﻿ 自抗扰控制算法船舶动力定位仿真分析
 舰船科学技术  2023, Vol. 45 Issue (12): 103-106    DOI: 10.3404/j.issn.1672-7619.2023.12.019 PDF

Simulation analysis of active disturbance rejection control algorithm for ship dynamic positioning
XU Liang
Jiangsu Shipping College, Nantong 226010, China
Abstract: In the ocean and deep sea, if the ship adopts the traditional anchoring mode, on the one hand, there is a problem of poor flexibility, on the other hand, the angle deviation caused by the length of the anchor chain will lead to the poor positioning accuracy of the ship. Therefore, the ship dynamic positioning system has become an important functional system of the ship. In the process of ship dynamic positioning, wind and waves will interfere with the accuracy of dynamic positioning. To solve this problem, an active disturbance rejection control algorithm is proposed in this paper. The algorithm uses key elements such as tracking differential, state observer and error feedback module to achieve accurate control of ship dynamic positioning thrusters and improve the accuracy of ship dynamic positioning. In addition, the simulation analysis of active disturbance rejection control technology of dynamic positioning system is carried out based on Simulink simulation platform.
Key words: active disturbance rejection     dynamic positioning     differentiator     state observer
0 引　言

1 船舶动力定位的数学建模

 $\varGamma (X,Y,t) = A\cos \left( {\dfrac{{2\text{π} }}{\lambda }\left( {Y\cos \theta + X\sin \theta - {w_1}t + \varphi } \right)} \right)。$

 图 1 船舶动力定位坐标系 Fig. 1 The coordinate system of the ship's dynamic positioning

 $\left\{ {\begin{array}{*{20}{l}} {{F_{\text{h}}} = 0.025m{V_l}^2 + 1.9} ，\\ {{T_0} = - 0.0026m{V_l}^3 + 0.0046m{V_l}^2} \text{，} \\ {{T_1} = m\dfrac{4}{5}\sqrt {\left( {{V_l}^2 + {U^2}} \right)} \sqrt {{\lambda _{}}} } 。\end{array}} \right.$

 $\vec M = \vec J\left( M \right)\vec V 。$

 $\vec {\boldsymbol{J}}\left( M \right) = \left[ {\begin{array}{*{20}{c}} { - \cos \alpha }&{\cos \alpha }&0 \\ 1&{\sin \alpha }&0 \\ { - \sin \alpha }&0&1 \end{array}} \right]。$

 $\vec G{\vec V} + R\left( {{{\vec V}}} \right) + \vec F\left( {{{\vec V}} - {{\vec V}}_c} \right) = {\vec \tau _0} 。$

 $\overrightarrow {\boldsymbol{G}} = \left[ \begin{gathered} m - {X_r}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \\ 0{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} m - {Y_r} \\ 0{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 1 \\ \end{gathered} \right.\left. \begin{gathered} 0 \\ {\kern 1pt} {\kern 1pt} {Y_r} \\ {I_z} - {N_r} \\ \end{gathered} \right] \text{，}$
 $\vec {\boldsymbol{F}} = \left[ {\begin{array}{*{20}{c}} { - {X_r}}&0&0 \\ 0&{{Y_r}}&{ - {Y_r}} \\ 0&1&{ - {N_r}} \end{array}} \right] 。$

2 船舶动力定位的自抗扰控制器数学建模

 图 2 船舶动力定位控制系统的工作原理 Fig. 2 The working principle of the ship dynamic positioning control system

 图 3 船舶动力定位控制系统自抗扰控制器原理 Fig. 3 Principle of ship dynamic positioning control system self-disturbance rejection controller

1）跟踪微分器

 $\left\{ {\begin{array}{*{20}{l}} {{x_1}(k + 1) = {x_1}(k) + h{x_2}(k)}，\\ {{x_2}(k + 1) = {x_2}(k) + h \cdot fh}，\\ {f = K\left( {{x_1}(k) - v(t),{x_2}(k),r,{h_0}} \right)} 。\end{array}} \right.$

2）扩展状态观测器

 $\begin{gathered} {d_1} = - {u_1}{G_i}\left( s \right) + \theta {Q_i}\left( s \right)p\left( s \right)，\\ {d_2} = - {u_2}q\left( s \right){Q_i}\left( s \right) - {f_d}\left( d \right)。\\ \end{gathered}$

 $\begin{gathered} {\theta _1} = {u_1}\frac{{{G_i}\left( s \right) + \theta {Q_i}\left( s \right)}}{{q\left( s \right){Q_i}\left( s \right)}} - \theta ，\\ {\theta _2} = \frac{{p\left( s \right){u_2} - {f_d}\left( d \right)}}{{{Q_i}\left( s \right)}} + \theta。\\ \end{gathered}$

 图 4 自抗扰控制器的航向角误差e的隶属度函数 Fig. 4 Membership function of course angle error e of active disturbance rejection controller
3 基于自抗扰控制器的船舶动力定位系统仿真分析

 图 5 基于自抗扰控制器的船舶动力定位原理 Fig. 5 Principle of ship dynamic positioning based on active disturbance rejection controller

 $\begin{array}{*{20}{l}} {\dot \mu = R\left( \psi \right)v}，\\ {M\dot v = - Dv + \tau + w}，\\ {\tau = 0.3 \times \dfrac{{\delta v}}{{\delta t}}}。\end{array}$

 $\delta {\text{ = }}\eta - {\eta _0} \text{，}$

 $\frac{\rm d}{{{\rm{d}}t}}\delta {\text{ = }}\dot \eta - {\dot \eta _0} = R\left( \psi \right)v - \frac{{{\rm{d}}{{\dot \eta }_0}}}{{{\rm{d}}t}} 。$

 $f\left( t \right) = \frac{{\displaystyle\sum\limits_0^{{n_1}} {\sum\limits_0^{{n_2}} {\left( {\left( {R\left( t \right)v - {\eta _0}} \right)} \right)} } }}{{\displaystyle\sum\limits_0^{{n_1}} {\sum\limits_0^{{n_2}} {\eta \left( t \right)} } }} 。$

 图 6 船舶自抗扰动力定位的航向角变化曲线 Fig. 6 Heading angle change curve of ship self-disturbance rejection dynamic positioning
4 结　语

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