本論文旨在利用二次線性調節器(LQR控制器)應用到科技廠房設備之微振動防治。建立有限元模型並透過電腦輔助程式來獲取結構物的系統參數。將得到的質量、阻尼與勁度矩陣，輸入至LQR控制器，再由LQR控制器，進一步對高科技廠房之設備進行微振動控制。分析中使用微振動等級VC-Curve，判斷高科技設備受控制前後的影響。並與被動控制的結果做比較，來判別此方法的有效性。
本研究使用兩種不同類型的機台，模擬敏感設備在高科技廠房的實際情況。於高科技設備的有限元模型，我們添加自定義的擾動力，以模擬機台本身造成的振動。在科技廠房本身則是設有軌道所引起的不規則力影響，可以將其視作環境因素。於被動控制方面，使用不同勁度的彈簧與阻尼，比較被動控制下的微振動曲線。於主動控制方面，將LQR控制器放置在模型的三個節點上，輸入自定義的權重矩陣，並給予各三個自由度的控制力。討論控制前後的微振動曲線，了解在微振動等級下LQR控制的結果的有效性。
由研究分析結果來看，被動控制可以減少由樓板傳遞至機台的微振動，但無法降低機器本身所引起的微振動。而LQR控制方法對敏感設備在科技廠房的微振動則有良好的控制結果。透過逐步分析可以看到被動控制與LQR主動控制的差異性。藉由主被動控制結合，可以克服敏感設備在科技廠房受到的微振動。電腦輔助分析程式由朱聖浩教授研究團隊所開發，分析程式及研究成果皆為公開資源。

This paper aims to apply the Linear Quadratic Regulator (LQR) to prevent and control micro-vibration in high-tech factory equipment. The finite element model is established by a computer-aided program and the system parameters of the structure are obtained. The LQR control uses the received parameters to control micro-vibration in high-tech factories. The micro-vibration level VC-Curve was used in the analysis to determine the impact of high-tech equipment before and after control. The effectiveness of this approach is discussed in comparison with the results of passive control.
In this study, two different types of machines are used to simulate the actual situation of sensitive equipment in a high-tech factory. For finite element models of high-tech equipment, we add custom irregular forces to simulate vibrations caused by the machine itself. On the other hand, in high-tech factories, there are rail irregularities as an environmental factor. In terms of passive control, different stiffness and damping parameters are used to compare the controlled micro-vibration results. In terms of LQR control, controllers are placed on three nodes of the model, with a custom weight matrix as input, each given three degrees of freedom control forces. The micro-vibration curves before and after control are discussed to understand the effectiveness of the LQR control results in preventing micro-vibration.
According to the research and analysis results, passive control can reduce the micro-vibration transmitted from the floor to the machine, but not the micro-vibration caused by the machine itself. The LQR control method has good control effects for the micro-vibration of sensitive equipment in high-tech factories. Combining active and passive control can overcome the micro-vibration of sensitive equipment in high-tech factories. The computer-aided analysis programs are developed by Shen-Haw Ju’s research team and are free to use.

[1] J. S. Hwang, Y. N. Huang, Y. H. Hung, and J. C. Huang, "Applicability of seismic protective systems to structures with vibration-sensitive equipment," JOURNAL OF STRUCTURAL ENGINEERING-ASCE, vol. 130, no. 11, pp. 1676-1684, NOV 2004, doi: 10.1061/(ASCE)0733-9445(2004)130:11(1676).
[2] C. H. Chen, T. C. Huang, and Y. Y. Ko, "In-situ ground vibration tests in Southern Taiwan Science Park," JOURNAL OF VIBRATION AND CONTROL, vol. 17, no. 8, pp. 1211-1234, JUL 2011, doi: 10.1177/1077546309356053.
[3] C. L. Lee, Y. P. Wang, and R. K. L. Su, "A study on AGV-induced floor micro-vibration in TFT-LCD high-technology fabs," STRUCTURAL CONTROL & HEALTH MONITORING, vol. 19, no. 3, pp. 451-471, APR 2012, doi: 10.1002/stc.445.
[4] C. L. Lee, Y. P. Wang, and R. K. L. Su, "Assessment of vibrations induced in factories by automated guided vehicles," PROCEEDINGS OF THE INSTITUTION OF CIVIL ENGINEERS-STRUCTURES AND BUILDINGS, vol. 166, no. 4, pp. 182-196, APR 2013, doi: 10.1680/stbu.11.00036.
[5] S. H. Ju and H. H. Kuo, "Experimental and Numerical Study of Wind-Induced Vibration in High-Tech Factories," JOURNAL OF PERFORMANCE OF CONSTRUCTED FACILITIES, vol. 34, no. 3, JUN 1 2020, Art no. 04020026, doi: 10.1061/(ASCE)CF.1943-5509.0001432.
[6] S. H. Ju, C. C. Yuantien, and W. K. Hsieh, "Study of Lead Rubber Bearings for Vibration Reduction in High-Tech Factories," APPLIED SCIENCES-BASEL, vol. 10, no. 4, FEB 2020, Art no. 1502, doi: 10.3390/app10041502.
[7] S. H. Ju, H. H. Kuo, S. W. Yu, and S. H. Ni, "Investigation of vibration induced by moving cranes in high-tech factories," JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL, vol. 39, no. 1, pp. 84-97, MAR 2020, doi: 10.1177/1461348419837416.
[8] Z. C. Yang and Y. L. Xu, "Active platform for suppressing train-induced microvibration of high tech facilities," in PROGRESS IN EXPERIMENTAL AND COMPUTATIONAL MECHANICS IN ENGINEERING, vol. 243-2, M. Geni and M. Kikuchi Eds., 2003, ch. International Conference on Experimental and Computational Mechanics in Engineering, pp. 123-128.
[9] Y. L. Xu, Z. C. Yang, J. Chen, H. J. Liu, and J. Chen, "Microvibration control platform for high technology facilities subject to traffic-induced ground motion," ENGINEERING STRUCTURES, vol. 25, no. 8, pp. 1069-1082, JUL 2003, doi: 10.1016/S0141-0296(03)00049-X.
[10] Y. L. Xu and A. X. Guo, "Microvibration control of coupled high tech equipment-building systems in vertical direction," INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, vol. 43, no. 21, pp. 6521-6534, OCT 2006, doi: 10.1016/j.ijsolstr.2006.01.004.
[11] Y. L. Xu, H. J. Liu, and Z. C. Yang, "Hybrid platform for vibration control of high-tech equipment in buildings subject to ground motion. Part 1: Experiment," EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, vol. 32, no. 8, pp. 1185-1200, JUL 10 2003, doi: 10.1002/eqe.267.
[12] Z. C. Yang, Y. L. Xu, J. Chen, and H. J. Liu, "Hybrid platform for vibration control of high-tech equipment in buildings subject to ground motion. Part 2: Analysis," EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, vol. 32, no. 8, pp. 1201-1215, JUL 10 2003, doi: 10.1002/eqe.268.
[13] Y. L. Xu and B. Li, "Hybrid platform for high-tech equipment protection against earthquake and microvibration," EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, vol. 35, no. 8, pp. 943-967, JUL 10 2006, doi: 10.1002/eqe.564.
[14] Y. L. Xu, Z. F. Yu, and S. Zhan, "Experimental study of a hybrid platform for high-tech equipment protection against earthquake and microvibration," EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, vol. 37, no. 5, pp. 747-767, APR 25 2008, doi: 10.1002/eqe.784.
[15] Y. Wang and H. J. Liu, "SIX DEGREE-OF-FREEDOM MICROVIBRATION HYBRID CONTROL SYSTEM FOR HIGH TECHNOLOGY FACILITIES," INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS, vol. 9, no. 3, pp. 437-460, SEP 2009, doi: 10.1142/S0219455409003168.
[16] X. J. Hong, S. Y. Zhu, and Y. L. Xu, "Three-dimensional vibration control of high-tech facilities against earthquakes and microvibration using hybrid platform," EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, vol. 39, no. 6, pp. 615-634, MAY 2010, doi: 10.1002/eqe.960.
[17] H. S. Kim and J. W. Kang, "Smart Platform for Microvibration Control of High-Tech Industry Facilities," INTERNATIONAL JOURNAL OF STEEL STRUCTURES, vol. 17, no. 1, pp. 155-164, MAR 2017, doi: 10.1007/s13296-016-0160-2.
[18] C. S. Tsai, Y. C. Lin, W. S. Chen, and H. C. Su, "Tri-directional shaking table tests of vibration sensitive equipment with static dynamics interchangeable-ball pendulum system," EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION, vol. 9, no. 1, pp. 103-112, MAR 2010, doi: 10.1007/s11803-010-9009-4.
[19] C. Alhan and F. Sahin, "Protecting vibration-sensitive contents: an investigation of floor accelerations in seismically isolated buildings," BULLETIN OF EARTHQUAKE ENGINEERING, vol. 9, no. 4, pp. 1203-1226, AUG 2011, doi: 10.1007/s10518-010-9236-0.
[20] M. H. Shih, W. P. Sung, and C. L. Chen, "Vibration control and shock absorption techniques for Hi-Tech manufacturing plants," STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGS, vol. 21, no. 7, pp. 505-523, JUL 2012, doi: 10.1002/tal.625.
[21] F. Casciati, J. Rodellar, and U. Yildirim, "Active and semi-active control of structures - theory and applications: A review of recent advances," JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, vol. 23, no. 11, pp. 1181-1195, JUL 2012, doi: 10.1177/1045389X12445029.
[22] M. P. Singh, E. E. Matheu, and L. E. Suarez, "Active and semi-active control of structures under seismic excitation," EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, vol. 26, no. 2, pp. 193-213, FEB 1997, doi: 10.1002/(SICI)1096-9845(199702)26:2<193::AID-EQE634>3.0.CO;2-#.
[23] M. G. Soto and H. Adeli, "Placement of control devices for passive, semi-active, and active vibration control of structures," SCIENTIA IRANICA, vol. 20, no. 6, pp. 1567-1578, DEC 2013.
[24] M. Barbieri, S. Ilanko, and F. Pellicano, "Active vibration control of seismic excitation," NONLINEAR DYNAMICS, vol. 93, no. 1, pp. 41-52, JUL 2018, doi: 10.1007/s11071-017-3853-y.
[25] M. Ramirez-Neria, J. Morales-Valdez, and W. Yu, "Active vibration control of building structure using active disturbance rejection control," JOURNAL OF VIBRATION AND CONTROL, Art no. 10775463211009377, doi: 10.1177/10775463211009377.
[26] A. Rodriguez-Torres, J. Morales-Valdez, and W. Yu, "Alternative tuning method for proportional-derived gains for active vibration control in a building structure," TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, Art no. 01423312211021052, doi: 10.1177/01423312211021052.
[27] A. Yanik, "Absolute Instantaneous Optimal Control Performance Index for Active Vibration Control of Structures under Seismic Excitation," SHOCK AND VIBRATION, vol. 2019, NOV 12 2019, Art no. 4207427, doi: 10.1155/2019/4207427.
[28] R. Kleinwort et al., "Experimental comparison of different automatically tuned control strategies for active vibration control," CIRP JOURNAL OF MANUFACTURING SCIENCE AND TECHNOLOGY, vol. 35, pp. 281-297, NOV 2021, doi: 10.1016/j.cirpj.2021.06.019.
[29] T. Watanabe, K. Yoshida, T. Shimogou, T. Suzuki, M. Kageyama, and A. Nohata, "REDUCED-ORDER ACTIVE VIBRATION CONTROL FOR HIGHRISE BUILDINGS," JSME INTERNATIONAL JOURNAL SERIES C-DYNAMICS CONTROL ROBOTICS DESIGN AND MANUFACTURING, vol. 37, no. 3, pp. 482-487, SEP 1994, doi: 10.1299/jsmec1993.37.482.
[30] C. H. Loh, P. Y. Lin, and N. H. Chung, "Experimental verification of building control using active bracing system," EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, vol. 28, no. 10, pp. 1099-1119, OCT 1999, doi: 10.1002/(SICI)1096-9845(199910)28:10<1099::AID-EQE857>3.0.CO;2-#.
[31] A. Alavinasab, H. Moharrami, and A. Khajepour, "Active control of structures using energy-based LQR method," COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, vol. 21, no. 8, pp. 605-611, NOV 2006, doi: 10.1111/j.1467-8667.2006.00460.x.
[32] K. Miyamoto, J. H. She, D. Sato, and N. Yasuo, "Automatic determination of LQR weighting matrices for active structural control," ENGINEERING STRUCTURES, vol. 174, pp. 308-321, NOV 1 2018, doi: 10.1016/j.engstruct.2018.07.009.
[33] B. Moghaddasie and A. Jalaeefar, "Optimization of LQR method for the active control of seismically excited structures," SMART STRUCTURES AND SYSTEMS, vol. 23, no. 3, pp. 243-261, MAR 2019, doi: 10.12989/sss.2019.23.3.243.
[34] Q. Xu, J. Y. Chen, J. Li, C. Y. Yuan, and C. F. Zhao, "Study on LQR control algorithm using superelement model," JOURNAL OF CENTRAL SOUTH UNIVERSITY, vol. 23, no. 9, pp. 2429-2442, SEP 2016, doi: 10.1007/s11771-016-3302-y.
[35] L. Yulianti, A. Nazra, Zulakmal, A. Bahar, and Muhafzan, "On discounted LQR control problem for disturbanced singular system," ARCHIVES OF CONTROL SCIENCES, vol. 29, no. 1, pp. 147-156, 2019, doi: 10.24425/acs.2019.127528.
[36] D. Sato, Y. L. Chen, K. Miyamoto, and J. H. She, "A spectrum for estimating the maximum control force for passive-base-isolated buildings with LQR control," ENGINEERING STRUCTURES, vol. 199, NOV 15 2019, Art no. 109600, doi: 10.1016/j.engstruct.2019.109600.
[37] J. P. Lynch and K. H. Law, "Market-based control of linear structural systems," EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, vol. 31, no. 10, pp. 1855-1877, OCT 2002, doi: 10.1002/eqe.193.
[38] U. Aldemir, M. Bakioglu, and S. S. Akhiev, "Optimal control of linear buildings under seismic excitations," EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, vol. 30, no. 6, pp. 835-851, JUN 2001, doi: 10.1002/eqe.41.
[39] K. K. F. Wong and R. Yang, "Evaluation of response and energy in actively controlled structures," EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, vol. 30, no. 10, pp. 1495-1510, OCT 2001, doi: 10.1002/eqe.74.
[40] E. E. Ungar and C. G. Gordon, "Vibration challenges in microelectronics manufacturing," Shock Vibration Information Center Shock Vibration Bulletin, pp. 51-58, 1983.
[41] E. E. Ungar and C. G. Gordon, "Vibration criteria for microelectronics manufacturing equipment," in INTER-NOISE and NOISE-CON Congress and Conference Proceedings, 1983, vol. 1983, no. 3: Institute of Noise Control Engineering, pp. 487-490.
[42] C. G. Gordon, "Generic vibration criteria for vibration-sensitive equipment," in Optomechanical Engineering and Vibration Control, 1999, vol. 3786: SPIE, pp. 22-33.
[43] H. Amick, M. Gendreau, T. Busch, and C. Gordon, "Evolving criteria for research facilities: vibration," in Buildings for Nanoscale Research and Beyond, 2005, vol. 5933: SPIE, pp. 16-28.