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Nonlinear Dynamics

, Volume 73, Issue 1–2, pp 1165–1186 | Cite as

Backstepping-based Lyapunov redesign control of hysteretic single degree-of-freedom structural systems

  • Mehdi Baradaran-nia
  • Ghasem Alizadeh
  • Sohrab Khanmohammadi
  • Bahman Farahmand Azar
Original Paper

Abstract

This paper considers the problem of active control design for a hysteretic single-degree-of-freedom (SDOF) structural system which is exposed to an earthquake excitation. First, backstepping-based control is used to design a controller for the structural system neglecting the effect of the earthquake disturbance. Then, Lyapunov redesign is utilized to design a robust controller for the system in the presence of the earthquake excitation. The hysteretic part of the structural system is modeled by the well-known Bouc–Wen equation, and this equation is directly utilized in the controller design. The controller is proposed for two cases: (a) when the parameters of the structure and the Bouc–Wen model are known, and (b) when these parameters are uncertain. A Lyapunov function is introduced for the closed-loop system, which guarantees the stability of the system equilibrium point. Since the controllers use the nominal and/or minimum and maximum values of the system parameters, the proposed methods are model based. Numerical evaluations are conducted to show the effectiveness of the proposed method. Seven different earthquakes are considered as the external excitations. Simulation results show that the displacement, velocity, and acceleration responses of the controlled structure are reduced significantly compared to the uncontrolled structure.

Keywords

Active structural control Bouc–Wen model Backstepping-based control Lyapunov redesign stabilization 

Notes

Acknowledgement

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which helped to improve the quality of the paper.

References

  1. 1.
    Cheng, F.Y., Jiang, H., Lou, K.: Smart Structures. Taylor & Francis, London (2008) CrossRefGoogle Scholar
  2. 2.
    Casciati, F., Magonette, G., Marazzi, F.: Technology of Semiactive Devices and Applications in Vibration Mitigation. Wiley, New York (2006) CrossRefGoogle Scholar
  3. 3.
    Zuk, W.: Kinetic structures. Civ. Eng. 39, 62–64 (1968) Google Scholar
  4. 4.
    Yao, J.T.P.: Concept of structural control. J. Struct. Div. 98, 1567–1574 (1972) Google Scholar
  5. 5.
    Symans, M.D., Constantinou, M.C.: Semi-active control systems for seismic protection of structures: a state-of-the-art review. Eng. Struct. 21, 469–487 (1999) CrossRefGoogle Scholar
  6. 6.
    Rodriguez, A., Pozo, F., Bahar, A., Acho, L., Vidal, Y., Rodellar, J.: Force-derivative feedback semi-active control of base-isolated buildings using large-scale MR fluid dampers. Struct. Control Health Monit. (2011). doi: 10.1002/stc.430 Google Scholar
  7. 7.
    Bouc, R.: Modèle mathématique d’hystérésis (A mathematical model for hysteresis). Acustica 24, 16–25 (1971) (in French) MATHGoogle Scholar
  8. 8.
    Wen, Y.: Method for random vibration of hysteretic systems. J. Eng. Mech. Div. 102, 249–263 (1976) Google Scholar
  9. 9.
    Guclu, R., Yazici, H.: Seismic-vibration mitigation of a nonlinear structural system with an ATMD through a fuzzy PID controller. Nonlinear Dyn. 58, 553–564 (2009) MATHCrossRefGoogle Scholar
  10. 10.
    Guclu, R., Yazici, H.: Self-tuning fuzzy logic control of a non-linear structural system with ATMD against earthquake. Nonlinear Dyn. 56, 199–211 (2009) MATHCrossRefGoogle Scholar
  11. 11.
    Pozo, F., Marc Montserrat, P., Rodellar, J., Acho, L.: Robust active control of hysteretic base-isolated structures: application to the benchmark smart base-isolated building. Struct. Control Health Monit. 15, 720–736 (2008) CrossRefGoogle Scholar
  12. 12.
    Ikhouane, F., Manosa, V., Rodellar, J.: Adaptive control of a hysteretic structural system. Automatica 41, 225–231 (2005) MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Acho, L., Pozo, F.: Sliding mode control of hysteretic structural systems. Int. J. Innov. Comput. Inf. Control 5, 1081–1087 (2009) Google Scholar
  14. 14.
    Ikhouane, F., Hurtado, J.E., Rodellar, J.: Variation of the hysteresis loop with the Bouc–Wen model parameters. Nonlinear Dyn. 48, 361–380 (2007) MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Ikhouane, F., Rodellar, J.: On the hysteretic Bouc–Wen model. Part I: Forced limit cycle characterization. Nonlinear Dyn. 42, 63–78 (2005) MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Ikhouane, F., Rodellar, J.: System with Hysteresis. Wiley, New York (2007) CrossRefGoogle Scholar
  17. 17.
    Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: Nonlinear and Adaptive Control Design. Wiley, New York (1995) Google Scholar
  18. 18.
    Ikhouane, F., Manosa, V., Rodellar, J.: Adaptive backstepping control of some uncertain nonlinear oscillators. In: Proc. 42nd IEEE Conf. Decis. Control, Hawaii, USA (2003) Google Scholar
  19. 19.
    Kokotovic, P.V.: The joy of feedback: nonlinear and adaptive. Control Syst. Mag. 12, 7–17 (1992) MathSciNetCrossRefGoogle Scholar
  20. 20.
    Gutmanm, S.: Uncertain dynamical systems—a Lyapunov min–max approach. Trans. Autom. Control 24, 437–443 (1979) CrossRefGoogle Scholar
  21. 21.
    Corless, M., Leitmann, G.: Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems. Trans. Autom. Control 26, 1139–1144 (1981) MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Leitmann, G.: Deterministic control of uncertain systems. Acta Astronaut. 7, 1457–1461 (1980) MATHCrossRefGoogle Scholar
  23. 23.
    Kirk, E.D.: Optimal Control Theory: An Introduction. Dover, New York (2004) Google Scholar
  24. 24.
    Tay, T., Mareels, I., Moore, J.B.: High Performance Control. Birkhäuser, Boston (1997) MATHGoogle Scholar
  25. 25.
    Smyth, A.W., Masri, S.F., Chassiakos, A.G., Caughey, T.K.: On-line parametric identification of MDOF nonlinear hysteretic systems. J. Eng. Mech. 125, 133–142 (1999) CrossRefGoogle Scholar
  26. 26.
    Caffrey, J.P., Masri, S.F., Tasbihgoo, F., Smyth, A.W., Chassiakos, A.G.: A re-configurable test apparatus for complex nonlinear dynamic systems. Nonlinear Dyn. 36, 181–201 (2004) MATHCrossRefGoogle Scholar
  27. 27.
    Rochdi, Y., Giri, F., Ilkhouane, F., Chaoui, F.Z., Rodellar, J.: Parametric identification of nonlinear hysteretic systems. Nonlinear Dyn. 58, 393–404 (2009) MATHCrossRefGoogle Scholar
  28. 28.
    Narasimhan, S., Nagarajaiah, S., Johnson, E.A., Gavin, H.P.: Smart base-isolated benchmark building. Part I: Problem definition. Struct. Control Health Monit. 13, 573–588 (2006) CrossRefGoogle Scholar
  29. 29.
    Pozo, F., Ikhouane, F., Pujol, G., Rodellar, J.: Adaptive backstepping control of hysteretic base-isolated structures. J. Vib. Control 12, 373–394 (2006) MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    Aly, A.M.: Vibration control in structures due to earthquake effects using MR dampers. M.S. dissertation, Dept. Mech. Power. Eng, Alexandria Univ, Alexandria (2005) Google Scholar
  31. 31.
    Dyke, S.J.: Seismic protection of a benchmark building using magnetorheological dampers. In: Proc. 2nd World Conf. Struct. Control, Kyoto, Japan (1998) Google Scholar
  32. 32.
    Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice Hall, New York (2002) MATHGoogle Scholar
  33. 33.
    Ikhouane, F., Manosa, V., Rodellar, J.: Dynamic properties of the hysteretic Bouc–Wen model. Syst. Control Lett. 56, 197–205 (2007) MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    Ismail, M., Ikhouane, F., Rodellar, J.: The hysteresis Bouc–Wen model, a survay. Arch. Comput. Methods Eng. 16, 161–188 (2009) MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Mehdi Baradaran-nia
    • 1
  • Ghasem Alizadeh
    • 1
  • Sohrab Khanmohammadi
    • 1
  • Bahman Farahmand Azar
    • 2
  1. 1.Control Engineering Department, Faculty of Electrical and Computer EngineeringUniversity of TabrizTabrizIran
  2. 2.Structural Engineering Department, Faculty of Civil EngineeringUniversity of TabrizTabrizIran

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