﻿ 分离式尾舵潜艇卡单舵操纵控制技术研究
 舰船科学技术  2016, Vol. 38 Issue (5): 79-81 PDF

1. 武汉第二船舶设计研究所, 湖北 武汉 430064 ;
2. 中国船舶重工集团公司第七〇四研究所, 上海 200000

Research on motion control of submarine with jammed split stern plane
SHE Ying-ying1, HE Jin-qiu1, ZHI Ping2
1. Second Ship Design and Research Institute, Wuhan 430064, China ;
2. The 704 Research Institute of CSIC, Shanghai 200000, China
Abstract: The LQG/LTR motion control method for submarine with jammed split stern plane is proposed.The numerical simulation software in MATLAB environment is developed for the case of jammed split stern plane. The simulation results verify the efficiency and feasibility of the proposed method.
Key words: submarine     LQG/LTR     jammed stern plane     motion control
0 引言

1 数学模型分析

 $\left\{ \begin{array}{*{35}{l}} \overset{\cdot }{\mathop{{{x}_{p}}}}\,={{A}_{p}}{{x}_{p}}+{{B}_{p}}{{u}_{p}},\\ \overset{{}}{\mathop{{{y}_{p}}}}\,={{C}_{p}}{{x}_{p}}. \\ \end{array} \right.$

 $\left\{ {\begin{array}{*{20}{c}} {{{\mathop x\limits^ \cdot }_s} = {A_s}{x_s} + {B_s}{u_s}} ,\\ {{y_s} = {C_s}x}.\quad\quad\quad\quad \end{array}} \right.$ (1)
2 基于潜艇数学模型的多变量反馈设计 2.1 LQG/LTR 设计方法

 $0=A\sum{+\sum{{{A}^{\text{T}}}+\Xi -\sum{{{C}^{\text{T}}}{{\Theta }^{-1}}C\sum{{}}}}},$

 $0 = - {{KA}} - {{{A}}^{\rm{T}}}{{K}} - {{Q}} + {{KB}}{{{R}}^{ - 1}}{{{B}}^{\text{T}}}{{K}},$

$\varXi = {{B}}{{{B}}^{\text{T}}},\;{{\varTheta }} = \mu {{I}}$，因此可将 μ 看作设计参数。当 $\mu \to 0$ 时，有：

 \begin{align} & \sigma ({{T}_{KF}})=\sigma (C{{(sI-A)}^{-1}}H)\approx \\ & \frac{1}{\sqrt{\mu }}\sigma (C{{(sI-A)}^{-1}}B)=\sigma ({{T}_{FOL}}). \\ \end{align}

 \begin{align} & K(s)=G{{(sI-A+BG+HC)}^{-1}}H= \\ & G(sI-{{(A-BG-HC)}^{-1}})H. \\ \end{align}

 $\left\{ {\begin{array}{*{20}{c}} {\mathop {{z}}\limits^{{.}} = ({{A}} - {{BG}} - {{HC}}){{z}} - {{H}}e},\\ {{{u}} = - {{{G}z}}} .\qquad\qquad\qquad\quad\, \end{array}} \right.$

2.2 基于潜艇模型的 LQG/LTR 设计

 \left\{ \begin{align} & \overset{\cdot }{\mathop{\text{ }x}}\,=Ax+Bu,\\ & y=Cx. \\ \end{align} \right.

3 闭环控制系统仿真分析

 图 1 14 kn 航速潜艇的深度 Fig. 1 The depth of submarine under 14 kn

 图 2 14 kn 速潜艇的方向舵舵角 Fig. 2 The rudder angle of submarine under 14 kn

 图 3 14 kn 速潜艇的艉左水平舵舵角 Fig. 3 The left hydroplane angle of submarine under 14 kn

 图 4 14 kn 速潜艇的艉右水平舵舵角 Fig. 4 The right hydroplane angle of submarine under 14 kn

 图 5 14 kn 速潜艇的艏水平舵舵角 Fig. 5 The fore hydroplane angle of submarine under 14 kn

4 结语

 [1] 施生达. 潜艇操纵性[M]. 北京: 国防工业出版社, 1995 . [2] 孙元泉. 潜艇和深潜器的现代操纵理论与应用[M]. 北京: 国防工业出版社, 2001 .