Adaptive control for an active mass damper of a high-rise building with input backlash

This article introduces an adaptive control for high-rise building systems afflicted by input backlash. In this approach, the input backlash is deconstructed into an expected control and a bounded but unmeasurable nonlinear errors, and an adaptive term is employed to address the nonlinear error, resulting in the inclusion of a sign function term in the controller, which leads to the chattering phenomenon. In order to avoid it and enhance control effects, adaptive inverse dynamics of backlash are introduced, and a new adaptive inverse control strategy is formulated to achieve vibration control in high-rise buildings. Under the proposed control strategy, a suitable Lyapunov function is chosen for stability analysis, affirming that the system is uniformly ultimately bounded. Finally, results from both numerical simulations and experiments substantiate the efficacy of the proposed scheme.