﻿ 小型观测级ROV四自由度运动控制系统研究
 舰船科学技术  2020, Vol. 42 Issue (10): 83-89    DOI: 10.3404/j.issn.1672-7649.2020.10.017 PDF

1. 江苏海洋大学 电子工程学院，江苏 连云港 222002;
2. 江苏海洋大学 机械与海洋工程学院，江苏 连云港 222002;
3. 江苏科技大学 海洋装备研究院，江苏 镇江 212000

The development of control system in small monitoring ROV motion in 4 DOF
YANG Miao1,3, SHENG Zhi-bin2, WANG Hai-wen1, YIN Ge1
1. The Department of Electronic Engineering of Jiangsu Ocean University, Lianyungang 222002, China;
2. The Department of Mechanical and Ocean Engineering of Jiangsu Ocean University, Lianyungang 222002, China;
3. Institute of Marine equipment, Jiangsu University of Science and Technology, Zhenjiang 212000, China
Abstract: This work focus on a RBFNN(Radial Basis Function Neural Network) based adaptive sliding mode control(RBFSMC) for a kind of small monitoring ROV in 4 degrees of freedom motion. In this paper, the ROV model uncertainties were considered, and the mathematical model of the ROV model uncertainties were given. By using RBF neural network, the ROV model uncertainties were compensated. In addition, for reducing the chattering of conventional sliding mode control(CSMC), the sign function in CSMC was replaced by arctan function. According to Lyapunov stability theorem, the global asymptotic stability of the system was proven. The Matalb/Simulink experiment results validate the effectiveness of RBFSMC.
Key words: ROV     RBFNN     sliding mode control     model uncertainties
0 引　言

1 ROV模型数学描述 1.1 ROV运动学模型

 图 1 小型观测级ROV模型 Fig. 1 The model of small monitoring ROV

 $\dot \eta = J(\eta )\nu\text{，}$ (1)

 ${ {J}}({ {\eta}} ) = \left[ {\begin{array}{*{20}{c}} {{J_1}(\eta )}&{{0_{3 \times 3}}} \\ {{0_{3 \times 3}}}&{{J_2}(\eta )} \end{array}} \right]\text{，}$ (2)

 $\begin{split}{J_1}(\eta ) = & \left[ {\begin{array}{*{20}{c}} {\cos \psi }&{ - \sin \psi \cos \varphi + \cos \psi \sin \theta \sin \varphi }&\\ {\sin \psi \cos \theta }&{\cos \psi \cos \varphi + \sin \varphi \sin \theta \sin \psi }&\\ { - \sin \theta }&{\cos \theta \sin \varphi }& \end{array}} \right. \\ & \left. \begin{array}{l} \sin \psi \sin \varphi + \cos \psi \cos \varphi \sin \theta \\ - \cos \psi \sin \varphi + \sin \theta \sin \psi \cos \varphi \\ \cos \theta \cos \varphi \end{array} \right]\text{，}\\[-25pt]\end{split}$ (3)
 ${J_{\rm{2}}}(\eta ) = \left[ {\begin{array}{*{20}{c}} {\rm{1}}&{\sin \varphi \tan \theta }&{\cos \varphi \tan \theta } \\ 0&{\cos \varphi }&{ - \sin \varphi } \\ 0&{\sin \varphi /\cos \theta }&{\cos \varphi /\cos \theta } \end{array}} \right]\text{。}$ (4)

 $\left[ {\begin{array}{*{20}{c}} x \\ y \\ z \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {\cos \psi }&{ - \sin \psi }&0&0 \\ {\sin \psi }&{\cos \psi }&0&0 \\ 0&0&1&0 \\ 0&0&0&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} u \\ v \\ w \\ r \end{array}} \right]\text{。}$ (5)
1.2 ROV动力学模型

 ${{M}}\dot \nu + {{C}}(\nu )\nu + {{D}}(\nu )\nu + g(\eta ) = \tau + {\tau _d}\text{，}$ (6)

 $M = {\rm{diag}}\{\!\! \begin{array}{*{20}{c}} {m - {X_{\bar u}},}&{m - {Y_{\bar v}},}&{\begin{array}{*{20}{c}} {m - {Z_{\bar w}},}&{{I_z} - {N_{\bar r}}} \end{array}} \!\! \end{array}\} \text{，}$ (7)

Cv）∈R4×4为科氏力和向心力矩阵，定义为：

 ${{C}}(\nu ) = \left[ {\begin{array}{*{20}{c}} 0&0&0&{ - (m - {Y_{\bar v}}v)} \\ 0&0&0&{ - (m - {X_{\bar u}}u)} \\ 0&0&0&0 \\ { - (m - {Y_{\bar v}}v)}&{ - (m - {X_{\bar u}}u)}&0&0 \end{array}} \right]\text{，}$ (8)

Dv）∈R4×4为阻尼系数矩阵，定义为：

 $\begin{split} {{D}}(\nu ) =& - {\rm{diag}}\{ {{X_u} + {X_{u\left| u \right|}}\left| u \right|,}\qquad{{Y_v} + {Y_{v\left| v \right|}}\left| v \right|,}\\ & {{Z_w} + {Z_{w\left| w \right|}}\left| w \right|,}\qquad{{N_r} + {N_{r\left| r \right|}}\left| r \right|} \}\text{。} \end{split}$ (9)

gη）∈R4为ROV恢复力和力矩向量，定义为：

 $g(\eta ) = \left[ {\begin{array}{*{20}{c}} 0 \\ 0 \\ { - (W - {W_B})} \\ 0 \end{array}} \right]\text{。}$ (10)

τR4τdR4分别为ROV的控制输入以及外部干扰。

 ${{{M}}_\eta }(\eta )\ddot \eta + {{{C}}_\eta }(\nu ,\eta )\dot \eta + {{{D}}_\eta }(\nu ,\eta )\dot \eta + {g_\eta }(\eta ) = {\tau _T} + d\text{。}$ (11)

2 控制器设计 2.1 经典滑模控制器设计

 $S = {\dot {\tilde \eta}} + \Lambda \tilde \eta \text{，}$ (12)

 ${\tau _T} = {\tau _{eq}} + {\tau _{sw}}\text{，}$ (13)

 $\dot S = {\ddot{\tilde \eta}} + \Lambda {\dot{\tilde \eta}} \text{，}$ (14)

 $\begin{split} {{{M}}_\eta }\dot S = & - {{{C}}_\eta }S - {{{D}}_\eta }S + {{{M}}_\eta }({\ddot \eta _d} + \Lambda {\dot{\tilde \eta}} ) + {{{C}}_\eta }({\dot \eta _d} + \Lambda \tilde \eta ) + \\ & {{{D}}_\eta }({\dot \eta _d} + \Lambda \tilde \eta ) + {g_\eta } - {\tau _T} - d\text{，} \end{split}$ (15)

 $\begin{split}{\tau _T} = & {{{M}}_\eta }({\ddot \eta _d} + \Lambda {\dot{\tilde \eta}} ) + {{{C}}_\eta }({\dot \eta _d} + \Lambda \tilde \eta ) + {{{D}}_\eta }({\dot \eta _d} + \Lambda \tilde \eta ) + \\ & {g_\eta } + {K_d}S - K{\rm{sgn}} (S)\text{。}\end{split}$ (16)

2.2 RBF神经网络自适应滑模控制器设计

 $y(b) = {W^{ * {\rm{T}}}}\mu (b) + \varepsilon \text{。}$ (17)

 图 2 RBF神经网络结构图 Fig. 2 The structure diagram of RBF neural network

 $y(b) = {{{M}}_\eta }({\ddot \eta _d} + \Lambda {\dot{\tilde \eta}} ) + {{{C}}_\eta }({\dot \eta _d} + \Lambda \tilde \eta ) + {{{D}}_\eta }({\dot \eta _d} + \Lambda \tilde \eta ) + {g_\eta }\text{，}$ (18)

 ${\mu _j}(b) = \exp ( - \frac{{{{\left\| {b - {C_j}} \right\|}^2}}}{{2{B^2}_j}}),\begin{array}{*{20}{c}} {}&{j = 1,\cdots,4} \end{array}\text{。}$ (19)

 $\hat y(b) = {\hat W^{\rm{T}}}\mu (b) + \varepsilon \text{，}$ (20)

 ${\dot{\hat W}} = \mu (b){S^{\rm{T}}}\text{。}$ (21)

 ${\tau _T} = {\hat W^{\rm{T}}}\mu (b) - {K_d}S - K\arctan (S)\text{。}$ (22)

RBF神经网络自适应滑模控制的框图如图3所示。

 图 3 RBF神经网络自适应滑模控制框图 Fig. 3 Block diagram of RBF neural network based adaptive sliding mode control

 $V(S,\tilde W) = \frac{1}{2}{S^{\rm{T}}}{{{M}}_\eta }S + \frac{1}{2}{\left\| {\tilde W} \right\|^2}\text{，}$ (23)

 $\begin{split} \frac{{{\rm d}V(S,\tilde W)}}{{{\rm d}t}} = & {S^{\rm{T}}}[ - {{{C}}_\eta }S - {{{D}}_\eta }S + \hat y(b) - d - {\tau _T}] + \\ & \frac{1}{2}{S^{\rm{T}}}{\dot {{M}}_\eta }S - {\tilde W^{\rm{T}}}{\dot{\hat W}}\text{，} \end{split}$ (24)

 $\begin{split} &\frac{{{\rm d}V(S,\tilde W)}}{{{\rm d}t}} = \frac{1}{2}{S^{\rm{T}}}({\dot {{M}}_\eta } - {{{C}}_\eta })S - {S^{\rm{T}}}{{{D}}_\eta }S - {S^{\rm{T}}}{K_d}S +\\ & \;\;\;\;\;\;\;\;{\tilde W^{\rm{T}}}[\mu (b){S^{\rm{T}}} - {\dot{\hat W}}] + {S^{\rm{T}}}[\varepsilon - d - K\arctan (S)]\text{。} \end{split}$ (25)

 $\frac{{{\rm d}V(S,\tilde W)}}{{{\rm d}t}} = - {S^{\rm{T}}}{{{D}}_\eta }S - {S^{\rm{T}}}{K_d}S - K\left\| S \right\| - {S^{\rm{T}}}(\varepsilon - d)\text{。}$ (26)

3 仿真分析

 图 4 RBF神经网络逼近ROV模型不确定项 Fig. 4 The RBF neural network approximates the ROV model uncertainties

 图 8 ROV位姿轨迹跟踪误差 Fig. 8 Tracking errors of ROV position and attitude

 图 5 ROV三维轨迹跟踪 Fig. 5 Position tracking results of ROV in xyz plot

 图 6 ROV位姿相轨迹图 Fig. 6 Phase portrait of ROV position and attitude

 图 7 ROV位姿运动轨迹跟踪 Fig. 7 ROV position and attitude tracking results
4 结　语

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