﻿ 基于鲁棒滑模控制的水下航行器运动控制仿真研究
 舰船科学技术  2016, Vol. 38 Issue (6): 92-96 PDF

Non-linear robust slide-model control for underwater vehicle
HE Jin-qiu, SHE Ying-ying
Wuhan Second Ship Design and Research Institute, Wuhan 430205, China
Abstract: Based on the standard six-degree of freedom space motion equation, a non-linear robust slide-model control protocol is proposed for the underwater vehicle with retractile fore hydroplane and separate helm. The simulation results verify the efficiency and feasibility of the proposed method.
Key words: underwater vehicle     retractile fore hydroplane     separate helm     non-linear robust slide-model control protocol
0 引 言

1 分离式尾舵水下航行器在首舵收回时的数学模型

 图 1 固定坐标系和随船坐标系 Fig. 1 The fixed coordinate system and ship coordinate system

 图 2 欧拉角 Fig. 2 Euler angles

 $\frac{\text{d}}{\text{d}t}{{[{{\xi }_{o}},{{\eta }_{o}},{{\zeta }_{o}}]}^{\text{T}}}={{T}_{1}}\left[ \begin{matrix} u \\ v \\ w \\ \end{matrix} \right],$

 ${{T}_{1}}={{T}_{1}}(\varphi ,\theta ,\psi )=\left[ \begin{matrix} \cos \psi \cos \theta & -\sin \psi \cos \varphi +\cos \psi \sin \theta \sin \varphi & \sin \psi \sin \varphi +\cos \psi \sin \theta \cos \varphi \\ \sin \psi \cos \theta & \cos \psi \cos \varphi +\sin \psi \sin \theta \sin \varphi & -\cos \psi \sin \theta +\sin \psi \sin \theta \cos \theta \\ -\sin \theta & \cos \theta \sin \varphi & \cos \theta \cos \varphi \\ \end{matrix} \right],$

 $\frac{\text{d}}{\text{d}t}{{[\varphi ,\theta ,\psi ]}^{\text{T}}}={{T}_{2}}\left[ \begin{matrix} p \\ q \\ r \\ \end{matrix} \right],$

 ${{T}_{2}}=\left[ \begin{matrix} 1 & \sin \varphi \tan \theta & \cos \varphi \tan \theta \\ 0 & \cos \varphi & -\sin \varphi \\ 0 & \frac{\sin \varphi }{\cos \theta } & \frac{\cos \varphi }{\cos \theta } \\ \end{matrix} \right]\circ$

 \begin{aligned} & {{U}^{2}}={{u}^{2}}+{{w}^{2}}+{{v}^{2}}\text{，} \\ & {{{\dot{\xi }}}_{0}}=u\cos \psi \cos \theta +v(\cos \psi \sin \theta \sin \phi -\sin \psi \cos \phi )+ \\ & \quad \quad w(\cos \psi \sin \theta \cos \phi +\sin \psi \sin \phi )\text{，} \\ & {{{\dot{\eta }}}_{0}}=u\sin \psi \cos \theta +v(\sin \psi \sin \theta \sin \phi +\cos \psi \cos \phi )+ \\ & \quad \quad w(\sin \psi \sin \theta \cos \phi -\cos \psi \sin \phi )\text{，} \\ & {{{\dot{\zeta }}}_{0}}=-u\sin \theta +v\cos \theta \sin \phi +w\cos \theta \cos \phi \text{，} \\ & \dot{\phi }=p+q\tan \theta \sin \phi +r\tan \theta \cos \phi \text{，} \\ \end{aligned}
 \begin{aligned} & \dot{\theta }=q\cos \phi -r\sin \phi \text{，} \qquad\qquad\qquad\qquad\quad\\ & \dot{\psi }={}^{\displaystyle(q\sin \phi +r\cos \phi )}\!\!\diagup\!\!{}_{\cos \theta }\; \text{，}\qquad\qquad\qquad\qquad\quad\\ \end{aligned}

2 非线性鲁棒滑模控制算法

 $C £ \tilde x = C\tilde x.$

 $\dot{x}=Ax+{{B}_{{}}}{{u}_{{}}}+\delta f\circ$

 $u=\hat{u}+\bar{u},$

 $\hat{u}=-Kx\circ$

 \begin{align} & \dot{x}={{A}_{c}}x+B\bar{u}+\delta f, \\ & {{A}_{c}}=A-BK\circ \\ \end{align}

 $u=\hat{u}+\bar{u}=-Kx+{{(CB)}^{-1}}[C{{\dot{x}}_{d}}-C\delta \hat{f}-\eta \text{sgn}(\sigma )]$

 $\begin{array}{l} u = \hat u + \bar u= - { K}x + {({ CB})^{ - 1}}[{ C}{{\dot x}_d} -{ C} \delta \hat f - \eta \tanh (\frac{\sigma }{\phi })] \end{array}$

 $u=\left\{ \begin{array}{*{35}{l}} -Kx+{{(CB)}^{-1}}[C{{{\dot{x}}}_{d}}-C\delta \hat{f}-\eta \text{sgn}(\sigma )] \\ \text{discontinuousversion}, \\ -Kx+{{(CB)}^{-1}}[C{{{\dot{x}}}_{d}}-C\delta \hat{f}-\eta \tanh (\frac{\sigma }{\varphi })] \\ \text{continuousversion} \\ \end{array} \right.$
3 水下航行器非线性鲁棒滑模控制系统设计

 ${{\delta }_{r}}=\left\{ \begin{array}{*{35}{l}} -{{k}_{1}}v-{{k}_{2}}r+{{(hB)}^{-1}}[{{h}_{2}}{{{\dot{r}}}_{d}}+{{h}_{3}}{{r}_{d}}-h\delta \hat{f}-\eta \text{sgn}(\sigma )] \\ \text{discontinuousversion} \\ -{{k}_{1}}v-{{k}_{2}}r+{{(hB)}^{-1}}[{{h}_{2}}{{{\dot{r}}}_{d}}+{{h}_{3}}{{r}_{d}}-h\delta \hat{f}-\eta \tanh (\frac{\sigma }{\varphi })] \\ \text{continuousversion}. \\ \end{array} \right.$

 ${{\delta }_{2}}=\left\{ \begin{array}{*{35}{l}} -{{k}_{1}}p-{{k}_{2}}\varphi +{{(hB)}^{-1}}[-h\delta \hat{f}-\eta \text{sgn}(\sigma )] \\ \text{discontinuousversion} \\ -{{k}_{1}}p-{{k}_{2}}\varphi +{{(hB)}^{-1}}[-h\delta \hat{f}-\eta \tanh (\frac{\sigma }{\varphi })] \\ \text{continuousversion}. \\ \end{array} \right.$

 $\left[ \begin{array}{*{35}{l}} {{\delta }_{1}} \\ {{\delta }_{b}} \\ \end{array} \right]=\left\{ \begin{array}{*{35}{l}} -Kx+{{(CB)}^{-1}}[C{{{\dot{x}}}_{d}}-C\delta \hat{f}-\eta \text{sgn}(\sigma )] \\ \text{discontinuousversion} \\ -Kx+{{(CB)}^{-1}}[C{{{\dot{x}}}_{d}}-C\delta \hat{f}-\eta \tanh (\frac{\sigma }{\varphi })] \\ \text{continuousversion}. \\ \end{array} \right.$
4 首舵收回情况下的分离式尾舵独立控制数学仿真结果

 图 3 纵向速度历时曲线 Fig. 3 The curve of Longitudinal velocity

 图 4 横向速度历时曲线 Fig. 4 The curve of transverse velocity

 图 5 垂向速度历时曲线 Fig. 5 The curve of vertical velocity

 图 6 横倾角历时曲线 Fig. 6 The curve of heeling angle

 图 7 纵倾角历时曲线 Fig. 7 The curve of trim angle

 图 8 首向角历时曲线 Fig. 8 The curve of heading angle

 图 9 纵向位移历时曲线 Fig. 9 The curve of longitudinal displacement

 图 10 横向位移历时曲线 Fig. 10 The curve of lateral displacement

 图 11 深度历时曲线 Fig. 11 The curve of depth
5 结 语

 [1] 施生达. 潜艇操纵性[M]. 北京: 国防工业出版社, 1995 : 78 -181. [2] 金鸿章, 姚绪梁. 船舶控制原理[M]. 哈尔滨: 哈尔滨工程大学出版社, 2002 : 149 -164. [3] 张瑾, 连琏, 葛彤. 潜艇近水面运动鲁棒控制及仿真研究[J]. 海洋工程 , 2006, 24 (4) :32–37. ZHANG Jin, LIAN Lian, GE Tong. Robust control and simulation of near-surface submarine[J]. The Ocean Engineering , 2006, 24 (4) :32–37. [4] 王薇. 非线性系统的滑模控制研究[D]. 青岛:中国海洋大学, 2005:13-31. WANG Wei. The sliding mode control of nonlinear systems[D]. Qingdao:Ocean University of China, 2005:13-31. [5] 田宏奇. 滑模控制理论及其应用[M]. 武汉: 武汉出版社, 1995 . [6] ZHAO Wen-jie, LIU Ji-zhen. An improved method of sliding mode control with boundary layer[J]. Journal of System Simulation , 2005, 17 (1) :156–158. [7] 金鸿章, 罗延明, 肖真, 等. 抑制滑模抖振的新型饱和函数法研究[J]. 哈尔滨工程大学学报 , 2007, 28 (3) :288–291. JIN Hong-zhang, LUO Yan-ming, XIAO Zhen, et al. Investigation of a novel method of saturation function for chattering reduction of sliding mode control[J]. Journal of Harbin Engineering University , 2007, 28 (3) :288–291. [8] 李殿璞. 船舶运动与建模[M]. 哈尔滨: 哈尔滨工程大学出版社, 2005 : 214 -230. [9] 魏巍. Matlab控制工程工具箱技术手册[M]. 北京: 国防工业出版社, 2004 : 1 -4. [10] 于浩洋, 初红霞, 王希凤, 等. Matlab实用教程-控制系统仿真与应用[M]. 北京: 化学工业出版社, 2009 : 12 -14.