Bang-Bang and Semiactive Control with Variable Stiffness TMDs

Abstract

A semiactive control strategy for the vibration control of structures using a stiffness varying tuned mass damper (TMD) with application of bang-bang control force to TMD is proposed. The control strategy involves a combination of controlling the response of structure using bang-bang control with a control force applied to the TMD, and the use of the principle of minimizing the maximum value of the frequency response function (FRF) for the coupled structure-variable stiffness TMD system. The optimal tuning parameter and damping ratio for the TMD are obtained based on this principle. When the control force is applied to the TMD, the TMD is simultaneously retuned (by varying the stiffness) in real time to achieve the minimax principle for the desired level of response reduction. When the active control is ineffective or is turned off, the damper system acts as a passive TMD. The performance of the control strategy is examined under harmonic excitations and is compared to previous results on bang-bang control and minimax shaping of the FRF when the TMD is not retuned in real time. In order to examine the robustness of the controller, a wind excitation obtained from the Davenport spectrum is applied to a structure with low natural frequency. The control strategy is shown to achieve substantial response reduction with relatively low control force requirements.