Backstepping Control Using Barrier Lyapunov Function for Dynamic Positioning Control System with Passive Observer

Guoqing Xia,Bo Zhao,Jingjing Xue,Chuang Sun

doi:10.1155/2019/8709369

Guoqing Xia, Bo Zhao + Show 2 more

Open Access

https://doi.org/10.1155/2019/8709369

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Abstract

This paper presents a backstepping controller using barrier Lyapunov function (BLF) for dynamic positioning (DP) system. For safety reasons, the position and heading of DP ship are to be maintained in certain range. Thus, in this paper, a control law based on BLF and backstepping technique is proposed to limit the position and heading. The closed-loop system is proved stable in the sense of Lyapunov stability theories. In addition, since the velocities of ship are not measurable and the wave frequency (WF) motion is unavailable, a passive observer is adopted to estimate the velocities and the effect of WF motion. The simulation results show that the proposed controller can limit the position and heading of the vessel in a predefined range and verify the performance of the proposed controller and the passive observer.

Highlights

With the exploration of ocean resources such as oil and gas, dynamic positioning (DP) control system is increasingly applied in deep sea drilling operations
This paper presents a backstepping controller using barrier Lyapunov function (BLF) for dynamic positioning (DP) system
The study of DP control system focuses on nonlinearity, unmodeled dynamics, unknown environmental disturbances, input saturation, time-delay, and so on (see [1,2,3,4] (Sørensen A J, 2005; 2011; Rabanal O M R, Brodtkorb A H, Breivik M, 2016; Xia G, Xue J, Jiao J et al, 2016))

Summary

Introduction

With the exploration of ocean resources such as oil and gas, dynamic positioning (DP) control system is increasingly applied in deep sea drilling operations. The study of DP control system focuses on nonlinearity, unmodeled dynamics, unknown environmental disturbances, input saturation, time-delay, and so on (see [1,2,3,4] (Sørensen A J, 2005; 2011; Rabanal O M R, Brodtkorb A H, Breivik M, 2016; Xia G, Xue J, Jiao J et al, 2016)) Among those control strategies, backstepping method is a common technique to achieve a control law via defining error variables and a corresponding Lyapunov function of each subsystem to ensure system stability. To tackle the constraint problems, the study in [14] (Kong L, He W, Yang C et al, 2018) utilized an asymmetric time-varying BLF to the design of adaptive fuzzy neural network control, proved that closed-loop system was stable by Lyapunov stability theory, and verified the effectiveness of proposed control by comparative simulations.

Problem Formulation

Backstepping Control Using BLF

Stability Analysis

Simulation Study

Conclusions