Delayed proportional-integral control for offshore steel jacket platforms

• Published in: Journal of the Franklin Institute Vol. 356; no. 12; pp. 6373 - 6387
• Main Authors: Zhang, Bao-Lin, Cai, Zhihui, Gao, Shouwan, Tang, Gong-You
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.08.2019; Elsevier Science Ltd
• Subjects: Asymptotic methods; Closed loop systems; Computer simulation; Control systems design; Controllers; Current distribution; Feedback control; Integrals; Linear matrix inequalities; Mathematical analysis; Matrix methods; Nonlinear systems; Offshore drilling rigs; Offshore platforms; Stability analysis; Stability criteria; Systems stability
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2019.03.030

This paper is concerned with the problem of delayed proportional-integral control of an offshore platform subject to self-excited nonlinear hydrodynamic force. By using current and distributed delayed states, a delayed proportional-integral controller is designed to stabilize the offshore platform. Under such a controller, the closed-loop system of the offshore platform is modeled as a nonlinear system with discrete and distributed delays, which allows us to employ the Lyapnov–Krasovskii functional method to analyze its asymptotic stability. Since an affine Wirtinger-based inequality is exploited to estimate the derivative of the Lyapunov–Krasovskii functional, a new stability criterion for the closed-loop system is derived, based on which, suitable control gains can be designed provided that a set of linear matrix inequalities are feasible. It is found through simulation results that the proposed control scheme can improve the control performance remarkably. Moreover, (i) compared with the existing delay-free controllers, the proposed controller can reduce the required control force and the oscillation amplitudes of the platform significantly; and (ii) compared with several delayed controllers, the proposed controller requires less control cost.