Adaptive Control of a Base Isolated System for Protection of Building Structures

In this paper, we present two adaptive backstepping control algorithms for a second-order uncertain hysteretic structural system found in base isolation scheme for seismic active protection of building structures. The hysteretic nonlinear behavior is described by a Bouc–Wen model. The structural parameters and isolation parameters are all uncertain parameters. In the first scheme, there is no apriori information required from these parameters and the residual effect of the hysteresis is treated as a bounded disturbance. An update law is used to estimate the bound involving this partial hysteresis effect and external disturbance. In the second scheme, we further take the structure of the Bouc–Wen model describing the hysteresis into account in the controller design, if apriori knowledge on some parameters of the model is available. It is shown that not only is global stability guaranteed by the proposed controller, but also both transient and asymptotic performances are quantified as explicit functions of the design parameters so that designers can tune the design parameters in an explicit way to obtain the required closed loop behavior.