Fault-tolerant control for ships with thruster faults based on improved adaptive control allocation

Table 1. Main scale of the experimental prototype
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Table 1. Main scale of the experimental prototype
参数数值
总长$ {L_{{\mathrm{oa}}}} $/m 2.646
垂线间长$ {L_{{\mathrm{pp}}}} $/m 2.456
船宽B/m 0.874
型深D/m 0.456
吃水d/m 0.21
满载重量M/kg 267.46

Table 2. Parameters of the thruster
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Table 2. Parameters of the thruster
推进器 $ l_x/\rm{m} $ $ l_y/\rm{m} $ $ {{{u_{\min }}} /{\rm{N}}} $ $ {{{u_{\max }}} /{\rm{N}}} $
#1 −1.18 −0.17 0 60
#2 −1.18 0.17 0 60
#3 −0.77 − −20 20
#4 0.92 − −20 20
#5 1.07 − −20 20

Table 3. Experiment setup for each group

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Table 3. Experiment setup for each group

组别	类型	故障时间t/s	效率损失矩阵
实验1	仿真实验	100	${\rm{diag}} (1,1,0.5,0.5,1,1,1)$
实验1	仿真实验	300	${\rm{diag}} (1,1,0.5,0.5,1,1,0)$
实验2	模型实验	200	${\rm{diag}} (1,1,0.5,0.5,1,1,1)$
实验3	模型实验	200	${\rm{diag}} (1,1,1,1,1,1,0)$

Table 4. Simulation environment parameters

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Table 4. Simulation environment parameters

符号	数值
风速${V_{\rm{wind} }}$/（m·s−1）	4.0
风向角${\beta _{\rm{wind}}}$/rad	$ {\text{π}}/4 $
流速${V_{\rm{c}}}$/（m·s−1）	0.5
流向角${\beta _{\rm{c}}}$/rad	${\text{π}}/6$
平均波高${H_{\rm{wave}}}$/m	0.1
波浪角${\beta _{\rm{wave}}}$/rad	${\text{π}}/4$

Table 5. Relevant parameters of different CA methods

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Table 5. Relevant parameters of different CA methods

增益	ACA^[23]	IACA
$ {{\boldsymbol{A}}_{\rm{m}} } $	$ - {\rm{diag}} \left( {0.2,0.2,0.1} \right) $	$ - {\rm{diag}} \left( {0.2,0.2,0.1} \right) $
Q	$ {\rm{diag}} \left( {1,1,1} \right) $	$ {\rm{diag}} \left( {1,1,1} \right) $
P	$ {\rm{diag}} \left( {2.5,2.5,5} \right) $	$ {\rm{diag}} \left( {2.5,2.5,5} \right) $
$ {{\boldsymbol{e}}_0} $	$ {[0.1, - 0.1,0.1]^{\rm{T}} } $	$ {[0.1, - 0.1,0.1]^{\rm{T}} } $
$ {{\boldsymbol{\theta }}_0} $	$ {\left( {{{\boldsymbol{B}}^\dagger }} \right)^{\rm{T}}} $	$ {\left( {{{\boldsymbol{B}}^\dagger }} \right)^{\rm{T}}} $
$ {\boldsymbol{\varepsilon }} $	$ 0.002{\rm{diag}} \left( {1,1,1} \right) $	$ 0.002{\rm{diag}} \left( {1,1,1} \right) $
$ {{\boldsymbol{\varepsilon }}_{\rm{d}}} $	/	$ 0.01{\rm{diag}} \left( {1,1,1} \right) $

Table 6. Maximum positioning errors under three CA algorithms in experiment 1

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Table 6. Maximum positioning errors under three CA algorithms in experiment 1

方法	$ {{\max \left( {\left\| {{e_x}} \right\|} \right)} /{{\mathrm{m}}} } $	$ {{\max \left( {\left\| {{e_y}} \right\|} \right)} / {{\mathrm{m}}} } $	$ {{\max \left( {\left\| {{e_{\textit{z}}}} \right\|} \right)} / {(^\circ }}) $
QPCA	0.696 3	0.229 8	13.846 7
ACA	0.110 2	0.068 0	1.947 0
IACA	0.048 1	0.031 8	0.290 6

Table 7. Maximum positioning errors under two CA algorithms in experiment 2 and 3

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Table 7. Maximum positioning errors under two CA algorithms in experiment 2 and 3

组别	方法	$ \max \left( {\left\| {{e_x}} \right\|} \right) $/m	$ \max \left( {\left\| {{e_y}} \right\|} \right) $/m	$ \max \left( {\left\| {{e_{\textit{z}}}} \right\|} \right) $/(°)
实验2	QPCA	1.194 3	1.291 8	4.079
实验2	IACA	0.248 6	0.230 7	2.070
实验3	QPCA	1.499 1	2.550 5	11.044
实验3	IACA	0.418 9	1.501 8	2.630

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Qi LANG, Haixiang XU, Wenzhao YU, Zhe DU, Hongmei WANG, Jinlong CHEN. Fault-tolerant control for ships with thruster faults based on improved adaptive control allocation[J]. Chinese Journal of Ship Research, 2025, 20(1): 289

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