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

Abstract

Summary 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.

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

“…Criteria J7 to J11 are calculated similarly to the first five criteria, but peak values are used instead of RMS values. For each criteria of performance values, less than 1.0 implies an improvement in control response compared with the uncontrolled scenario, except for the J5, J6, J11, and J12 performance indices (Ümütlü et al, 2022; Varadarajan and Nagarajaiah, 2004).…”

“…This structure is nonlinearized according to the Duffing nonlinearity rules, and this nonlinearity is explained in equations ( 1)-( 4). In the nonlinear structure, instead of the TMD damper used in the literature, optimal TMD with the same mass as the original TMD (Hacioglu & Yagiz, 2012;Ümütlü et al, 2022) and much better performance is used. Calculations for optimal TMD are taken from Krenk (2005).…”