Null-space-based active disturbance rejection control allocation for ship autonomous berthing

系数	数值
M	$ \left[ {\begin{array}{*{20}{c}} {6.764\;4 \times {{10}^6}}&0&0 \\ 0&{1.134\;1 \times {{10}^7}}&{ - 3.401\;6 \times {{10}^7}} \\ 0&{ - 3.401\;6 \times {{10}^7}}&{4.452\;4 \times {{10}^9}} \end{array}} \right] $
D	$ \left[ {\begin{array}{*{20}{c}} {7.703\;2 \times {{10}^4}}&0&0 \\ 0&{2.545\;5 \times {{10}^5}}&{ - 2.033\;1 \times {{10}^6}} \\ 0&{ - 6.722\;4 \times {{10}^5}}&{3.848\;1 \times {{10}^8}} \end{array}} \right] $
${{\boldsymbol{M}}_0}$	$ \left[ {\begin{array}{*{20}{c}} {6 \times {{10}^6}}&0&0 \\ 0&{1 \times {{10}^7}}&{ - 3 \times {{10}^7}} \\ 0&{ - 3 \times {{10}^7}}&{4 \times {{10}^9}} \end{array}} \right] $
${{\boldsymbol{D}}_0}$	$ \left[ {\begin{array}{*{20}{c}} {8 \times {{10}^4}}&0&0 \\ 0&{3 \times {{10}^5}}&{ - 2 \times {{10}^6}} \\ 0&{ - 7 \times {{10}^5}}&{4 \times {{10}^8}} \end{array}} \right] $

Table 2. Parameter of the thruster
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Table 2. Parameter of the thruster
编号距中心位置l_i /m 最大推力/kN 推力变化率/(kN·s⁻¹)
1 4.65 1283.80 641.90
2 4.65 1283.80 641.90
3 34.39 268.52 134.26
4 32.10 268.52 134.26
5 24.69 725.20 362.60
6 33.07 268.52 134.26

Table 3. Environmental parameters

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Table 3. Environmental parameters

参数	数值
风速$ V_{\text{wind}}\text{/(m}\cdot\text{s}^{-1}\text{)} $	5.7
风向角$ \beta_{\text{wind}}/(^{\circ}\text{)} $	−30
流速$ {V_{\text{c}}}/({\mathrm{m}}\cdot {\mathrm{s}}^{-1}) $	0.2
流向角$ {\beta _{\text{c}}}/(^\circ ) $	−60
平均波高$ {H_{{\text{wave}}}}/{\mathrm{m}} $	0.2
浪向角$ {\beta _{{\text{wave}}}}/{\text{(}}^\circ {\text{)}} $	−30
主波频率$ {\omega _{{\text{0wave}}}}/({\mathrm{rad}} \cdot {\mathrm{s}}^{-1}) $	0.952

Table 4. Gains of the controller

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Table 4. Gains of the controller

参数	数值
$ {{\boldsymbol{K}}_1} $	$ {\text{diag}}\left( {\left[ {\begin{array}{*{20}{c}} {{\text{1}}{\text{.8}}}&{{\text{1}}{\text{.8}}}&{{\text{1}}{\text{.8}}} \end{array}} \right]} \right) $
$ {{\boldsymbol{K}}_2} $	$ {\text{diag}}\left( {\left[ {\begin{array}{*{20}{c}} {{\text{1}}{\text{.08}}}&{{\text{1}}{\text{.08}}}&{{\text{1}}{\text{.08}}} \end{array}} \right]} \right) $
$ {{\boldsymbol{K}}_3} $	$ {\text{diag}}\left( {\left[ {\begin{array}{*{20}{c}} {{\text{0}}{\text{.216}}}&{{\text{0}}{\text{.216}}}&{{\text{0}}{\text{.216}}} \end{array}} \right]} \right) $
$ \gamma_{_{\mathrm{W}}} $	0.005
$ K_{_{\mathrm{W}}} $	0.0002
$ {{\boldsymbol{K}}_{\text{p}}} $	$ {\text{diag}}\left( {\left[ {\begin{array}{*{20}{c}} {{\text{0}}{\text{.01}}}&{{\text{0}}{\text{.001}}}&{{\text{0}}{\text{.05}}} \end{array}} \right]} \right) $
$ {{\boldsymbol{K}}_{\text{d}}} $	$ {\text{diag}}\left( {\left[ {\begin{array}{*{20}{c}} {{\text{0}}{\text{.15}}}&{{\text{0}}{\text{.06}}}&{{\text{0}}{\text{.25}}} \end{array}} \right]} \right) $

Table 5. Results comparison of the control allocation methods of PAN, QP and PI

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Table 5. Results comparison of the control allocation methods of PAN, QP and PI

比较项	PI	PAN	QP
$ {T_{{\text{comp}}}}{\text{/s}} $	0.0293	0.0537	4.1519
$ {\delta _{{\text{AAE}}u}}/{\text{N}} $	242.61	3253.10	236.22
$ {\delta _{{\text{AAE}}v}}/{\text{N}} $	6.00×104	7.80×103	1.01×104
$ {\delta _{{\text{AAE}}r}}/\left( {{\text{N}} \cdot {\text{m}}} \right) $	1.86×106	4.99×104	1.04×102
$ {\delta _{{\text{MAE}}u}}/{\text{N}} $	1.70×105	2.67×105	1.51×105
$ {\delta _{{\text{MAE}}v}}/{\text{N}} $	5.93×105	5.92×105	5.92×105
$ {\delta _{{\text{MAE}}r}}/\left( {{\text{N}} \cdot {\text{m}}} \right) $	1.52×107	5.55×106	6.14×104

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Ling YANG, Haixiang XU, Wenzhao YU. Null-space-based active disturbance rejection control allocation for ship autonomous berthing[J]. Chinese Journal of Ship Research, 2024, 19(1): 128

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