Smart Structures and Systems

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Optimization of LQR method for the active control of seismically excited structures

  • Moghaddasie, Behrang (Department of Civil Engineering, Ferdowsi University of Mashhad) ;
  • Jalaeefar, Ali (Department of Civil Engineering, North Tehran Branch, Islamic Azad University)
  • Received : 2018.06.24
  • Accepted : 2019.01.19
  • Published : 2019.03.25
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Abstract

This paper introduces an appropriate technique to estimate the weighting matrices used in the linear quadratic regulator (LQR) method for active structural control. For this purpose, a parameter is defined to regulate the relationship between the structural energy and control force. The optimum value of the regulating parameter, is determined for single degree of freedom (SDOF) systems under seismic excitations. In addition, the suggested technique is generalized for multiple degrees of freedom (MDOF) active control systems. Numerical examples demonstrate the robustness of the proposed method for controlled buildings under a wide range of seismic excitations.

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References

  1. Akhiev, S.S., Aldemir, U. and Bakioglu, M. (2002), "Multipoint instantaneous optimal control of structures", Comput. Struct., 80(11), 909-917. https://doi.org/10.1016/S0045-7949(02)00059-7
  2. Alavinasab, A., Moharrami, H. and Khajepour, A. (2006), "Active control of structures using energy-based LQR method", Comput.-Aided Civil Infrastruct. Eng., 21(8), 605-611. https://doi.org/10.1111/j.1467-8667.2006.00460.x
  3. Aldemir, U. (2009), "Evaluation of disturbance weighting parameter of minimax attenuation problems", Comput.-Aided Civil Infrastruct. Eng., 24(4), 302-308. https://doi.org/10.1111/j.1467-8667.2008.00590.x
  4. Aldemir, U. and Bakioglu, M. (2001), "Active structural control based on the prediction and degree of stability", J. Sound Vib., 247(4), 561-576. https://doi.org/10.1006/jsvi.2001.3689
  5. Aldemir, U., Bakioglu, M. and Akhiev, S.S. (2001), "Optimal control of linear buildings under seismic excitations", Earthq. Eng. Struct. D., 30(6), 835-851. https://doi.org/10.1002/eqe.41
  6. Aldemir, U., Yanik, A. and Bakioglu, M. (2012), "Control of structural response under earthquake excitation", Comput.-Aided Civil Infrastruct. Eng., 27(8), 620-638. https://doi.org/10.1111/j.1467-8667.2012.00776.x
  7. Amini, F., Hazaveh, N.K. and Rad, A.A. (2013), "Wavelet PSObased LQR algorithm for optimal structural control using active tuned mass dampers", Comput.-Aided Civil Infrastruct. Eng., 28(7), 542-557. https://doi.org/10.1111/mice.12017
  8. Amini, F. and Samani, M.Z. (2014), "A wavelet-based adaptive pole assignment method for structural control", Comput. -Aided Civil Infrastruct. Eng., 29(6), 464-477. https://doi.org/10.1111/mice.12072
  9. Amini, F. and Vahdani, R. (2008), "Fuzzy optimal control of uncertain dynamic characteristics in tall buildings subjected to seismic excitation", J. Vib. Control, 14(12), 1843-1867. https://doi.org/10.1177/1077546308091206
  10. Anderson, B.D.O. and Moore, J.B. (1989), Optimal Control: Linear Quadratic Methods, Prentice Hall, Eaglewood Cliffs, New Jersey.
  11. Assimakis, N.D., Lainiotis, D.G., Katsikas, S.K. and Sanida, F.L. (1997), "A survey of recursive algorithms for the solution of the discrete time Riccati equation", Nonlinear Anal. Theory, Methods Appl., 30(4), 2409-2420. https://doi.org/10.1016/S0362-546X(97)00062-X
  12. Bahar, O., Banan, M.R., Mahzoon, M. and Kitagawa, Y. (2003), "Instantaneous optimal wilson-${\theta}$ control method", J. Eng. Mech. - ASCE, 129(11), 1268-1276. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:11(1268)
  13. Bakioglu, M. and Aldemir, U. (2001), "A new numerical algorithm for sub-optimal control of earthquake excited linear structures", Int. J. Numer. Meth. Eng., 50(12), 2601-2616. https://doi.org/10.1002/nme.137
  14. Bani-Hani, K. and Ghaboussi, J. (1998), "Neural networks for structural control of a benchmark problem, active tendon system", Earthq. Eng. Struct. D., 27(11), 1225-1246. https://doi.org/10.1002/(SICI)1096-9845(1998110)27:11<1225::AID-EQE780>3.0.CO;2-T
  15. Barbosa, F.S. and Battista, R.C. (2007), "A numerical tool for solving Riccati equation applied to modal optimal control of structures", Struct. Control Health Monit., 14(6), 915-930. https://doi.org/10.1002/stc.194
  16. Braz-Cesar, M.T. and Barros, R. (2018), "Semi-active fuzzy based control system for vibration reduction of a SDOF structure under seismic excitation", Smart Struct. Syst., 21(4), 389-395. https://doi.org/10.12989/SSS.2018.21.4.389
  17. Cao, H. and Li, Q.S. (2004), "New control strategies for active tuned mass damper systems", Comput. Struct., 82(27), 2341-2350. https://doi.org/10.1016/j.compstruc.2004.05.010
  18. Chang, S., Kim, D., Kim, D.H. and Kang, K.W. (2012), "Earthquake response reduction of building structures using learning-based lattice pattern active controller", J. Earthq. Eng., 16(3), 317-328. https://doi.org/10.1080/13632469.2011.626104
  19. Chase, J.G. and Smith, H.A. (1996), "Robust $H{\infty}$ control considering actuator saturation. I: theory", J. Eng. Mech. - ASCE, 122(10), 976-983. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:10(976)
  20. Cheng, F.Y., Jiang, H. and Lou, K. (2010), Smart Structures: Innovative Systems for Seismic Response Control, CRC Press, New York, USA.
  21. Choi, C.H. (1990), "A survey of numerical methods for solving matrix Riccati differential equations", Southeastcon'90. Proceedings., IEEE.
  22. Chung, L.L., Lin, C.C. and Lu, K.H. (1995), "Time-delay control of structures", Earthq. Eng. Struct. D., 24(5), 687-701. https://doi.org/10.1002/eqe.4290240506
  23. Datta, T.K. (2003), "A state-of-the-art review on active control of structures", ISET J. Earthq. Technol., 40(1), 1-17.
  24. Davison, E.J. and Maki, M.C. (1973), "The numerical solution of the matrix Riccati differential equation", IEEE T. Autom. Control, 18(1), 71-73. https://doi.org/10.1109/TAC.1973.1100210
  25. de Souza, L.C.G. (2006), "Design of satellite control system using optimal nonlinear theory", Mech. Based Des. Struct., 34(4), 351-364. https://doi.org/10.1080/15397730601044853
  26. Fisco, N.R. and Adeli, H. (2011), "Smart structures: Part I-Active and semi-active control", Scientia Iranica, Transaction A: Civil Eng., 18(3), 275-284. https://doi.org/10.1016/j.scient.2011.05.034
  27. Fisco, N.R. and Adeli, H. (2011), "Smart structures: Part II-Hybrid control systems and control strategies", Scientia Iranica, Transaction A: Civil Eng., 18(3), 285-295. https://doi.org/10.1016/j.scient.2011.05.035
  28. Fu, T.S. and Johnson, E.A. (2017), "Semiactive control for a distributed mass damper system", Struct. Control Health Monit., 24(4), e1888. https://doi.org/10.1002/stc.1888
  29. Gluck, N., Reinhorn, A.M., Gluck, J. and Levy, R. (1996), "Design of supplemental dampers for control of structures", J. Struct. Eng. - ASCE, 122(12), 1394-1399. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:12(1394)
  30. Guoping, C. and Jinzhi, H. (2002), "Optimal control method for seismically excited building structures with time-delay in control", J. Eng. Mech. - ASCE, 128(6), 602-612. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:6(602)
  31. Hashemi, S.M.A., Haji Kazemi, H. and Karamodin, A. (2016), "Localized genetically optimized wavelet neural network for semi-active control of buildings subjected to earthquake", Struct. Control Health Monit., 23(8), 1074-1087. https://doi.org/10.1002/stc.1823
  32. Jang, D.D., Jung, H.J. and Moon, Y.J. (2014), "Active mass damper system using time delay control algorithm for building structure with unknown dynamics", Smart Struct. Syst., 13(2), 305-318. https://doi.org/10.12989/sss.2014.13.2.305
  33. Kim, S.B. and Yun, C.B. (2000), "Sliding mode fuzzy control: Theory and verification on a benchmark structure", Earthq. Eng. Struct. D., 29(11), 1587-1608. https://doi.org/10.1002/1096-9845(200011)29:11<1587::AID-EQE974>3.0.CO;2-W
  34. Korkmaz, S. (2011), "A review of active structural control: challenges for engineering informatics", Comput. Struct., 89(23), 2113-2132. https://doi.org/10.1016/j.compstruc.2011.07.010
  35. Lee, J.D., Shen, S., Manzari, M.T. and Shen, Y.L. (2008), "Structural control algorithms in earthquake resistant design", J. Earthq. Eng., 4(1), 67-96. https://doi.org/10.1080/13632460009350363
  36. Lee, S.H., Min, K.W., Hwang, J.S. and Kim, J. (2004), "Evaluation of equivalent damping ratio of a structure with added dampers", Eng. Struct., 26(3), 335-346. https://doi.org/10.1016/j.engstruct.2003.09.014
  37. Li, Z. and Adeli, H. (2016), "New discrete-time robust H2/$H{\infty}$ algorithm for vibration control of smart structures using linear matrix inequalities", Eng. Appl. Artif. Intel., 55, 47-57. https://doi.org/10.1016/j.engappai.2016.05.008
  38. Lu, L.T., Chiang, W.L. and Tang, J.P. (1998), "LQG/LTR control methodology in active structural control", J. Eng. Mech. - ASCE, 124(4), 446-454. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:4(446)
  39. Lynch, J.P. and Law, K.H. (2002), "Market-based control of linear structural systems", Earthq. Eng. Struct. D., 31(10), 1855-1877. https://doi.org/10.1002/eqe.193
  40. Ma, T.W. and Yang, H.T.Y. (2004), "Adaptive feedbackfeedforward control of building structures", J. Eng. Mech. - ASCE, 130(7), 786-793. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:7(786)
  41. Marco, A., Hennig, P., Bohg, J., Schaal, S. and Trimpe, S. (2016), "Automatic LQR tuning based on Gaussian process global optimization", Proceedings of the International Conference on Robotics and Automation (ICRA 2016), IEEE.
  42. Mariani, C. and Venini, P. (1998), "On the use of stochastic models of uncertainty in active control and structural optimization", Comput. Struct., 67(1), 105-117. https://doi.org/10.1016/S0045-7949(97)00162-4
  43. Materazzi, A.L. and Ubertini, F. (2012), "Robust structural control with system constraints", Struct. Control Health Monit., 19(3), 472-490. https://doi.org/10.1002/stc.447
  44. Miller, R.K., Masri, S.F., Dehghanyar, T.J. and Caughey, T.K. (1988), "Active vibration control of large civil structures", J. Eng. Mech. - ASCE, 114(9), 1542-1570. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:9(1542)
  45. Min, K.W., Hwang, J.S., Lee, S.H. and Chung, L. (2003), "Probabilistic approach for active control based on structural energy", Earthq. Eng. Struct. D., 32(15), 2301-2318. https://doi.org/10.1002/eqe.327
  46. Miyamoto, K., She, J., Imani, J., Xin, X. and Sato, D. (2016), "Equivalent-input-disturbance approach to active structural control for seismically excited buildings", Eng. Struct., 125, 392-399. https://doi.org/10.1016/j.engstruct.2016.07.028
  47. Miyamoto, K., She, J., Sato, D. and Yasuo, N. (2018), "Automatic determination of LQR weighting matrices for active structural control", Eng. Struct., 174, 308-321. https://doi.org/10.1016/j.engstruct.2018.07.009
  48. Morales-Beltran, M. and Paul, J. (2015), "Technical note: active and semi-active strategies to control building structures under large earthquake motion", J. Earthq. Eng., 19(7), 1086-1111. https://doi.org/10.1080/13632469.2015.1036326
  49. Nguyen, T.A. and Bestle, D. (2007), "Application of optimization methods to controller design for active suspensions", Mech. Based Des. Struct., 35(3), 291-318. https://doi.org/10.1080/15397730701421621
  50. Ohtori, Y., Christenson, R.E., Spencer Jr., B.F. and Dyke, S.J. (2004), "Benchmark control problems for seismically excited nonlinear buildings", J. Eng. Mech. - ASCE, 130(4), 366-385. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:4(366)
  51. Park, K.S. and Ok, S.Y. (2015), "Modal-space reference-modeltracking fuzzy control of earthquake excited structures", J. Sound Vib., 334, 136-150. https://doi.org/10.1016/j.jsv.2014.09.009
  52. Pnevmatikos, N.G. and Gantes, C.J. (2011), "Influence of time delay and saturation capacity to the response of controlled structures under earthquake excitations", Smart Struct. Syst., 8(5), 449-470. https://doi.org/10.12989/sss.2011.8.5.449
  53. Reinhorn, A.M., Lavan, O. and Cimellaro, G.P. (2009), "Design of controlled elastic and inelastic structures", Earthq. Eng. Eng. Vib., 8(4), 469-479. https://doi.org/10.1007/s11803-009-9126-0
  54. Reinhorn, A.M., Soong, T.T., Riley, M.A., Lin, R.C., Aizawa, S. and Higashino, M. (1993), "Full-scale implementation of active control. II: Installation and performance", J. Struct. Eng. - ASCE, 119(6), 1935-1960. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:6(1935)
  55. Sajeeb, R., Manohar, C.S. and Roy, D. (2007), "Use of particle filters in an active control algorithm for noisy nonlinear structural dynamical systems", J. Sound Vib., 306(1), 111-135. https://doi.org/10.1016/j.jsv.2007.05.043
  56. Schmitendorf, W.E., Jabbari, F. and Yang, J.N. (1994), "Robust control techniques for buildings under earthquake excitation", Earthq. Eng. Struct. D., 23(5), 539-552. https://doi.org/10.1002/eqe.4290230506
  57. Shukla, P., Ghodki, D., Manjarekar, N.S. and Singru, P.M. (2016), "A Study of H infinity and H2 synthesis for active vibration control", IFAC-PapersOnLine, 49(1), 623-628.
  58. Singh, M.P., Matheu, E.E. and Suarez, L.E. (1997), "Active and semi-active control of structures under seismic excitation", Earthq. Eng. Struct. D., 26(2), 193-213. https://doi.org/10.1002/(SICI)1096-9845(199702)26:2<193::AID-EQE634>3.0.CO;2-#
  59. Song, G., Lin, J., Williams, F.W. and Wu, Z. (2006), "Precise integration strategy for aseismic LQG control of structures", Int. Int. J. Numer. Meth. Eng., 68(12), 1281-1300. https://doi.org/10.1002/nme.1765
  60. Soong, T.T. (1988), "State-of-the-art review: Active structural control in civil engineering", Eng. Struct., 10(2), 74-84. https://doi.org/10.1016/0141-0296(88)90033-8
  61. Soong, T.T., Reinhorn, A.M., Wang, Y.P. and Lin, R.C. (1991), "Full-scale implementation of active control. I: Design and simulation", J. Struct. Eng. - ASCE, 117(11), 3516-3536. https://doi.org/10.1061/(ASCE)0733-9445(1991)117:11(3516)
  62. Soong, T.T. and Spencer Jr., B.F. (2000), "Active, semi-active and hybrid control of structures", Bull. New Zealand National Soc. Earthq. Eng., 33(3), 387-402. https://doi.org/10.5459/bnzsee.33.3.387-402
  63. Spencer Jr., B.F. and Nagarajaiah, S. (2003), "State of the art of structural control", J. Struct. Eng. - ASCE, 129(7), 845-856. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:7(845)
  64. Spencer Jr., B.F. and Sain, M.K. (1997), "Controlling buildings: a new frontier in feedback", IEEE Control Syst. Mag. Emerg. Technol., 17(6), 19-35.
  65. Symans, M.D. and Constantinou, M.C. (1999), "Semi-active control systems for seismic protection of structures: a state-ofthe-art review", Eng. Struct., 21(6), 469-487. https://doi.org/10.1016/S0141-0296(97)00225-3
  66. Tarantino, J., Bruch Jr., J.C. and Sloss, J.M. (2004), "Instantaneous optimal control of seismically-excited structures using a maximum principle", J. Vib. Control, 10(8), 1099-1121. https://doi.org/10.1177/1077546304042749
  67. Teng, J., Xing, H.B., Lu, W., Li, Z.H. and Chen, C.J. (2016), "Influence analysis of time delay to active mass damper control system using pole assignment method", Mech. Syst. Signal Pr., 80, 99-116. https://doi.org/10.1016/j.ymssp.2016.04.008
  68. Wang, N. and Adeli, H. (2015), "Self-constructing wavelet neural network algorithm for nonlinear control of large structures", Eng. Appl. Artif. Intel., 41, 249-258. https://doi.org/10.1016/j.engappai.2015.01.018
  69. Wang, S.G. (2003), "Robust active control for uncertain structural systems with acceleration sensors", J. Struct. Control, 10(1), 59-76. https://doi.org/10.1002/stc.17
  70. Wang, Z., Chen, S. and Han, W. (1999), "Integrated structural and control optimization of intelligent structures", Eng. Struct., 21(2), 183-191. https://doi.org/10.1016/S0141-0296(97)90158-9
  71. Wong, K.K.F. and Hart, G.C. (1997), "Active control of inelastic structural response during earthquakes", Struct. Des. Tall Build., 6(2), 125-149. https://doi.org/10.1002/(SICI)1099-1794(199706)6:2<125::AID-TAL84>3.0.CO;2-G
  72. Wong, K.K.F. and Yang, R. (2001), "Effectiveness of structural control based on control energy perspectives", Earthq. Eng. Struct. D., 30(12), 1747-1768. https://doi.org/10.1002/eqe.76
  73. Xing, L., Tachibana, E. and Inoue, Y. (2000), "QN control method for building vibration caused by periodic excitation acting on intermediate story", Earthq. Eng. Struct. D., 29(8), 1079-1091. https://doi.org/10.1002/1096-9845(200008)29:8<1079::AID-EQE947>3.0.CO;2-1
  74. Xu, J.Y., Tang, J. and Li, Q.S. (2002), "An efficient method for the solution of Riccati equation in structural control implementation", Appl. Acoust., 63(11), 1215-1232. https://doi.org/10.1016/S0003-682X(02)00031-2
  75. Yamada, K. and Kobori, T. (2001), "Fundamental dynamics and control strategies for aseismic structural control", Int. J. Solids Struct., 38(34), 6079-6121. https://doi.org/10.1016/S0020-7683(00)00363-2
  76. Yang, J.N., Lin, S. and Jabbari, F. (2003), "H2-based control strategies for civil engineering structures", J. Struct. Control, 10(3-4), 205-230. https://doi.org/10.1002/stc.26

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