﻿ 两种船舶运动模型间参数对应转化方法
 舰船科学技术  2020, Vol. 42 Issue (10): 30-34    DOI: 10.3404/j.issn.1672-7649.2020.10.007 PDF

The transformation method of the parameters between two kinds of ship models
ZHANG Zhi-ying, LIU Yong, CHEN Yong-bing, ZHOU Gang
Electrical Engineering College, Naval University of Engineering, Wuhan 430033, China
Abstract: There are limitations of the ship model proposed by IEC62065 which is commonly used in existing detection platform of autopilot because the simplified physical parameters of propeller propulsion, fluid resistance and so on. Based on the stimulation experiment of four degree MMG model with considerable accuracy for ships, this paper complete the transformation from the MMG model to the IEC62065 model, using the method of obtaining the corresponding parameter values in the IEC62065 model by designing the MMG model simulation experiment. The simulation experiment proves the high fitting degree between the IEC62065 model and the MMG model by using this method. And a good model transformation effect is obtained.
Key words: ship model     autopilot     IEC62065 model     model transformation
0 引　言

1 船舶运动模型建立 1.1 IEC62065运动模型的建立

 \left\{ \begin{aligned} & {M_u}\dot u = X + {M_u}vr - {R_u}u \text{，}\\ & {M_v}\dot v = {M_v}ur - {R_v}v \text{，}\\ & {I_z}\dot r = {K_r}\frac{{{u_{\max }}{X^{'}}}}{L}{\delta _a} + \gamma L{R_v}(v - \gamma Lr) - {R_r}r \text{。} \end{aligned} \right. (1)

 \left\{ \begin{aligned} & {\tau _u}\dot u + u = {u_{\max }}{X^{'}} + {\tau _u}vr \text{，}\\ & {\tau _v}\dot v + v = {\tau _v}ur \text{，}\\ & {\tau _r}\dot r + r = {\tau _r}\frac{{K_r^{'}{u_{\max }}{X^{'}}}}{L}\frac{{{\delta _a}}}{{{\delta _{\max }}}} + \frac{{12\gamma (v - \gamma Lr){\tau _r}}}{{L{\tau _v}}} \text{。} \end{aligned} \right. (2)

1.2 MMG模型的建立

 \left\{ \begin{aligned} &(m + {m_{11}})\dot u - (m + {m_{22}})vr = {X_{HH}} + {X_{HP}} + {X_{HR}} \text{，}\\ &(m + {m_{22}})\dot v + (m + {m_{11}})u = {Y_H} \text{，}\\ &({I_x} + {m_{44}})\dot p = {K_H} + {K_\phi } + {K_{\dot \phi }} \text{，}\\ &({I_z} + {m_{66}})\dot r = {N_H} \text{。} \end{aligned} \right. (3)

${X_{HH}}$ 为粘性流体动力，表示为关于纵速 $u$ 的一元三次回归表达式，系数通过约束船模实验并对实验结果进行回归分析得到； ${X_{HR}}$ 为舵水动力， ${X_{HP}}$ 为螺旋桨水动力，求取办法参照平野数学模型中的计算公式。

${K_H}$ 为船体横倾力矩，本模型将作用在船体上的水动力通过泰勒级数展开，表示为关于 $v$ $r$ $\delta$ 以及其2阶、3阶量的多元函数； ${K_\phi }$ 为静扶力矩， ${K_{\dot \phi }}$ 为横倾阻尼力矩，求取办法参照平野数学模型中的计算公式。

2 模型转化方案及实验设计

1）纵移运动方程 ${\tau _u}$ 的等效求取

 $u(t) = {u_0}{e^{ - t/{\tau _u}}}\text{。}$ (4)

2）横移运动方程 ${\tau _v}$ 的等效求取

 ${\tau _v} = \frac{v}{{ur}}\text{。}$ (5)

3）首向运动模型 ${K_r}^{'}$ ${\tau _r}$ 的等效求取

 ${\tau _r}\dot r + r = {K_{}}\delta \text{，}$ (6)

 $K = \frac{r}{\delta }\text{，}$ (7)

 $r(s) = \frac{{{K_{}}\delta (s) + {\tau _r}r(0)}}{{{\tau _r}s + 1}}\text{。}$ (8)

 $r(t) = K{\delta _{ss}}(1 - {e^{ - t/{\tau _r}}}) + r(0){e^{ - t/{\tau _r}}}\text{，}$ (9)

$\delta = - {\delta _{ss}}$ ，航向变化率稳定后： $r(0) = - {K_r}{\delta _{ss}}$ ，则式（9）变形为：

 $r(t) = K{\delta _{ss}}(1 - 2{e^{ - t/{\tau _r}}})\text{，}$ (10)

 ${\tau _{\rm{r}}}{\rm{ = }}\frac{{{t}}}{{\ln 2}}\text{。}$ (11)

3 实验结果分析及转化方案改进

 图 1 5°舵角下各参数时间历史曲线 Fig. 1 The time curve of each parameter under the rudder angle of 5 degrees

 图 2 25°舵角下各参数时间历史曲线 Fig. 2 The time curve of each parameter under the rudder angle of 25 degrees

 图 3 5°舵角下各参数时间历史曲线 Fig. 3 The time curve of each parameter under the rudder angle of 5 degrees

 图 4 25°舵角下各参数时间历史曲线 Fig. 4 The time curve of each parameter under the rudder angle of 25 degrees

4 结　语

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