﻿ 舵鳍联合动态校正最优控制自航船模试验研究
 舰船科学技术  2022, Vol. 44 Issue (14): 52-56    DOI: 10.3404/j.issn.1672-7649.2022.14.012 PDF

1. 天津航海仪器研究所九江分部，江西 九江 332007;
2. 中国船舶及海洋工程设计研究院，上海 200011

Experimental verification research on the optimal control of rudder fin joint dynamic correction with self-propelled ship model
REN Yuan-zhou1, GUO Jian2, WANG Ya-sen2, LIU Hao1, GUO Yi-ping1
1. Jiujiang Branch of Tianjin Nautical Instrument Research Institute, Jiujiang 332007, China;
2. Marine Design and Research Institute of China, Shanghai 200011, China
Abstract: Aiming at ship anti-rolling control problems, based on the self-propelled dynamic model, this paper adopted the optimal control of dynamic correction, and established the optimal rudder speed and fin speed feedback controller, state controller and dynamic corrector that are automatically dispatched with the ship speed. Taking a certain type of self-propelled ship model as the application object, the pool test under severe sea conditions has been completed. The test result shows, compared to individual control algorithm of rudder-heading control and fin-roll reduction control, the proposed joint optimal control algorithm of rudder-fin can guarantee the heading control performance index, as well as improve the heel control capability of maneuvering and roll reduction control effect under severe sea conditions.
Key words: roll reduction     rudder fin joint     self-propelled ship model     optimal control     dynamic correction
0 引　言

2008年以来，王新屏[10-11]利用MMG建模思想，建模仿真了舵鳍联合非线性数学模型，开展了舵鳍联合简捷非线性鲁棒控制技术研究。2017年，郭亦平等[12-13]等在总结分析文献基础上，开展了舵鳍联合非线性数学模型基础上的舵鳍联合最优控制和模型预测控制算法研究，仿真结果表明提出的舵鳍联合控制具有较强的环境适应性，减摇控制效果良好。

1 基于动态校正的舵鳍联合最优控制算法设计

 $\left\{ \begin{gathered} m(\dot u - vr) = X ，\\ m(\dot v + ur) = Y ，\\ {I_{xx}}\dot p = K ，\\ {I_{zz}}\dot r = N 。\\ \end{gathered} \right.$ (1)

 $\left\{ \begin{gathered} {{\dot x}_0} = u\cos \phi - v\cos \varphi \sin \phi，\\ {{\dot y}_0} = u\sin \phi + v\cos \varphi \cos \phi ，\\ \dot \varphi = p ，\\ \dot \phi = r\cos \varphi 。\\ \end{gathered} \right.$ (2)

 $\left\{ \begin{gathered} \dot v = {a_{11}}v + {a_{12}}r + {a_{14}}p + {a_{15}}\phi + {b_{11}}{\delta _r} + {b_{12}}{\delta _f} ，\\ \dot r = {a_{21}}v + {a_{22}}r + {b_{21}}{\delta _r} ，\\ \dot \varphi = r，\\ \dot p = {a_{41}}v + {a_{42}}r + {a_{44}}p + {a_{45}}\phi + {b_{41}}{\delta _r} + {b_{42}}{\delta _f}，\\ \dot \phi = p\; 。\\ \end{gathered} \right.$ (3)

 $\begin{gathered} \dot x = Ax + B\delta ，\\ y = Cx。\\ \end{gathered}$ (4)

 $\left\{ \begin{gathered} {{\dot \delta }_r} = {u_r} ，\\ {{\dot \delta }_f} = {u_f} 。\\ \end{gathered} \right.$ (5)

 $J(u) = \int_0^\infty {({{\boldsymbol {x}}^{\rm{T}}}Qx + {u^{\rm{T}}}Ru){\rm{d}}t}。$ (6)

 $\begin{split} &{u_r} = - {k_{11}}v - {k_{12}}p - {k_{13}}r - {k_{14}}\phi - {k_{15}}(\varphi - {\varphi _z}) - {k_{16}}{\delta _r} - {k_{17}}{\delta _f} ，\\ &{u_f} = - {k_{21}}v - {k_{22}}p - {k_{23}}r - {k_{24}}\phi - {k_{25}}(\varphi - {\varphi _z}) - {k_{26}}{\delta _r} - {k_{27}}{\delta _f}，\\ &K = \left[ {\begin{array}{*{20}{c}} {{k_{11}}}&{{k_{12}}}&{{k_{13}}}&{{k_{14}}}&{{k_{15}}}&{{k_{16}}}&{{k_{17}}} \\ &{{k_{21}}}&{{k_{22}}}&{{k_{23}}}&{{k_{24}}}&{{k_{25}}}&{{k_{26}}}&{{k_{27}}} \end{array}} \right]。\\[-15pt] \end{split}$ (7)

 $\begin{gathered} {u_r} = {\mu _{11}}\dot v + {\mu _{12}}\dot p + {\mu _{13}}\dot r + {\mu _{14}}p + {u_{15}}r + {\nu _{11}}(\varphi - {\varphi _z}) + {\nu _{12}}\phi ，\\ {u_f} = {\mu _{21}}\dot v + {\mu _{22}}\dot p + {\mu _{23}}\dot r + {\mu _{24}}p + {u_{25}}r + {\nu _{21}}(\varphi - {\varphi _z}) + {\nu _{22}}\phi 。\\ \end{gathered}$ (8)

 ${\boldsymbol{\mu}} = \left[ {\begin{array}{*{20}{c}} {{\mu _{11}}}&{{\mu _{12}}}&{{\mu _{13}}}&{{\mu _{14}}}&{{\mu _{15}}} \\ {{\mu _{21}}}&{{\mu _{22}}}&{{\mu _{23}}}&{{\mu _{24}}}&{{\mu _{25}}} \end{array}} \right] \text{，} {\boldsymbol{\nu}} = \left[ {\begin{array}{*{20}{c}} {{\nu _{11}}}&{{\nu _{12}}} \\ {{\nu _{21}}}&{{\nu _{22}}} \end{array}} \right] 。$

 $\left\{ \begin{gathered} \dot z = Az + B\delta + L(y - Cz)，\\ \dot \delta = Kz + {K_0}\delta + {\nu _0}y。\\ \end{gathered} \right.$ (9)

 $K = \mu (A - LC) \text{，}$
 ${K_0} = \mu B \text{，}$
 ${\nu _0} = \mu L + \nu 。$

 $\left\{ \begin{gathered} \dot p = {\alpha _ * }p + {\beta _ * }\zeta ，\\ \xi = \gamma p 。\\ \end{gathered} \right.$ (10)

 ${\boldsymbol{F}}(s) = {\boldsymbol{\gamma}} {(Is - {\alpha _ * })^{ - 1}}{{\boldsymbol{\beta}} _ * } 。$ (11)

 $\begin{split}{{\boldsymbol{\alpha} _ * }} = \left[ {\begin{array}{*{20}{c}} {{a_1}_ * }&0 \\ 0&{{a_2}_ * } \end{array}} \right] \text{，} {{\boldsymbol{\beta} _ * }} = \left[ {\begin{array}{*{20}{c}} {{\beta _{11}}}&{{\beta _{12}}} \\ {{\beta _{12}}}&{{\beta _{12}}} \end{array}} \right],\\ {{\boldsymbol{\beta _{ij}}}} = {\left[ {\begin{array}{*{20}{c}} 0&{{\beta _1}}&{{\beta _2}}&{{\beta _3}}&{{\beta _4}}&{{\beta _5}}&{{\beta _6}} \end{array}} \right]^{\rm{T}}}，\end{split}$
 ${\boldsymbol{\gamma }} = \left[ {\begin{array}{*{20}{c}} {{\gamma _{11}}}&0 \\ 0&{{\gamma _{22}}} \end{array}} \right],{\gamma _{ii}} = \left[ {\begin{array}{*{20}{c}} 0&1&0&0&0&0&0 \end{array}} \right]。$

 图 1 船舶舵鳍联合控制闭环控制方框图 Fig. 1 Close loop control block diagram of rudder/fin joint control of ship

 $\left[ {\begin{array}{*{20}{c}} {\dot z} \\ {\dot \delta } \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {A - LC}&B \\ K&{{K_0}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} z \\ \delta \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} L&{{0_{3 \times 1}}} \\ {{\nu _0}}&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} \psi \\ \xi \end{array}} \right]，$ (12)
 $\left[ {\begin{array}{*{20}{c}} \delta \\ \zeta \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{0_{1 \times 3}}}&1 \\ { - C}&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} z \\ \delta \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 0&0 \\ 1&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} \psi \\ \xi \end{array}} \right]。$ (13)

 $\left[ {\begin{array}{*{20}{c}} \delta \\ \zeta \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{T_{11}}(s)}&{{T_{12}}(s)} \\ {{T_{21}}(s)}&{{T_{22}}(s)} \end{array}} \right]\left[ \begin{gathered} \psi \\ \xi \\ \end{gathered} \right]。$ (14)

 $\xi = F(s)\zeta。$ (15)

 ${F_{\psi \delta }}(s) = {T_{11}}(s) + {T_{12}}(s)F(s){\left[ {1 - {T_{22}}(s)F(s)} \right]^{ - 1}}{T_{21}}(s)。$ (16)

 $\delta = {F_{\psi \delta }}(s)\psi。$ (17)

 ${{{{\boldsymbol{F}}}}_{_{\psi \delta }}}(j{\omega _0},{\boldsymbol{F}}) = {\boldsymbol{R}}。$ (18)

2 自航船模验证试验及结果分析

1） 规则波对比试验

 图 2 规则波下舵鳍分别控制试验曲线 Fig. 2 Trial curve controlled by rudder or fin alone under regular wave

 图 3 舵鳍联合控制试验曲线 Fig. 3 Trial curve of rudder/fin joint control

2） 不规则波对比试验

3.637 kn航速下的航向保持、舵鳍分别控制和舵鳍联合控制对比曲线如图4图6所示。

 图 4 不规则波下航向保持控制试验曲线 Fig. 4 Control test curve of heading keeping under irregular wave

 图 5 不规则波下舵鳍分别控制试验曲线 Fig. 5 Test curve controlled by rudder or fin alone under irregular wave

 图 6 不规则波下舵鳍联合控制试验曲线 Fig. 6 Test curve of rudder/fin joint control under irregular wave

1）舵鳍分别控制方式的航向稳定精度与不减摇时相差不大，说明鳍对航向保持性能的影响极小；

2）舵鳍联合控制方式的减摇率最高、减摇效果最好、比舵鳍分别控制方式的减摇率高5%以上。

3）舵鳍联合减摇控制方式中最大舵角值比不减摇时大，说明该控制方式下鳍减摇起主要作用，舵主要负责航向保持，辅助减摇。

3 结　语

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