Near-Optimal Control for Offshore Structures with Nonlinear Energy Sink Mechanisms

To improve the safety and reliability of offshore structures subject to wave loading, the active vibration control problem is always one of significant issues in the field of ocean engineering. This paper deals with the near–optimal control problem of offshore structures with a nonlinear energy sink (NES) mechanism. By taking the dominant vibration mode of the offshore structure with the NES into account, a nonlinear dynamic model of the steel–jacket structure subject to wave loading is presented first. Then, using the parameter perturbation approach to solve a nonlinear two–point boundary value problem, an NES–based optimal controller with the form of infinite series sum is presented to suppress the vibration of the offshore structure. Third, an iteration algorithm is provided to obtain the near–optimal controller. Simulation results demonstrate that the NES–based near–optimal controller can mitigate the oscillation amplitude of offshore structures significantly. Moreover, the NES–based optimal controller outperforms the one based on active tuned mass damper.