Observer-based sliding mode H$H_\infty$ control for offshore structures with nonlinear energy sink mechanisms

It is significant to reduce the wave-induced vibration and ensure the safety of the offshore structure. This paper deals with the observer-based sliding mode H & INFIN;$H_\infty$ vibration control problem of offshore structures with nonlinear energy sink (NES) mechanisms. By considering the coupled nonlinear characteristics of unmodelled dynamics, system uncertainty, and external wave force, a more general nonlinear system model of the offshore structure equipped with an NES mechanism is presented. Then, an observer-based sliding mode H & INFIN;$H_\infty$ control scheme for the nonlinear structure-NES system is developed. The existence condition and the design algorithm of the observer-based sliding mode H & INFIN;$H_\infty$ controller are provided. Simulation results show that the observer-based sliding mode H & INFIN;$H_\infty$ controller is capable of reducing the wave-induced vibration amplitude of offshore structures effectively. Compared with the NES-based passive control, the observer-based sliding mode H & INFIN;$H_\infty$ controller can further reduce the response amplitudes of the offshore structure remarkably. In addition, the designed observer-based sliding mode H & INFIN;$H_\infty$ controller is robust the variations of structure parameters and the external wave loads, thereby presenting potential advantages of the active damping control of the offshore structure.