Robust unified dissipativity vibration control design for offshore steel jacket platform in ocean environments under self-excited nonlinear wave force

Abstract

This paper addresses the challenge of delayed proportional integral control (DPIC) of an offshore steel jacket platform (OSJP) subjected to a self-excited nonlinear wave force and structural uncertainty using the unified criteria. By introducing discrete and distributed state delays in the control input, a DPIC was established to stabilize the OSJPs. The goal of this study is to design a proper controller that will stabilize the dynamic of an OSJP while subjected to structural uncertainty and nonlinear wave force. The OSJP is investigated as a nonlinear dynamics with mixed state delays, allowing us to study its robust asymptotic stability using the Lyapunov-Krasovskii function (LKF) in the context of the extended dissipativity performance index. A novel closed-loop system-based stability criterion is derived as a result of using tighter integral inequalities to estimate the upper bounds of the delay and influential control gains can be achieved if a set of linear matrix inequalities (LMIs) is checked by simulation results, that the proposed control scheme can significantly improve the control’s performance. Finally, it was demonstrated that the proposed control approach is more effective and multi-dynamic performances have been illustrated through the comparisons to previously published results in the literature.