Adaptive back-stepping control on container ships for path following

doi:10.23919/JSEE.2020.000053

Abstract

Abstract:

A feedback-dominance based adaptive back-stepping (FDBAB) controller is designed to drive a container ship to follow a predefined path. In reality, current, wave and wind act on the ship and produce unwanted disturbances to the ship control system. The FDBAB controller has to compensate for such disturbances and steer the ship to track the predefined (or desired) path. The difference between the actual and the desired path along which the ship is to sail is defined as the tracking error. The FDBAB controller is built on the tracking error model which is developed based on Serret-Frenet frame transformation (SFFT). In additional to being affected by external disturbances, the ship has more outputs than inputs (under-actuated), and is inherently nonlinear. The back-stepping controller in FDBAB is used to compensate the nonlinearity. The adaptive algorithms in FDBAB is employed to approximate disturbances. Lyapunov's direct method is used to prove the stability of the control system. The FDBAB controlled system is implemented in Matlab/Simulink. The simulation results verify the effectiveness of the controller in terms of successful path tracking and disturbance rejection.

Key words: under-actuated, nonlinear, environmental disturbance, path following, Serret-Frenet frame transformation (SFFT), ship steering

Yang ZHAO, Lili DONG. Adaptive back-stepping control on container ships for path following[J]. Journal of Systems Engineering and Electronics, 2020, 31(4): 780-791.

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Coefficient	Value	Unit
$m_{11}$	544.55$\times $10$^{5}$	kg
$m_{22}$	101.34$\times $10$^{6}$	kg
$m_{33}$	242.48$\times $10$^{9}$	kg$\cdot $m$^{2}$
$d_{v1}$	248.37$\times $10$^{4}$	kg$\cdot $s$^{ - 1}$
$d_{v2}$	156.57$\times $10$^{4}$	kg$\cdot $m$^{ - 1}$
$d_{v3}$	0	kg$\cdot $s$\cdot $m$^{ - 2}$
$d_{r1}$	528.57$\times $10$^{8}$	kg$\cdot $m$^{2}$$\cdot $s$^{ - 1}$
$d_{r2}$	0	kg$\cdot $m$^{2}$
$d_{r3}$	134.98$\times $10$^{11}$	kg$\cdot $m$^{2}$$\cdot $s

Coefficient	Value
$c_1$	0.2
$c_2$	50$c_1$
$c_3$	500$c_1$
$q_1$	10
$q_2$	10
$q_3$	10

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