Adaptive backstepping control with estimation for the vibration isolation of buildings

A new adaptive backstepping controller with estimation for uncertain systems is presented in this study. The uncertainties are due to an unknown control coefficient and unknown or uncertain terms included in the system equations. The backstepping control technique is preferred because it has a systematic design procedure and guarantees the stability of the system, since it is based on Lyapunov's direct method. The proposed controller is used for the vibration isolation of a nine-story building model with an active tuned mass damper installed on the top floor. The results indicate that the proposed controller effectively suppresses the vibrations of the building.