﻿ 两种响应型船舶运动模型的对比及适用性分析
 舰船科学技术  2016, Vol. 38 Issue (6): 14-19 PDF

The comparison and applicability analysis of two kinds of responding ship model
SUN Jian, CHEN Yong-bing, ZHOU Gang, LI Wen-kui
Electrical Engineering College, Naval University of Engineering, Wuhan 430033, China
Abstract: Ship model is the foundation and core of detection platform of autopilot. It has important significance for research and development of autopilot and design of ship motion control algorithms. There are limitations of the simplified first order linear KT equation which is commonly used in existing detection platform of autopilot because the neglect of the speed loss and the coupling relationship between transverse velocity and yawing angle. This paper introduces the ship model proposed by IEC62065. Comparison analysis on the simulation of this ship model and traditional KT equation show the application scope of the simplified first order linear KT equation. Meanwhile, this paper also introduces improved nonlinear KT equation. The simulation experiment proves the similarity between this model and the model proposed by IEC62065. And the nonlinear KT equation decreases the calculation workload.
Key words: ship model     autopilot     KT equation
0 引言

1 IEC62065 运动模型的建立及仿真试验

 图 1 船舶运动模型原理框图
1.1 推力杆和舵机模型

IEC62065 中提出的船舶运动模型将复杂的螺旋桨推进力模型简化为线性的推进装置响应方程，并进行归一化处理，经处理后的响应模型如下：

 \dot X{'} = \left\{ {\begin{aligned} & {2/{T_P},X{'} < {P_d}{'}}\text{，}\\ & {0,X{'} = {P_d}{'}}\text{，}\\ & {-2/{T_P},X{'} > {P_d}{'}}\text{。} \end{aligned}} \right. (1)

 {\dot \delta _a} = \left\{ {\begin{aligned} & {2{\delta _{\max }}/{T_\delta },{\delta _a} < {\delta _d} + \Delta }\text{，}\\ & {0,{\delta _a} = {\delta _d} + \Delta }\text{，}\\ & {-2{\delta _{\max }}/{T_\delta },{\delta _a} > {\delta _d} + \Delta }\text{。} \end{aligned}} \right. (2)

1.2 船舶运动方程

 ${M_u}\dot u = X + {M_u}vr-{R_u}u\text{。}$ (3)

 ${\tau _u}\dot u + u = {u_{\max }}X{'} + {\tau _u}vr\text{，}$ (4)

 ${M_v}\dot v = {M_v}ur-{R_v}v\text{。}$ (5)

 ${\tau _v}\dot v + v = {\tau _v}ur\text{。}$ (6)

 ${I_z}\dot r = {K_r}\frac{{{u_{\max }}X{'}}}{L}{\delta _a} + \gamma L{R_v}(v-\gamma Lr)-{R_r}r\text{。}$ (7)

 $\dot r = {K_r}{'}{\delta _a}{K_u}X{'}{\tau _u}/L{\delta _{\max }} + 12\gamma (v-\gamma Lr)/L{\tau _v}-r/{\tau _r}\text{。}$ (8)

 $\left[{\begin{array}{*{20}{c}} {\dot x}\\ {\dot y}\\ {\dot \psi } \end{array}} \right] = \left[{\begin{array}{*{20}{c}} {\cos \psi } & {-\sin \psi } & 0\\ {\sin \psi } & {\cos \psi } & 0\\ 0 & 0 & 1 \end{array}} \right]\left[{\begin{array}{*{20}{c}} u\\ v\\ r \end{array}} \right]\text{。}$ (9)
2 一阶线性 KT 方程的建立

 \left\{ \begin{aligned} & (m + {m_x})\dot u-(m + {m_y})vr = {X_H} + {X_P} + {X_R}\text{，}\\ & (m + {m_y})\dot v + (m + {m_x})ur = {Y_H} + {Y_P} + {Y_R}\text{，}\\ & ({I_{zz}} + {J_{zz}})\dot r = {N_H} + {N_P} + {N_R}\text{。} \end{aligned} \right. (10)

 \left. {\begin{aligned} {(m + {m_y})\dot v = {Y_v}v + ({Y_r}-(m + {m_x}){u_0})r + {Y_\delta }\delta }& \\ {({I_{zz}} + {J_{zz}})\dot r = {N_v}v + {N_r}r + {N_\delta }\delta }& \end{aligned}}\,\,\right\}\text{。} (11)

 $H(s) = \frac{{r(s)}}{{\delta (s)}} = \frac{{K(1 + {T_3}s)}}{{(1 + {T_1}s)(1 + {T_2}s)}}\text{，}$ (12)

 $H(s) = \frac{{r(s)}}{{\delta (s)}} = \frac{K}{{Ts + 1}}\text{，}$ (13)

 $\left. {\begin{array}{*{20}{c}} {x(t) = x(0) + \int_0^t {u\cos \psi (t){\rm d}t} }\\ [5pt] {y(t) = y(0) + \int_0^t {u\sin \psi (t){\rm d}t} } \end{array}} \right\}\text{。}$ (14)
3 两种模型的输出首摇角对比分析

2种船型的模型参数如表 1 所示。

 图 2 B 型船的 Z 型运动仿真试验

 图 3 不同舵角下首摇角时间历史曲线

 $T\dot r + r + a{r^3} = K\delta \text{，}$ (15)

 $r + a{r^3} = K\delta \text{。}$ (16)

 图 4 不同舵角下艏摇角时间历史曲线

4 结语

1）对于上述仿真实验中 B 型船这样的中速集装箱船，其受力特点是横向力作用点与船舶重心基本重合，故可以忽略横向速度对转首力矩的影响，进而两模型可以等价转换。然而对于 A 型船这样的小型高速渡轮，横向力对转首力矩的影响较大，首摇角速度与横向速度之间的耦合不可以忽略，故两运动模型输出首摇角的误差随输入舵角的变化而产生的变化较大，在 35° 舵角下，500 s 内，输出首摇角的最大误差达到 25.9%。

2）加入非线性项的一阶 KT 方程能够较好地对线性 KT 方程进行修正。在小舵角范围内误差和线性 KT 方程相近，而在 35° 舵角下，500 s 内，输出首摇角的最大误差缩小至 4.7%，可以认为与 IEC62065 提供的运动模型有较好的相似度。对于航迹航向舵自动检测平台而言，非线性的一阶 KT 方程考虑到了船舶运动方程中的非线性项，能够更好地模拟船舶的真实运动状态，同时减少了计算量，使用较为方便。

 [1] 陈永冰, 周岗, 李文魁. 舰船航迹控制系统运行检测平台的设计与实现[J]. 海军工程大学学报 , 2011, 23 (4) :38–42. CHEN Yong-bing, ZHOU Gang, LI Wen-kui. Design and implement of operation and detection platform for ship track control system[J]. Journal of Naval University of Engineering , 2011, 23 (4) :38–42. [2] 贾欣乐, 杨盐生. 舰船运动数学模型[M]. 大连: 大连海事大学出版社, 1999 : 1 -2. [3] IEC. Maritime navigation and radiocommunication equipment and systems-track control systems-operational and performance requirements, methods of testing and required test results:IEC62065-2014[S].[S.l.]:IEC, 2014. [4] 岳晋, 任光, 曹辉. 基于Simulink的船舶运动模型动态仿真研究[J]. 大连海事大学学报 , 2009, 35 (4) :13–16. YUE Jin, REN Guang, CAO Hui. Dynamic simulation of ship motion model based on Simulink[J]. Journal of Dalian Maritime University , 2009, 35 (4) :13–16. [5] GROSENBAUGH M A. Transient behavior of towed cable systems during ship turning maneuvers[J]. Ocean Engineering , 2007, 34 (11/12) :1532–1542. [6] PéREZ F L, CLEMENTE J A. The influence of some ship parameters on manoeuvrability studied at the design stage[J]. Ocean Engineering , 2007, 34 (3/4) :518–525. [7] 陈宁, 龚苏斌. 船舶回转运动仿真[J]. 舰船科学技术 , 2013, 35 (3) :9–14. CHEN Ning, GONG Su-bin. The research on the ship turning movement based on Simulink[J]. Ship Science and Technology , 2013, 35 (3) :9–14. [8] TZENG C Y, CHEN J F. Fundamental properties of linear ship steering dynamic models[J]. Journal of Marine Science and Technology , 1999, 7 (2) :79–88. [9] ABKOWITZ M A. Measurement of hydrodynamic characteristics from ship maneuvering trials by system identification[J]. SNAME Transaction , 1980, 33 (88) :283–318. [10] 孙才勤, 王心红, 许建, 等. 船舶自动舵仿真模拟器的研制[J]. 大连海事大学学报 , 2014, 40 (1) :1–4. SUN Cai-qin, WANG Xin-hong, XU Jian, et al. Research of simulator for automatic hydraulic steering gear[J]. Journal of Dalian Maritime University , 2014, 40 (1) :1–4.