Smart Structures and Systems

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Nonlinear optimal control for reducing vibrations in civil structures using smart devices

  • Contreras-Lopez, Joaquin (Faculty of Electrical Engineering, Universidad Michoacana de San Nicolas de Hidalgo, Ciudad Universitaria) ;
  • Ornelas-Tellez, Fernando (Faculty of Electrical Engineering, Universidad Michoacana de San Nicolas de Hidalgo, Ciudad Universitaria) ;
  • Espinosa-Juarez, Elisa (Faculty of Electrical Engineering, Universidad Michoacana de San Nicolas de Hidalgo, Ciudad Universitaria)
  • Received : 2018.03.09
  • Accepted : 2019.01.28
  • Published : 2019.03.25
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Abstract

The frequently excessive vibrations presented in civil structures during seismic events or service conditions may result in users' discomfort, or worst, in structures failure, producing economic and even human casualties. This work contributes in proposing the synthesis of a nonlinear optimal control strategy for semiactive structural control, with the main characteristic that the synthesis considers both the structure model and the semiactive actuator nonlinear dynamics, which produces a nonlinear system that requires a nonlinear controller design. The aim is to reduce the unwanted vibrations in the response of civil structures, by means of intelligent fluid semiactive actuator such as the Magnetorheological Damper (MRD), which is a device with a low level of power consumption. The civil structures for which the proposed control methodology can be applied are those admitting a state-dependent coefficient factorized representation model, such as buildings, bridges, among others. A scaled model of a three storey building is analyzed as a case study, whose dynamical response involves displacement, velocity and acceleration of each one of the storeys, subjected to the North-South component of the September 19th., 2017, Puebla-Morelos (7.1M), Mexico earthquake. The investigation rests on comparing the structural response over time for two different conditions: with no control device installed and with one MRD installed between the first floor and the ground, where a nonlinear optimal signal for the MRD input voltage is determined. Simulation results are presented to show the effectiveness of the proposed controller for reducing the building's dynamical response.

Keywords

References

  1. Alavinasab, A. and Moharrami, H. (2006), "Active control of structures using energy-based LQR method", Comput.-Aided Civil Infrastruct. Eng., 21, 605-611. https://doi.org/10.1111/j.1467-8667.2006.00460.x
  2. Anderson, B.D.O. and Moore, J.B. (1990), Optimal Control: Linear Quadratic Methods, Prentice-Hall, Englewood Cliffs, NJ, USA.
  3. Askari, M., Li, J. and Samali, B. (2016), "Semi-active control of smart building-MR damper systems using novel TSK-Inv and max-min algorithms", Smart Struct. Syst., 18 (5), 1005-1028. https://doi.org/10.12989/sss.2016.18.5.1005
  4. Banks, H.T., Lewis, B.M. and Tan, H.T. (2007), "Nonlinear feedback controllers and compensators: a state-dependent Riccati equation approach", Comput. Optim. Appl., 37(2), 177-218. https://doi.org/10.1007/s10589-007-9015-2
  5. Chen, C.W., Chiang, W.L., Hsiao, F.H. and Tsai, C.H. (2004), "$H_{\infty}$Fuzzy control of structural systems using Takagi-Sugeno fuzzy model", Proceedings of the IEEE International Conference on Mechatronics, Istanbul, Turkey, June.
  6. Chopra, A.K. (2012), Dynamics of Structures: Theory and Applications to Earthquake Engineering, (4th Ed.), Pearson, Mexico City, Mexico.
  7. Cloutier, J.R. (1997), "State-dependent Riccati equation techniques: an overview", Proceedings of the American Control Conference, Albuquerque, New Mexico, USA, June.
  8. Constantinou, M.C., Soong, T.T. and Dargush, G.F. (1998), Passive Energy Dissipation Systems for Structural Design and Retrofit, MCEER Monograph 1, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY, USA.
  9. Dyke, S.J. (1996), "Acceleration feedback control strategies for active and semi-active control systems: modeling, algorithm development, and experimental verification", Ph.D. Dissertation, Graduate School of the University of Notre Dame, Notre Dame, IN, USA.
  10. Dyke, S.J., Spencer-Jr., B.F., Sain, M.K. and Carlson, J.D. (1996), "Modeling and control of magnetorheological dampers for seismic response reduction", Smart Mater. Struct., 5, 565-575. https://doi.org/10.1088/0964-1726/5/5/006
  11. Enriquez-Zarate, J., Silva-Navarro, G. and Cabrera-Amado, A. (2015), "Semiactive vibration control in a three-story buildinglike structure using a magnetorheological damper", Dynamics of civil structures. Proceedings of the 33rd IMAC, A conference and exposition on Structural Dynamics, Bethel, CT, USA.
  12. Fisco, N.R. and Adeli, H. (2011a), "Smart structures: part I-active and semi-active control", Scientia Iranica, Transactions A: Civil Engineering, 18(3), 275-284. https://doi.org/10.1016/j.scient.2011.05.034
  13. Fisco, N.R. and Adeli, H. (2011b), "Smart structures: part IIhybrid control systems and control strategies", Scientia Iranica, Transactions A: Civil Engineering, 18(3), 285-295. https://doi.org/10.1016/j.scient.2011.05.035
  14. Floden, O., Persson, K. and Sandberg, G. (2015), "Numerical investigation of vibration reduction in multi-storey lightweight building", Dynamics of civil structures. Proceedings of the 33rd IMAC, A conference and exposition on Structural Dynamics, Bethel, CT, USA.
  15. Forrai, A., Hashimoto, S., Funato, H. and Kamiyama, K. (2001), "Structural control technology: system identification and control of flexible structures", Comput. Control Eng., 257-262.
  16. Guclu, R. (2006), "Sliding mode and PID control of a structural system against earthquake", Math. Comput. Model., 44(1-2), 210-217. https://doi.org/10.1016/j.mcm.2006.01.014
  17. Guclu, R. and Yazici, H. (2008), "Vibration control of a structure with ATMD against earthquake using fuzzy logic controllers", J. Sound Vib. 318, 36-49. https://doi.org/10.1016/j.jsv.2008.03.058
  18. Ha, Q.P., Nguyen, M.T., Li, J. and Kwok, N.M. (2013), "Smart structures with current-driven MR dampers: modeling and second-order sliding mode control", IEEE/ASME T. Mechatron., 18(6), 1702-1712. https://doi.org/10.1109/TMECH.2013.2280282
  19. Haessig, D.A. and Friedland, B. (2002), "State dependent differential Riccati equation for nonlinear estimation and control", Proceedings of the 15th IFAC World Congress, Barcelona, Spain.
  20. Hochrainer, M.J. (2015), "Active tuned liquid column gas damper in structural control", Dynamics of civil structures. Proceedings of the 33rd IMAC, A conference and exposition on Structural Dynamics, Bethel, CT, USA.
  21. Housner, G.W., Bergman, L.A., Caughey, T.K., Chassiakos, A.G., Claus, R.O., Masri, S.F., Skelton, R.E., Soong, T.T., Spencer, B.F. and Yao, J.T.P. (1997), "Structural control: past, present and future", J. Eng. Mech., 123(9), 897-971. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:9(897)
  22. Javanbakht, M. and Amini, F. (2016), "Application of simple adaptive control to an MR damper-based control system for seismically excited nonlinear buildings", Smart Struct. Syst., 18(6), 1251-1267. https://doi.org/10.12989/sss.2016.18.6.1251
  23. Jung, H.J., Spencer-Jr., B. and Ni, Y.Q. (2004), "State-of-the-art of semiactive control systems using MR fluid dampers in civil engineering applications", Struct. Eng. Mech., 17(3-4), 493-526. https://doi.org/10.12989/sem.2004.17.3_4.493
  24. Kerboua, M., Benguediab, M., Megnounif, A., Benrahou, K.H. and Kaoulala, F. (2014), "Semi active control of civil structures, analytical and numerical studies", Physics Procedia, 8th. International Conference on Material Sciences, CSM8-ISM5, 55, 301-306.
  25. Kirk, D.E. (2004), Optimal Control Theory, Dover, Mineola, NY, USA.
  26. Kori, J.G. and Jangid, R.S. (2009), "Semi-active MR dampers for seismic control of structures", Bulletin of the New Zealand Society for Earthquake Engineering, 42(3), 157-166. https://doi.org/10.5459/bnzsee.42.3.157-166
  27. Korkmaz, S. (2011), "A review of active structural control: challenges for engineering informatics", Comput. Struct., 89(23-24), 2113-2132. https://doi.org/10.1016/j.compstruc.2011.07.010
  28. Lin, L., Wenjin, C. and Qingshan, Y. (2010), "Control of seismic response of bridges by smart dampers", Proceedings of the 29th Chinese Control Conference, Beijing, China, July.
  29. Luca, S.G., Chira, F. and Rosca, V.O. (2005), "Passive, Active and Semi-active control systems in Civil Engineering", Buletinlul Institutului Politehnic Din Iasi, Constructii. Arhitectura, LI (LV)(3-4), 23-31.
  30. Maddaloni, G. and Occhiuzzi, A. (2014), "Seismic protection of structures by smart passive control system using regional algorithms", Environmental Energy and Structural Monitoring Systems (EESMS), IEEE Workshop on, Naples, Italy, September.
  31. Medina, J., Marichal, M. and Simon, M. (2008), "Desarrollo de dos modelos inversos de un amortiguador magneto-reologico para el control de vibraciones en estructuras civiles", Boletin Tecnico, Instituto de Materiales y Modelos Estructurales (IMME), Universidad Central de Venezuela, 46(2), 1-22.
  32. Nerves, A.C. and Krishnan, R. (1995), "Active control strategies for tall civil structures", Proceedings of the IEEE, International Conference on Industrial Electronics, Control, and Instrumentation, Orlando, FL, USA, November.
  33. Nezhad, S.M. and Rofooei, F.R. (2007), "Decentralized sliding mode control of multistory buildings", Struct. Des. Tall Spec. Build., 16, 181-204. https://doi.org/10.1002/tal.310
  34. Nguyen, M.T., Kwok, N.M., Ha, Q.P., Li, J. and Samali, B. (2007), "Semi-active direct control of civil structure seismic responses using magneto-rheological dampers", Proceedings of the 24th International Symposium on Automation & Robotics in Construction (ISARC), Kochi, India.
  35. Nyawako, D., Reynolds, P. and Hudson, E. (2015), "Dynamic compensators for floor vibration control", Dynamics of civil structures. Proceedings of the 33rd IMAC, A conference and exposition on Structural Dynamics, Bethel, CT, USA.
  36. Ornelas-Tellez, F., Rico-Melgoza, J.J., Espinosa-Juarez, E. and Sanchez, E.N. (2017), "Optimal and robust control in DC Microgrids", IEEE T. Smart Grid, 20(1), 38-44.
  37. Park, W., Park, K.S. and Koh, H.M. (2008), "Active control of large structures using a bilinear pole-shifting transform with $H_{\infty}$ control method", Eng. Struct., 30, 3336-3344. https://doi.org/10.1016/j.engstruct.2008.05.009
  38. Rao, S.S. (2011), Mechanical Vibrations, (5th Edition), Prentice Hall, Upper Saddle River, NJ, USA.
  39. Reza, K.M. and Fariba, H. (2017), "Implementation of Uniform Deformation Theory in semi-active control of structures using fuzzy controller", Smart Struct. Syst., 19(4), 351-360. https://doi.org/10.12989/sss.2017.19.4.351
  40. Saedi, S., Dizaji, F.S., Ozbulut, O.E. and Karaca, H.E. (2017), "Structural vibration control using high strength and damping capacity shape memory alloys", Dynamics of civil structures. Proceedings of the 35th IMAC, A conference and exposition on Structural Dynamics, Bethel, CT, USA.
  41. Saragih, R. (2010), "Designing active vibration control with minimum order for flexible structures", 8th IEEE International Conference on Control and Automation, Xiamen, China, June.
  42. Sepulchre, R., Jankovic, M. and Kokotovic, P. (1997), Constructive Nonlinear Control, Springer-Verlag, Berlin, Germany.
  43. Song, G., Sethi, V. and Li, H.N. (2006), "Vibration control of civil structures using piezoceramic smart materials: a review", Eng. Struct., 28(11), 1513-1524. https://doi.org/10.1016/j.engstruct.2006.02.002
  44. Soong, T.T. and Dargush, G.F. (1997), Passive Energy Dissipation Systems in Structural Engineering, John Wiley and Sons, New York, NY, USA.
  45. Soong, T.T. and Spencer., B.F. (2000), "Active, semi-active and hybrid control of structures", Bulletin of the New Zealand Society for Earthquake Engineering, 33(3), 387-402. https://doi.org/10.5459/bnzsee.33.3.387-402
  46. Soong, T.T. and Spencer-Jr., B.F. (2002), "Supplemental energy dissipation: state-of-the-art and state-of-the-practice", Eng. Struct., 24, 243-259. https://doi.org/10.1016/S0141-0296(01)00092-X
  47. Spencer, B.F., Dyke, S.J., Sain, M.K. and Carlson, J.D. (1997), "Phenomenological model of a magnetorheological damper", J. Eng. Mech. -ASCE, 123(3), 230-238. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:3(230)
  48. Spencer-Jr., B.F. and Sain, M.K. (1997), "Controlling buildings: a new frontier in feedback", IEEE Control Systems: Special Issue on Emerging Technologies, 17(6), 19-35. https://doi.org/10.1109/37.642972
  49. Spencer-Jr., B.F. and Soong, T.T. (1999), "New applications and development of active, semi-active and hybrid control techniques for seismic and non-seismic vibration in the USA", Proceeding of the International Post-SMiRT Conference Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control of Vibration of Structures, Cheju, Korea, August.
  50. Spiegel, M.R. and Stephens, L.J. (2008), Statistics, (4th Ed.), McGraw-Hill, New York, NY, USA.
  51. Stengel, R.F. (1994), Control and Estimation, Dover, New York, NY, USA.
  52. 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, 469-487. https://doi.org/10.1016/S0141-0296(97)00225-3
  53. Thenozhi, S. and Yu, W. (2013), "Advances in modeling and vibration control of buildings structures", Annu. Rev. Control, 37, 346-364. https://doi.org/10.1016/j.arcontrol.2013.09.012
  54. Utkin, V.I. (1990), Sliding Modes in Control and Optimization, Springer-Verlag, Berlin, Germany.
  55. Wang, Y., Utsunomiya, K. and Bortoff, S.A. (2011), "Nonlinear control design for a semi-active vibration reduction system", Proceedings of the 30th Chinese Control Conference, Yantai, China, July.
  56. Weber, F., Distl, H. and Braun, C. (2017), "Semi-active base isolation of civil engineering structures based on optimal viscous damping and zero dynamic stiffnes", Dynamics of civil structures. Proceedings of the 35th IMAC, A conference and exposition on Structural Dynamics, Bethel, CT, USA.
  57. Wen, Y.K. (1976), "Method of random vibration of hysteretic systems", J. Eng. Mech. Div. - ASCE, 102(2), 249--263. https://doi.org/10.1061/JMCEA3.0002106
  58. Williams, M. (2016), Structural Dynamics, CRC press, Taylor & Francis group, Boca Raton, FL, USA.
  59. Xu, Y.L. and He, J. (2017), Smart Civil Structures, CRC press, Taylor & Francis group, Boca Raton, FL, USA.
  60. Yakut, O. and Alli, H. (2011), "Neural based sliding-mode control with moving sliding surface for the seismic isolation of structures", J. Vib. Control, 17, 2103-2116. https://doi.org/10.1177/1077546310395964
  61. Yao, J.T.P. (1972), "Concept of structural control", J. Struct. Div., 98(7), 1567-1574. https://doi.org/10.1061/JSDEAG.0003280
  62. Zhang, J. and Roschke, P.N. (1999), "Active control of a tall structure excited by wind", J. Wind Eng. Ind. Aerod., 83(1-3), 209-223. https://doi.org/10.1016/S0167-6105(99)00073-2