﻿ 基于相位匹配的零航速减摇鳍控制策略研究
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 哈尔滨工程大学学报  2018, Vol. 39 Issue (9): 1539-1545  DOI: 10.11990/jheu.201706091 0

### 引用本文

LIANG Lihua, ZHAO Peng, ZHANG Songtao, et al. Control strategy for zero-speed fin stabilizer based on phase matching[J]. Journal of Harbin Engineering University, 2018, 39(9), 1539-1545. DOI: 10.11990/jheu.201706091.

### 文章历史

Control strategy for zero-speed fin stabilizer based on phase matching
LIANG Lihua, ZHAO Peng, ZHANG Songtao, YUAN Jia
College of Automation, Harbin Engineering University, Harbin 150001, China
Abstract: The zero-speed fin stabilizer has different force generation mechanisms in normal anti-rolling mode (NAM) and Zero-speed anti-rolling mode (ZSAM), such difference causes different control strategies. In this paper, the feedback control strategies for the two modes were obtained by analyzing the phase relationships among wave disturbance, rolling of ship, fin movement and the anti-rolling force generated on the fin on basis of the force generation mechanisms of the two working modes. By comparing with the control method of the conventional fin stabilizer, both the correctness of the control strategies in the normal anti-rolling mode and the applicability of the phase matching analysis method were verified; while the effectiveness of the control strategies obtained in the zero-speed anti-rolling mode was demonstrated through simulations and water tank test. The results show that the control strategies obtained on basis of phase matching are effective and practical, they can provide a reference for actual engineering application.
Keywords: phase matching    zero speed    rolling reduction    fin stabilizer    control strategy    hydrodynamic characteristics    numerical simulation    water tank experiment

1 零航速减摇鳍水动力特性分析

 Download: 图 1 零航速减摇鳍模型 Fig. 1 Model of zero-speed fin stabilizer
1.1 常规减摇模式

 $L = \frac{1}{2}\rho A{V^2}{C_L}\left( \alpha \right)$ (1)

 ${C_L}\left( \alpha \right) = {C_{L0}}\alpha + \frac{{{C_{DC}}}}{\Lambda }{\left( {\frac{\alpha }{{57.3}}} \right)^2}$ (2)

 ${C_{L0}} = \frac{{0.9\left( {2{\rm{ \mathsf{ π} }}} \right)\Lambda }}{{57.3[\sqrt {{\mathit{\Lambda }^2} + 4{e_0}} + 1.8]}}$ (3)

1.2 零航速模式

1.2.1 形状阻力

 ${F_{{\rm{fd}}}} = \frac{1}{6}{C_D}\rho s{\omega ^2}[{(c - {c_1})^3} - {c_1}^3]$ (4)

1.2.2 旋涡阻力

 $\begin{array}{l} {F_{vd}} = \frac{1}{6}\rho s{\omega ^2}[3{k_2}{(c - {c_1})^2} - 3k_2^2(c - {c_1}) + \\ \;\;\;\;\;\;\;(k_2^3 - c_1^3)] \end{array}$ (5)

1.2.3 附加质量力

 ${F_{{\rm{ad}}}} = \frac{1}{8}{k_a}{\rm{ \mathsf{ π} }}\rho s{c^2}(c - 2{c_1})\dot \omega$ (6)

1.2.4 总水动力

 $F = {F_{{\rm{fd}}}} + {F_{{\rm{vd}}}} + {F_{{\rm{ad}}}}$ (7)

 $F = {K_1}\omega |\omega | + {K_2}\dot \omega$ (8)

 $\left\{ \begin{array}{l} {K_1} = \frac{1}{6}{C_D}\rho s[{(c - {c_1})^3} - c_1^3] + \frac{1}{6}\rho s[3{k_2}(c - \\ \;\;\;\;\;\;\;\;{c_1}{)^2} - 3k_2^2(c - {c_1}) + (k_2^3 - c_1^3)]\\ {K_2} = \frac{1}{8}{k_a}{\rm{ \mathsf{ π} }}\rho s{c^2}(c - 2{c_1}) \end{array} \right.$ (9)

2 相位匹配分析 2.1 未减摇时船舶横摇运动

 $({I_{xx}} + \delta {I_{xx}})\ddot \phi + 2{N_u}\dot \phi + Dh\phi = W$ (10)

 Download: 图 3 常规减摇模式下船舶横摇运动相位矢量图 Fig. 3 Phase vector diagram of ship roll motion under NAM
 ${K_C} = S\exp [{\rm{i}}({\omega _e}t - {\gamma _s} + \xi )]$ (14)

1) 若采用单一信号反馈控制，则应使鳍角按横摇角速度负反馈进行控制，即

 ${K_{{\rm{C}}{{\rm{C}}_{\rm{1}}}}} = {K_{{\rm{Cvel}}}}\dot \phi$ (15)

2) 若采用多用信号反馈的复合控制，考虑到横摇角速度的微分和积分即为横摇角加速度和横摇角度，分别对应于PID控制中的P、D和I，则应将横摇角速度作为主反馈控制信号，横摇角和横摇角加速度作为辅助反馈控制信号，即

 ${K_{{\rm{C}}{{\rm{C}}_{\rm{2}}}}} = {K_{{\rm{Cang}}}}\phi + {K_{{\rm{Cvel}}}}\dot \phi + {K_{{\rm{Cacc}}}}\ddot \phi$ (16)

 $W = ({I_{xx}} + \delta {I_{xx}})\ddot \phi + (2{N_u} + {K_{{\rm{Cvel}}}})\dot \phi + Dh\phi$ (17)

2.2.2 零航速模式

 Download: 图 4 鳍的运动以及鳍上产生的水动力 Fig. 4 Fin′s movement and the hydrodynamic forces

 $\phi = {\phi _s}\exp [{\rm{i}}({\omega _e}t - {\gamma _s})]$ (18)

 $\alpha = {\alpha _a}\exp [{\rm{i}}({\omega _e}t - {\gamma _s} + \varepsilon )]$ (19)

 Download: 图 5 零航速模式下船舶横摇运动相位矢量图 Fig. 5 Phase vector diagram of ship roll motion under ZSAM

1) 若采用单一信号反馈控制，则应使鳍角按照横摇角负反馈进行控制，对应于PID控制中的P控制，即

 ${K_{{\rm{Z}}{{\rm{C}}_{\rm{1}}}}} = {K_{{\rm{Zang}}}}\phi$ (20)

2) 若采用多信号反馈的复合控制，考虑到以横摇角度为主反馈信号，对应于PID控制中的P控制，其微分为横摇角速度，而积分无实际意义，故在以鳍角为最终表现，且仅考虑船舶横摇角和角速度信号作为反馈控制量时，对应于PD控制，即

 ${K_{{\rm{Z}}{{\rm{C}}_{\rm{2}}}}} = {K_{{\rm{Zang}}}}\phi + {K_{{\rm{Zvel}}}}\dot \phi$ (21)

3 仿真及实验 3.1 仿真分析 3.1.1 系统建模

 Download: 图 6 船舶减摇控制系统结构图 Fig. 6 Structure diagram of ship roll reduction control system

1) 船舶横摇运动模型

 ${W_\phi }\left( s \right) = \frac{1}{{1.82{s^2} + 0.33s + 1}}$ (22)

2) 海浪干扰模型

 ${S_\zeta }\left( \omega \right) = \frac{{0.0081{g^2}}}{{{\omega ^5}}}\exp \left( { - \frac{{3.11}}{{h_{1/3}^2{\omega ^4}}}} \right)$ (23)

 ${S_\alpha }\left( \omega \right) = {k^2}{S_\zeta }\left( \omega \right)$ (24)

 $\alpha \left( t \right) = \sum \sqrt {2{S_\alpha }\left( \omega \right)\Delta \omega } \cos ({\omega _i}t + {\varepsilon _i})$ (25)

3) 角速度陀螺

 ${G_{{\rm{rrg}}}}\left( s \right) = \frac{{400s}}{{{s^2} + 80s + 4000}}$ (26)

4) 随动系统

 ${G_{{\rm{ss}}}}\left( s \right) = \frac{1}{{s\left( {0.0063\;s + 1} \right)\left( {\frac{{{s^2}}}{{{{33.4}^2}}} + \frac{{0.6\;s}}{{33.4}} + 1} \right)}}$ (27)
3.1.2 仿真结果

 Download: 图 7 基于横摇角反馈控制的船舶横摇运动 Fig. 7 Ship roll with roll angle based feedback control
 Download: 图 8 基于横摇角/角速度的综合反馈控制的船舶横摇运动 Fig. 8 Ship roll with roll angle/rate integrated feedback control

3.2 水池试验

 Download: 图 9 零航速船模减摇控制系统 Fig. 9 Zero-speed ship model roll stabilization control system

4 结论

1) 常规减摇模式下减摇鳍的控制与常规减摇鳍相同，应以横摇角速度为主反馈信号。

2) 零航速减摇模式下减摇鳍的控制则应以横摇角为主反馈信号，辅以横摇角速度反馈。

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