Performance‐based near‐optimal vibration control for nonlinear offshore platforms with delayed input

Abstract

This paper investigates the vibration control problem for offshore platform, where the nonlinear characteristics, delayed input and external wave force are considered in time domain. By introducing a delay‐free reconstructional vector and applying the maximum principle, the original vibration problem for offshore platform is formulated as a nonlinear two‐point‐boundary‐value (TPBV) problem with delayed items. The major contribution of this paper is that a performance‐based near‐optimal vibration control strategy is proposed by solving this nonlinear TPBV problem, which includes a feedback item with offshore platform system state, a feedforward item with wave force state, and a compensator for nonlinear and delayed items with infinite supersensitive component. In particular, the designed compensator is calculated from two group series of linear differential equations by introducing a parameter for expending the Maclaurin series of nonlinear and delay items. Meanwhile, an iterative algorithm is designed to make the proposed vibration control scheme computable based on the control performance in each iterative procedure. Finally, experimental results show that the displacement, velocity and performance index of an employed offshore platform achieved small values under the proposed control strategy and designed algorithm.

Reinforcement learning-based optimal fault-tolerant control for offshore platforms

“…, where v is the horizontal velocity of the wave, which includes n components. As shown in Zhong et al, 10 if each wave velocity component is…”

“…Note v ¯ = [ v ¯ 1 , v ¯ 2 , v ¯ 3 , . . . , v ¯ n ] , where v ¯ is the horizontal velocity of the wave, which includes n components. As shown in Zhong et al, 10 if each wave velocity component is v ¯ i = A ¯ i cos ( − ω ¯ i t + ζ i ) , where A ¯ i and ζ i are the wave amplitude and random phase angle, v ¯...…”

“…and considering equations (6) and (7), f ( t ) , as demonstrated in Zhong et al, 10 is calculated as the output of the following exosystem…”

“…In Cao et al, 9 Hybrid-Driven-Based H Control is used for a linear offshore platform with irregular wave force. In Zhong et al, 10 with delayed control input, optimal vibration control is proposed for nonlinear offshore platforms. In Sarrafan et al, 11 a neuro-fuzzy control scheme was developed to mitigate wave-induced forces with magnetorheological dampers, and in Feng et al, 12 the steel-jacket offshore platform structure with the time-varying jacket platform mass was considered.…”