﻿ 船舶吊运机械臂海浪环境下的运动补偿控制与模拟
 舰船科学技术  2023, Vol. 45 Issue (7): 66-69    DOI: 10.3404/j.issn.1672-7649.2023.07.014 PDF

Motion compensation control and simulation of ship crane arm in sea wave environment
LI Kun, REN Li
Anhui Wenda University of Information Engineering, College of Intelligent Manufacturing, Hefei 231201, China
Abstract: In the process of cargo transport and lifting in the field of ocean engineering, the influence of sea waves on the process of lifting must be considered, which mainly refers to all kinds of swaying, rolling and other motions caused by sea waves on the ship. These additional motion speed and acceleration will reduce the stability of the cargo lifting process, resulting in safety risks. The research direction of this paper is to use the motion of the platform with multiple degrees of freedom to compensate the influence of sea waves. On the one hand, the motion characteristics of the hull-robot arm in the process of ship lifting are analyzed. On the other hand, the motion compensation system is designed with PID controller, and the test platform is built to test the robustness of the robot arm in the interference environment.
Key words: lifting manipulator     motion compensation     PID     motion characteristics     robustness testing
0 引　言

1）海上作业平台的货物转运

2）港口装卸货物

1 海浪环境下的船舶吊运机械臂运动建模

 $\xi (t) = \sum\limits_{i = 1}^n {{\xi _0}(t)\cos ({w_0}t + \varphi )} \text{。}$

 $E({\omega _0}) = \frac{{{k_1}}}{{{\omega _0}^3}}\exp (\frac{{ - {k_2}}}{{{\omega _0}^4}}) \text{。}$

 $\begin{gathered} {E_x}{\text{ = }}\frac{\text π }{2}{\varphi _0}{\theta ^{kt}}\cos \left( {kx - {w_0}t} \right), \\ {E_y} = \frac{1}{2}{\varphi _0}{\theta ^{kt}}\sin \left( {kx - {w_0}t} \right)。\\ \end{gathered}$

 图 1 船舶吊运机械臂在海浪环境下的运动坐标系 Fig. 1 The moving coordinate system of ship lifting manipulator in sea wave environment

 ${I_z}\frac{{{\rm{d}}{w_z}}}{{{\rm{d}}t}} = {M_z} + {M_{sp}} \text{。}$

 \begin{aligned} & {m\frac{{{\rm{d}}v}}{{{\rm{d}}t}} = P\cos \left( {\alpha + \theta } \right) - Q - mg\sin \theta } ,\\ & {m\frac{{{\rm{d}}\theta }}{{{\rm{d}}t}} = P\sin \left( {\alpha + \theta } \right) - mg\cos \theta }, \\ & {{I_z}\frac{{{\rm{d}}{w_z}}}{{{\rm{d}}t}} = {M_z} + {M_{sp}}} ,\\ & {\frac{{{\rm{d}}x}}{{{\rm{d}}t}} = v\cos \theta }, \\ & {\frac{{{\rm{d}}h}}{{{\rm{d}}t}} = v\sin \theta } \text{。} \end{aligned}

 $\begin{gathered} X(t) = \sum\limits_{i = 1}^n {\left[ {{h_x}/n \cdot \cos \left( {{\omega _i}t + {\gamma _{xi}}} \right)} \right]}, \\[2.5pt] Y(t) = \sum\limits_{i = 1}^n {\left[ {{h_y}/n \cdot \cos \left( {{\omega _i}t + {\gamma _{ji}}} \right)} \right]} , \\[2.5pt] Z(t) = \sum\limits_{i = 1}^n {\left[ {{h_z}/n \cdot \cos \left( {{\omega _i}t + {\gamma _{zi}}} \right)} \right]}。\\ \end{gathered}$

3个坐标轴的角度模型为：

 $\begin{gathered} \gamma = \sum\limits_{i = 1}^n {\left[ {{A_r}/n \cdot \sin \left( {{\omega _r}t + {\varphi _r}} \right)} \right]}, \\[2.5pt] \theta = \sum\limits_{i = 1}^n {\left[ {{A_\theta }/n \cdot \sin \left( {{\omega _\theta }t + {\varphi _\theta }} \right)} \right]}, \\[2.5pt] \psi = \sum\limits_{i = 1}^n {\left[ {{A_\psi }/n \cdot \sin \left( {{\omega _\psi }t + {\varphi _\varphi }} \right)} \right]}。\\ \end{gathered}$

2 船舶吊运机械臂海浪环境下的运动补偿控制系统开发 2.1 PID控制器原理

PID控制器是一种应用广泛、可靠性高的反馈控制器，包括积分控制、微分控制和比例控制3部分，对于改善系统的稳态误差、非线性误差等效果明显，图2为PID控制器的原理。

 图 2 PID控制器原理图 Fig. 2 Schematic diagram of PID controller

PID控制器的工作流程包括：

1） 确定被控系统的信号采集周期；

2）利用比例控制和阶跃响应信号，确定PID控制器的比例放大系数 ${K_1}$

3）利用积分和微分控制环节，调节被控系统的信号超调量。

PID控制器的数学模型为：

 $K(S) = {K_1} + \frac{{{K_2}}}{S} + {K_3}S \text{。}$

PID控制器的传递函数为：

 $G(S) = \frac{{{\omega ^2}K}}{{{S^2} + 2\delta \xi {\omega ^2} + {D^2}}} \text{。}$

2.2 PID控制器的吊运机械臂电动机控制研究

 图 3 吊运机械臂运动补偿机构的原理图 Fig. 3 The principle diagram of the motion compensation mechanism of the lifting manipulator

 $\left[ {\begin{array}{*{20}{l}} {{u_a}} \\ {{u_b}} \\ {{u_c}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{R_s}}&0&0 \\ 0&{{R_s}}&0 \\ 0&0&{{R_s}} \end{array}} \right]\left[ {\begin{array}{*{20}{l}} {{i_a}} \\ {{i_b}} \\ {{i_c}} \end{array}} \right] + p\left[ {\begin{array}{*{20}{c}} {{\varphi _a}} \\ {{\varphi _b}} \\ {{\varphi _c}} \end{array}} \right] \text{。}$

 $\left[ {\begin{array}{*{20}{c}} {{\varphi _a}}\\ {{\varphi _b}}\\ {{\varphi _c}} \end{array}} \right] = \left[ {\begin{array}{*{20}{l}} {{L_{aa}}}&{{M_{ab}}}&{{M_{ac}}}\\ {{M_{ba}}}&{{L_{bb}}}&{{M_{bc}}}\\ {{M_{ca}}}&{{M_{cb}}}&{{L_{cc}}} \end{array}} \right]\left[ {\begin{array}{*{20}{l}} {{i_a}}\\ {{b_b}}\\ {{i_c}} \end{array}} \right] + {\varphi _r}\left[ {\begin{array}{*{20}{c}} {\cos \theta }\\ {\cos \left( {\theta - 120^\circ } \right)}\\ {\cos \left( {\theta + 120^\circ } \right)} \end{array}} \right]。$

 图 4 波浪补偿机构电机输出电压矢量图 Fig. 4 Wave compensation mechanism motor output voltage vector diagram
2.3 船舶吊运机械臂波浪补偿控制系统的搭建

 图 5 吊运机械臂的波浪补偿控制系统原理图 Fig. 5 Schematic diagram of wave compensation control system for lifting manipulator

 \begin{aligned} & {{u_a}{\text{ = }}{U_0}\cos wt}, \\ & {{u_b} = {U_0}\left( {\cos wt - {\raise0.7ex\hbox{{2{\text π} }$} \mathord{\left/ {\vphantom {{2{\text π} } 3}}\right.} \lower0.7ex\hbox{$3$}}} \right)}, \\ & {{u_c} = {U_0}\left( {\cos wt + {\raise0.7ex\hbox{${2{\text π} }$} \mathord{\left/ {\vphantom {{2{\text π} } 3}}\right.} \lower0.7ex\hbox{$3}}} \right)}。\end{aligned}

 图 6 波浪补偿前后的吊运机械臂位移量仿真 Fig. 6 Simulation of displacement of lifting manipulator before and after wave compensation
3 结　语

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