Robust adaptive sliding mode control based on wavelet kernel principal component for offshore steel jacket platforms subject to nonlinear wave-induced force

Abstract

This paper is concerned with adaptive integral sliding mode control (AISMC) based on a wavelet kernel support vector machine for offshore steel jacket platform subject to nonlinear wave-excited force and parameter perturbations. The sliding mode control technique is combined with adaptive control algorithm and wavelet support vector machine to achieve the desired attenuation on the wave-induced vibration and to limit the displacement of offshore platforms. In this method, wavelet kernel support vector machine is used to establish the adaptive controller and an on-line learning rule for the weighting vector and bias is derived. The most important feature of the proposed control strategy is its inherent robustness and its ability to handle the nonlinear behavior of the offshore platform. By means of this control scheme the performance of the AISMC has been improved. The performance of the proposed control strategy is compared with some existing control schemes. It is demonstrated that the proposed control scheme in this paper is more effective in improving the control performance of the offshore platform. This controller is designed based on solving a set of linear matrix inequalities. It has been illustrated through simulation results that the proposed control scheme is effective in improving the control performance of offshore platforms.

Digital-Control-Based Approximation of Optimal Wave Disturbances Attenuation for Nonlinear Offshore Platforms

“…Noting the parameters of (25) and (28), we can obtain the Riccati Equation (18) and Stein Equation (19). Because the pair (A, B) is controllable, it can be claimed that P 1 is the unique positive-semi-definite solution of (28).…”

“…Noting (11) and the first formula (26), we have that all of the eigenvalues of (A T P 1 S −1 BR −1 B T ) satisfy λ i (A T P 1 S −1 BR −1 B T ) < 1. Therefore, P 2 is the unique solution of the Stein matrix (19).…”

“…Unfortunately, the unsafely behaviors and destabilization of offshore platforms mainly result from nonlinear dynamics. Many researchers have engaged in the efforts to the implementation of control schemes for nonlinear offshore platforms, e.g., a robust mixed control method for wave-excited offshore jacket platforms is proposed in [17] to minimize the upper bound of the performance measure on platform dynamics satisfying some norm bound constraint simultaneously; a novel sliding mode control scheme is proposed by using information about mixed current and delayed states in [18]; by combining a sliding mode control technique, the adaptive control algorithm and wavelet support vector machine, an adaptive integral sliding mode control to handle the nonlinear behavior of the offshore platform in [19]. Meanwhile, the optimal vibration control theories provide efficient methods to improve the control performance of control systems with smaller control consumption [20][21][22][23].…”

Delayed adaptive output feedback sliding mode control for offshore platforms subject to nonlinear wave-induced force

“…It has been proved that appropriate selection of time delay is capable of reducing vibrations in dynamic systems. In the first control scheme, an adaptive output feedback integral sliding mode controller (AOF-ISMC) is designed for offshore steel jacket platforms subject to nonlinear wave-induced force by using an integral sliding mode controller and an adaptation technique (Li and Xu, 2010;Xiao et al, 2012;Pai, 2010;Nourisola and Ahmadi, 2014) to reduce oscillation amplitudes of the floors. In the second method, we will intentionally introduce a constant time delay into control channel to design a delayed adaptive output feedback integral sliding mode controller (DAOF-ISMC).…”

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

“…The basic object of active vibration control is to eliminate the displacement and velocity of offshore platform with smaller control energy. Thus the optimal vibration control problem has been a hot research topic from establishing the mathematical model with active actuator to the active vibration controller design for offshore platform, such as robust controller [4] and observer‐based optimal fault‐tolerant controller [5] design for continuous‐time model of offshore platform, feedback and feeforward optimal controller [6] and tracking controller [7] design for discrete‐time model of offshore platform, event‐triggered H∞ controller [8] and delay‐dependent state feedback controller [9] design for network‐based offshore platform systems, and the references therein.…”