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


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.


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



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


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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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