A backstepping control design for ATMD systems of building structure against earthquake excitations in the presence of parametric uncertainty

The design of a novel backstepping controller for using with active tuned mass damper (ATMD) system is investigated in this study. The main aim of this study is to design the controller for the ATMD system to reduce earthquake-induced vibrations in multistory buildings. Obtaining a generalizable control design for such systems is another important aim of this study. To reach this aim, the designed controller is based on the assumption that the system parameters are completely uncertain. The parametric uncertainty is coped with via adaptive compensation rules proposed in accordance with available system states. Effects of the control force on the displacement of the controller mass and the last floor of a multistory building are considered together. Owing to this approach, a control operation is provided in which zero convergence of the displacement of the mass of ATMD and all floors of the building can be guaranteed. Using Lyapunov-based arguments, theoretically, it has been proven that the designed controller can maintain its stability of the structure and controller mass while achieving this main control objective. The efficiency of the designed controller in terms of reaching the mentioned control objective is observed via numerical simulations. In these simulations, the designed controller is used in conjunction with an ATMD system placed on a multistory building model, and it has been shown that the controller designed in such structures can be used effectively for damping the earthquake-induced vibrations of these types of structures