本研究分別針對考慮即時濾波(Real-Time filter)之絕對加速度回饋相位控制主動調諧質量阻尼器(Phase Control absolute Acceleration feedback-Active Tuned Mass Damper, PCA-ATMD)與PCA-ATMD導入衝程限制(stroke limit)應用於多自由度結構，進行數值模擬與實驗驗證；以結構加裝考慮即時濾波之PCA-ATMD情況進行頻率反應函數、歷時反應、系統穩定性與敏感度之分析，再以PCA-ATMD導入衝程限制情況進行歷時反應分析，探討各情況之減震效果與特性，最後以構架試體進行振動台實驗並與數值模擬結果相互驗證。相位控制主動調諧質量阻尼器(PC-ATMD)是於調諧質量阻尼器(TMD)與結構間施加控制力，能即時調整TMD之運動，使TMD與結構維持-90度相位差，此時TMD有最大Power Flow，因此減震效果最佳。未結合濾波器之系統利用Direct Output Feedback求解時，能得到最佳增益矩陣，並不代表結合濾波器之即時濾波系統在求解時，也能求得最佳增益矩陣；若直接以未結合濾波器之系統利用Direct Output Feedback求解得到最佳增益矩陣來做設計，將可能導致加裝PCA-ATMD之系統受濾波器影響而不穩定；因此本研究以即時濾波系統利用Direct Output Feedback來求得最佳增益矩陣，將能避免上述情況發生，且只需藉由改變濾波器設計參數，便能讓加裝考慮即時濾波之PCA-ATMD系統能求得解。PCA-ATMD之衝程限制是利用一與ATMD相對速度及衝程有關之函式來計算衝程限制力，如此設計之衝程限制能有效降低衝程，且不會對結構絕對加速度造成明顯負面影響。結構加裝即時濾波PCA-ATMD與PCA-ATMD導入衝程限制之模擬與實驗結果顯示，從頻率反應函數與歷時反應能看出有良好的減震效果與衝程限制效果，且濾波器的加入使實驗與模擬更加相符。由系統穩定性分析看出，系統在一定範圍內為穩定可控的，有一定之強健性；敏感度分析看出，當考慮即時濾波之PCA-ATMD增益係數或振幅比有變化，減震效果受影響並不大。

The purpose of this study is to verify the application of the Phase Control absolute Acceleration feedback-Active Tuned Mass Damper (PCA-ATMD) with real-time filter and the stroke limitation. The multiple-degree-of-freedom (MDOF) structure is implemented with the PCA-ATMD for numerical simulation and experiment, respectively. The essential of Phase Control Active Tuned Mass Damper (PC-ATMD) is to apply a control force between the TMD mass and the structure, and then the PC-ATMD can achieve 90-degree phase lag of structure to induce maximum power flow resulting in outstanding vibration reduction capability. The optimal gain matrix is obtained by solving the Direct Output Feedback using the PCA-ATMD with real-time filter system, that ensures the control system is workable. The PCA-ATMD stroke limitation force is related to ATMD relative velocity and stroke, which is not only avoiding apparently negative affect in structural absolute acceleration, but also constraining stroke effectively. The result of numerical simulations show that the PCA-ATMD with real-time filter and the stroke limitation have a good performance on structural vibration reduction and stroke limitation. Besides, the system stability and sensitivity analysis show that the system is stable and durable in a certain range of gain parameters. Hence, the active phase control algorithm is robust. Finally, the shaking table experiment is carried out by using a three-story shear building frame. And, the experiment verifies that the result is in accordance with numerical simulation. The system combined with filter makes the simulation more consistent with the experiment.

[1] 內政部營建署，「建築物耐震設計規範及解說」，內政部台內營字第0990810250號令，中華民國100年1月。
[2] 羅偉宸，「主動式相位控制調諧質量阻尼器之研發與實驗驗證」，國立中央大學，碩士論文，中華民國109年6月。
[3] 常珮慈，「相位控制之主動調諧質量阻尼器應用於多自由度構架分析與實驗驗證」，國立中央大學，碩士論文，中華民國110年6月。
[4] Den Hartog J.P., “Mechanical Vibrations”, Fourth edition, McGraw Hill, New York, November 1956.
[5] Warburton G.B. and Ayorinde E.O., “Optimum absorber paraments for simple systems”, Earthquake Engineering and Structural Dynamics, 8, pp.197-217, 1980.
[6] Ayorinde E.O. and Warburton G.B., “Minimizing structural vibrations with absorbers”, Earthquake Engineering and structural Dynamics, 8, pp.219-236, 1980.
[7] Warburton G.B., “Optimum absorber paraments for various combinations of response and excitation parameters”, Earthquake Engineering and Structural Dynamics, 10, pp.381-401, 1982.
[8] Sadek F., Mohraz B., Taylor A.W. and Chung R.M., “A Method of Estimating the Parameters of Mass Dampers for Seismic Application”, Earthquake Engineering and structural Dynamics, 26, pp.617-635, 1997.
[9] Bakre S.V. and Jangid R.S., “Optimum parameters of tuned mass damper for damped main system”, Structure Control and Health Monitoring, 14, pp.448-470, 2007.
[10] 鍾立來、顧丁與、賴勇安和吳賴雲，「調諧質塊阻尼器於基底震動之最佳減震設計參數」，中華民國結構工程學會，《結構工程》，第二十七卷，第四期， 70-90頁，2012。
[11] 王哲夫，「被動調諧質量阻尼器之最佳設計暨應用」，國立中興大學，碩士論文，1996。
[12] Lee C.L., Chen Y.T., Chung L.L. and Wamg Y.P., “Optimal design theories and applications of tuned mass dampers”, Engineering Structures, 28, pp.43-53, 2006.
[13] Ghosh A. and Basu B., “A closed-form optimal tuning criterion for TMD in damped structures”, Structural Control and Health Monitoring, 14, pp.681-692, 2005.
[14] Chang C.C., “Mass dampers and their optimal designs for building vibration control”, Engineering Structures, 22, pp.454-463, 1999.
[15] Fujino Y. and Abe M., “Design formulas for tuned mass dampers based on a perturbation technique”, Earthquake Engineering and Structural Dynamics, 22, pp.833-854, 1993.
[16] Chang C.M., Shia S. and Lai Y.A., “Seismic Design of Passive Tuned Mass Damper Parameters Using Active Control Algorithm”, Journal of Sound and Vibration, 426, pp.150-165, 2018.
[17] Hadi N.S. and Aifiadi Y., “Optimum design of absorber for MDOF structures”, Journal of Structural Engineering, 124, pp.1272-1280, 1998.
[18] Soong T.T. and Manolis G.D., “Active structures”, Journal of Structural Engineering, 113, pp.2290-2301, 1987.
[19] Chung L.L., Reinhorn A.M. and Soong T.T., “Experiments on active control of seismic structures”, Journal of Engineering Mechanics, 114, pp.241-256, 1998.
[20] Reinhorn A.M., Soong T.T., Lin R.C., Riley M.A., Wang Y.P., Aizawa S. and Higashino M., “Active Bracing System: A Full Scale Implementation of Active Control”, National Center for Earthquake Engineering Research, Buffalo, August 1992.
[21] Spencer B.F. Jr., Suhardjo J. and Sain M.K., “Frequency domain optimal control strategies for aseismic protection”, Journal of Engineering Mechanics, 120, pp.135-158, 1994.
[22] Chang J.C.H. and Soong T.T., “Structure control using active tuned mass dampers”, Journal of Engineering Mechanics, 106, pp.1091-1098, 1980.
[23] Chung L.L., Lin R.C., Soong T,T. and Reinhorn A.M., “Experimental Study of Active Control for MDOF Seismic Structures”, J. Eng. Mech., 115, pp.1609-1627, 1989.
[24] Nishimura I., Kobori T., Sakamoto M., Koshika N., Sasaki K. and Ohrui S., “Active tuned mass damper”, Smart Materials and Structures, 1, pp.306-311, 1992.
[25] Chang C.C. and Yang H.T.Y., “Control of buildings using active tuned mass dampers”, Journal of Engineering Mechanics, 121, pp.355-366, 1995.
[26] Yang D.H., Shin J.H., Lee H.W., Kim S.K. and Kwak M.K., “Active vibration control of structure by Active Mass Damper and Multi-Modal Negative Acceleration Feedback control algorithm”, Journal of Sound and Vibration, 392, pp.18-30, 2017.
[27] Loh C.H. and Chao C.H., “Effectiveness of active tuned mass damper and seismic isolation on vibration control of multi-story building”, Journal of Sound and Vibration, 193, pp.773-792, 1996.
[28] Mackriell L.E., Kwok K.C.S. and Samali B., “Critical mode control of a wind-loaded tall building using an active tuned mass damper”, Engineering structures, 19, pp.834-842, 1997.
[29] Samali B. and Al-Dawod M., “Performance of a five-story benchmark model using an active tuned mass damper and a fuzzy controller”, Engineering structures, 25, pp.1597-1610, 2003.
[30] Kim Y.M., You K.P., You J, Y., Paek S.Y. and Nam B.H., “LQR Control of Along-Wind Responses of a Tall Building using Active Tuned Mass Damper”, The 2016 World Congress on Advances in Civil, Environmental and Materials Research(ACEM16), Korea, August 2016.
[31] 呂國華，「考慮時間延遲之離散時間系統最佳直接輸出回饋控制」，國立中興大學，碩士論文，1993。
[32] 余心權，「離散時間延遲系統直接加速度回饋控制」，國立中興大學，碩士論文，2001。
[33] 甘錫瀅、張敬昌和謝紹松，「細說台北101高樓」，科學月刊，第三十八卷，第八期，690-699頁，2003。
[34] Ankireddi S. and Yang H.T.Y., “Simple ATMD Control Methodology for Tall Buildings Subject to Wind Loads”, ASCE Journal of Structural Engineering, 122, pp.83-91, 1996.
[35] Mattei M. and Ricciardelli F., “Mathematical Model for Design of Mass Dampers for Wind Excited Structures”, ASCE Journal of Engineering Mechanics, 128, pp.979-988, 2002.
[36] Kareem A., Kijewski T. and Tamura T., “Mitigation of motions of tall buildings with specific examples of recent applications”, Wind and Structures, 2, pp.201-251, 1999.
[37] Yoshiki I., “Active and semi‐active vibration control of buildings in Japan—Practical applications and verification”, Structural Control Health Monitor, 16, pp.703-723, 2009.
[38] 鍾立來、吳賴雲、李明璆、楊培堅，「東帝士85國際廣場之結構主動控制」，結構工程，第十四卷，第二期，45-65頁，2004。
[39] Sutradhar S.R., Sayadat N., Rahman A., Munira S., Haque A.K.M.F. and Sakib S.N., “IIR Based Digital Filter Design and Performance Analysis”, IEEE, International Conference on Telecommunication and Networks, 2017.
[40] Zhang C.L. and Wang A.H., “IIR Digital Filter Design Research and Simulation on MATLAB”, International Conference on Signal Processing Systems, 2012.
[41] Dhar P.K., Jun H.S. and Kim J.M., “Design and implementation of digital filters for audio signal processing”, IEEE, Third International Forum on Strategic Technologies, August 2008.
[42] Shoucri R. and Benesch R., “On the computation of digital filter coefficients”, SAGE journals SIMULATION, 48, pp.103-105, Kingston, Ontario, Canada, March 1987.
[43] Cong C., “Decentralized control of vibrations in wind turbines using multiple active tuned mass dampers with stroke constraint”, SAGE journals Advances in Mechanical Engineering, 10, pp.1-12, Beijing, China, December 2018.
[44] Cong C., “Using active tuned mass dampers with constraint stroke to simultaneously control vibrations in wind turbine blades and tower”, SAGE journals Advances in Mechanical Engineering, 22, pp.1544-1553, Beijing, China, May 2019.
[45] Li T. and Xia G., “Wind-induced vibration control of power transmission tower using pounding tuned mass damper”, Journal of Vibroengineering, 17, pp.3693-3701, Jinan, November 2015.
[46] Kwon J.S., Chang S.P. and Yoo H., “Restrained Stroke Active Tuned Mass Damper”, Journal of the Earthquake Engineering Society of Korea, 9, pp.9-22, Korea, June 2005.
[47] Soong T.T. and Dargush G.F., “Passive Energy Dissipation Systems in Structural Engineering”, New York, 1997.
[48] Chung L.L., Lin C.C. and Chu S.Y., “Optimal discrete-time structural control using direct output feedback”, Engineering Structures, 18, pp.472-480, 1996.
[49] Lin C.C. and Soong T.T., “Seismic Protection of Structures Using Tuned Mass Dampers with Resettable Variable Stiffness”, Advances in Science and Technology, 83, pp 75-84, 2013.
[50] Chopra A.K., Dynamics of Structures Theory and Applications to Earthquake Engineering, Fourth edition, New York, Pearson, 2015.
[51] Hibbeler R.C., Mechanics of Materials, Tenth edition, Pearson, January 2017.