Semiactive vibration control of nonlinear structures through adaptive backstepping techniques with<i>H</i>_∞performance

This article presents a new approach to the vibration mitigation problem in structures subject to seismic motions. These kinds of structures are characterised by the uncertainties of the parameters that describe their dynamics, such as stiffness and damping coefficients. Moreover, the dampers used to mitigate the vibrations caused by earthquakes are usually nonlinear devices with frictional or hysteretic dynamics. We propose an adaptive backstepping controller to account for the uncertainties and the nonlinearities. The controller is formulated in such a way that it satisfies an H ∞ performance. It is designed for a 10-storey building whose base is isolated with a frictional damper (passive device) and a magnetorheological damper (semiactive device). Controller performance is analysed through numerical simulations.