Robust adaptive course-keeping control of under-actuated ships with the rudder failure

Table 1. The main parameters of Yukun
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Table 1. The main parameters of Yukun
参数数值
两柱间长L/m 105
船宽B/m 18
满载吃水T/m 5.4
方形系数C_b 0.559 5
舵叶面积A_δ /m² 11.8
排水体积V/m³ 5 710.2
重心距船舯距离x_c /m −0.51

Table 2. The parameters of mathematical model and rudder servo system
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Table 2. The parameters of mathematical model and rudder servo system
参数数值
α₁ 9.80
α₂ 10 468.90
旋回性指数K 0.32
追随性指数T 62.38
幅值饱和δ_max/(°) 30.0
速率饱和δ_max/(°)·s⁻¹ ±5.0

Table 3. The failure modes of the rudder

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Table 3. The failure modes of the rudder

故障名称	条件	类型
故障1	如果ko=1且$ \bar \delta $≠0	偏置故障
故障2	0$ \bar \delta $=0	部分失效故障(PLOE)
故障3	如果ko=0且$ \bar \delta $≠0	完全失效故障(TLOE)
故障4	如果ko=1且$ \bar \delta $=0	无故障

Table 4. Quantitative comparison of the control performance
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Table 4. Quantitative comparison of the control performance
指标参数本文算法数值文献[14]算法数值
MAE $ {\psi _{\rm{e}}}/(^\circ) $ 0.010 0.051
MAI $ \delta /(^\circ) $ 2.103 4.291
MTV $ \delta /(^\circ) $ 0.417 1.133

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Wenxin WANG, Shang LIU, Guoqing ZHANG, Xianku ZHANG. Robust adaptive course-keeping control of under-actuated ships with the rudder failure[J]. Chinese Journal of Ship Research, 2023, 18(1): 116

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