1577-1595, 2014
[27] N. S., Nise, 2000, “Control Systems Engineering”, John Wiley and Sons, New York.
[28] G. C., Goodwing, S. F. Graebe and M. E. Salgado, 2001, “Control System Design”, Prentice-Hall, New Jersey.