﻿ 基于模糊理论的水下航行器运动控制及仿真研究
 舰船科学技术  2017, Vol. 39 Issue (12): 59-63 PDF

Research on motion control and simulation of underwater vehicle based on fuzzy theory
HU Jin-hui, HU Da-bin, XIAO Jian-bo
Naval University of Engineering, Wuhan 430033, China
Abstract: In order to eliminate the control blind zone in the traditional fuzzy control, the combining of fuzzy control and PID control is adopted. Aiming at the characteristic of large amount of computation and low utilization ratio of reasoning rules for the existing variable universe fuzzy control, the method of hierarchical variable domain is proposed. The fuzzy PID controller for some type of Under Water (UV) is designed. And the simulation experiments are carried out. The results show that fuzzy PID controller has the advantages of fast speed, small overshoot and short settling time by comparing with the traditional PID control in the depth and vertical tilt control of UV. This is a good reference for the controller design of complex nonlinear object.
Key words: underwater vehicle     control     fuzzy theory
0 引　言

1 模糊PID控制器

 图 1 论域的收缩与膨胀 Fig. 1 Shrinking and expanding of the universe

 $U\left( u \right) = \left[ { - \alpha \left( u \right)E,\alpha \left( u \right)E} \right]\text{。}$ (1)

1） $\forall u \in U,\alpha \left( u \right) = \alpha \left( { - u} \right)$

2） $\mathop {\lim }\limits_{u \to \pm E} \alpha \left( u \right) = 1 + \delta ,\mathop {\lim }\limits_{u \to 0} \alpha \left( u \right) = \delta$ δ为充分小的正参数，一般取δE/1 000；

3）αu）在[0，E]上单调增；

4） $\forall u \in U,\left| u \right| \leqslant \alpha \left( u \right)E + \delta$

 $\alpha \left( u \right) = {\left| {\frac{u}{E}} \right|^\tau } + \delta ,\tau \in \left( {0,1} \right)\text{。}$ (2)

2 某型水下航行器深度纵倾模糊PID控制研究 2.1 水下航行器深度纵倾控制

2.2 水下航行器垂直面运动模型
 \left\{ \begin{aligned}m\left( {\dot w - uq} \right) = &\displaystyle\frac{1}{2}\rho {L^4}\left( {{{Z'}_{\dot q}}\dot q + {{Z'}_{\left. q \right|\left. q \right|}}\left. q \right|\left. q \right|} \right) +\displaystyle\frac{1}{2}\rho {L^3}\left( {{{Z'}_{\dot w}}\dot w }+\right. \\&\left.{{{Z'}_q}uq + {{Z'}_{\left. w \right|\left. q \right|}}\left. w \right|\left. q \right| + {{Z'}_{\left| q \right|{\delta _s}}}u\left| q \right|{\delta _s}} \right) + \displaystyle\frac{1}{2}\rho {L^2} \times \\& \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\left( {{{Z'}_{uu}}{u^2} + {{Z'}_w}uw +{{Z'}_{\left| w \right|}}u\left| w \right| + {{Z'}_{\left. w \right|\left. w \right|}}\left. w \right|\left. w \right| + {{Z'}_{ww}}{w^2}} \right)+\\ & \displaystyle\frac{1}{2}\rho {L^2}\left( {{{Z'}_{{\delta _s}}}{u^2}{\delta _s} + {{Z'}_{{\delta _b}}}{u^2}{\delta _b}} \right) + P\text{，}\\&\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{I_y}\dot q = \displaystyle\frac{1}{2}\rho {L^5}\left( {{{M'}_{\dot q}}\dot q + {{M'}_{\left. q \right|\left. q \right|}}\left. q \right|\left. q \right|} \right) + \displaystyle\frac{1}{2}\rho {L^4}\left( {{{M'}_{\dot w}}\dot w + {{M'}_q}uq +}\right.\\&\!\!\!\!\!\!\!\!\!\!\!\!\left.{{{M'}_{\left. w \right|\left. q \right|}}\left. w \right|\left. q \right| + {{M'}_{\left| q \right|{\delta _s}}}u\left| q \right|{\delta _s}} \right) +\displaystyle\frac{1}{2}\rho {L^3}\left( {{{M'}_{uu}}{u^2} +}\right.\\&\!\!\!\!\!\!\!\!\!\!\!\!\left.{{{M'}_w}uw + {{M'}_{\left| w \right|}}u\left| w \right| + {{M'}_{\left. w \right|\left. w \right|}}\left. w \right|\left. w \right|} \right.\left. { + {{M'}_{ww}}{w^2}} \right) +\\ &\!\!\!\!\!\!\!\!\!\!\!\!\displaystyle\frac{1}{2}\rho {L^3}\left( {{{M'}_{{\delta _{\rm{s}}}}}{u^2}{\delta _{\rm{s}}} +{{M'}_{{\delta _{\rm{b}}}}}{u^2}{\delta _{\rm{b}}}} \right) - mgh\sin \theta + Mp\text{，}\\&\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\dot \theta = q\text{，}\\&\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\dot \zeta = - u\sin \theta + w\cos \theta\text{。} \end{aligned} \right. (3)

 ${A}\left( {\begin{array}{*{20}{l}}{\dot w}\\{\dot q}\end{array}} \right) = \left( {\begin{array}{*{20}{l}}{{f_1}\left( {w,q,{\delta _s},{\delta _b}} \right)}\\{{f_2}\left( {w,q,{\delta _s},{\delta _b}} \right)}\end{array}} \right)\text{，}$ (4)

 $\begin{split}{f_1}&\left( {w,q,{\delta _s},{\delta _b}} \right) \!\!=\!\! \displaystyle\frac{1}{2}\rho {L^4}{{Z'}_{\left. q \right|\left. q \right|}}\left. q \right|\left. q \right|\! +\!\left( {\displaystyle\frac{1}{2}\rho {L^3}{{Z'}_q} \!+\! m} \right)uq +\!\!\!\\&\displaystyle\frac{1}{2}\rho {L^3}{{Z'}_{\left. w \right|\left. q \right|}}\left. w \right|\left. q \right|+\displaystyle\frac{1}{2}\rho {L^2}\left( {{{Z'}_{uu}}{u^2} }+\right.\\&\left.{{{Z'}_w}uw + {{Z'}_{\left| w \right|}}u\left| w \right| + {{Z'}_{\left. w \right|\left. w \right|}}\left. w \right|\left. w \right| + {{Z'}_{ww}}{w^2}} \right) + P\text{，}\end{split}$
 $\begin{split}{f_2}& \left( {w,q,{\delta _s},{\delta _b}} \right) =\displaystyle\frac{1}{2}\rho {L^5}\left( {{{M'}_{\left. q \right|\left. q \right|}}\left. q \right|\left. q \right|} \right) + \displaystyle\frac{1}{2}\rho {L^4}\left( {{{M'}_q}uq +}\right.\\&\left.{{{M'}_{\left. w \right|\left. q \right|}}\left. w \right|\left. q \right|} \right) + Mp+\displaystyle\frac{1}{2}\rho {L^3}\left( {{{M'}_{uu}}{u^2} + {{M'}_w}uw +}\right.\\ &\left.{{{M'}_{\left| w \right|}}u\left| w \right| + {{M'}_{\left. w \right|\left. w \right|}}\left. w \right|\left. w \right| + {{M'}_{ww}}{w^2}} \right) - mgh\sin \theta \text{。}\end{split}$

 ${T_E}\dot \delta = {K_E}\left( {{\delta _e} - \delta } \right)\text{。}$ (5)

2.3 分级变论域深度纵倾模糊PID控制器设计

 图 2 深度纵倾控制器原理结构 Fig. 2 Configuration of depth and pith fuzzy PID controller

 图 3 深度误差模糊集 Fig. 3 Fuzzy set of depth error

3 仿真试验及分析

 图 4 目标深度90 m控制效果 Fig. 4 Control result of depth aim 90 m

 图 5 纵倾控制效果 Fig. 5 Result of pitch control

 图 6 目标深度20 m控制效果 Fig. 6 Control result of depth aim 20 m

 图 7 跟踪深度时变信号控制效果 Fig. 7 Control result of variable depth signal
4 结　语

 [1] 熊瑛. 基于智能控制的水下航行器操纵运动仿真研究[D]. 武汉: 中国舰船研究院, 2011. [2] 李平. 非线性系统自适应模糊控制方法研究[D]. 沈阳: 东北大学, 2010. [3] 龙祖强. 变论域模糊控制器的若干重要问题研究[D]. 长沙: 中南大学, 2011. [4] 石辛民, 郝整清. 模糊控制及其MATLAB仿真[M]. 北京: 清华大学出版社, 北京交通大学出版社, 2008: 10–51. [5] 王先洲. 船舶及水下航行器操纵中的鲁棒控制研究[D]. 武汉: 华中科技大学, 2008. [6] Shun Hung Tsai, Tzuu Hseng S Li. Robust Fuzzy Control of a Class of Fuzzy Bilinear Systems with Time-delay[J]. Chaos Solitons and Fractals, 2009, 39 : 2028–2040. DOI: 10.1016/j.chaos.2007.06.057 [7] CHEN C S. Dynamic Structure Adaptive Neural Fuzzy Control for MIMO Uncertain Nonlinear Systems[J]. Information Sciences, 2009, 179 : 2676–2688. DOI: 10.1016/j.ins.2009.03.015 [8] 施生达. 水下航行器操纵性[M]. 北京: 国防工业出版社, 1995: 45–50. [9] 任洪亮, 边信黔. 基于模糊规则的多模型控制方法在AUV航向控制中的应用[J]. 自动化技术与应用, 2004, 23 (6): 1–4. REN Hong-liang, BIAN Xin-qian. Fuzzy rule-based mulit-model control strategy and its application in AUV YAM control[J]. Techniques of Automation and Applications, 2004, 23 (6): 1–4. [10] 程启明. Fuzzy控制和PID控制集成的船舶操纵控制器研究[J]. 上海电力学院学报, 2001, 17 (4): 7–12. CHENG Qi-ming. Integrated controllors of Fuzzy control and PID control for ship manoeuvring[J]. Journal of Shanghai University of Electric Power, 2001, 17 (4): 7–12.