A control algorithm for nonlinear offshore structural dynamical systems

A reasonable knowledge about the response of nonlinear offshore structural systems under environmental loads is necessary but challenging. This is due to the coupling of internal forces along with external excitations. In this paper, a mathematical model of nonlinear offshore systems is studied with the intention of keeping the response close to the desired one. This is achieved using a novel sub-optimal control mechanism derived from nonlinear quadratic regulator (NQR) theory. Herein, two linearized functions of nonlinear motions—displacement and velocity—are introduced such that the parametrization of the state-dependent system matrices is obtained. By doing so, the system becomes conditioned only on the present state and therefore one needs to solve only an algebraic state-dependent Riccati problem. This results in a control law which may either be partial or full rank for the dynamical system depending on measurable states. The performance of the controller is compared with conventional NQR. The performance of the proposed control strategy is illustrated through a range of models of nonlinear offshore problems. The motions (generalized displacements and velocities) show that the proposed controller was not only able to restrict the undesirable behaviour but also provide means of shaping the transient performance.