Adaptive backstepping control design for ATMD systems in nonlinear structures with nonlinear disturbance and parametric uncertainties

Active tuned mass damper (ATMD) devices are recommended in various structures to reduce vibrations. The performance of the ATMD system is closely tied to the control design utilized, according to research in the literature. The designed control input will take into account as much system dynamics as possible, making it possible to use it as a generalized controller in all similar systems. Nonlinear behavior is the natural behavior of engineering structures, and in order to obtain a more realistic and high-performance ATMD system, it can be considered as an appropriate approach to design the controller by considering the structural nonlinearities. In addition, unexpected external influences and parameter uncertainties must be taken into account during control design to ensure that control systems perform successfully in similar systems in all conditions. Therefore, in this study, the nonlinear model of the multi-story building was reconstructed by adding nonlinear disturbance to represent unknown external effects. Band-limited white noise is used as a disturbance function and Gaussian white noise is added to measured states in this study. To obtain a robust controller, unknown structural parameters are compensated for by using adaptive compensation terms. With the controller design supported by the Lyapunov-based stability analysis, the stability of the vibrating structure featuring an ATMD is theoretically guaranteed while achieving the main control goal. Performance analyses of the designed controllers are carried out with simulation studies. The efficiency of the developed Lyapunov-based controller in dampening the unwanted vibrations that occurred on the building is seen in simulation results.