﻿ 鳍-水舱综合减摇混沌系统控制方法研究
«上一篇
 文章快速检索 高级检索

 智能系统学报  2017, Vol. 12 Issue (3): 318-324  DOI: 10.11992/tis.201607012 0

### 引用本文

WANG Hui, CHE Chao, YU Lijun, et al. Control method for a fin/tank integrated stabilization chaotic system[J]. CAAI Transactions on Intelligent Systems, 2017, 12(3): 318-324. DOI: 10.11992/tis.201607012.

### 文章历史

Control method for a fin/tank integrated stabilization chaotic system
WANG Hui, CHE Chao, YU Lijun, LIU Shaoying, YOU Jiang
College of Automation, Harbin Engineering University, Harbin 150001, China
Abstract: Based on the ship roll problem, the dynamic model equations of an integrated stabilization system were analyzed and proved this to be a chaotic system.The analytical method of phase diagrams and Lyapunov indexes were used to verify the chaotic motion of the system under certain conditions, then a nonlinear feedback control method was used to control this chaotic motion by choosing reasonable control parameters. This method reduced the chaotic motion of the system without destroying the original dynamic characteristics.The chaos search algorithm was combined with an ant colony algorithm to search the best parameters for PID. Therefore, the chaos ant colony optimization algorithm not only had strong global optimization ability but also accelerated the convergence speed. As a result, the performance of the control system was significantly improved.
Key words: integrated stabilization    parameter optimization    nonlinear feedback    chaos search algorithm    colony algorithm    attractor phase diagram    ship roll

1 综合减摇系统横摇混沌行为分析 1.1 综合减摇系统微分方程模型

 $\left\{ \begin{array}{l} \left( {{I_1} + {J_{\rm{t}}} + C} \right)\ddot \phi + \left( {2{N_\phi } + B} \right)\dot \phi + \\ \left( {Dh' + A} \right)\phi - {\rho _{\rm{t}}}{S_0}{b^2}\ddot z - 2{\rho _{\rm{t}}}g{S_0}Rz = {K_\omega }\\ 2{\rho _{\rm{t}}}{S_0}{\lambda _{\rm{t}}}\ddot z + 2{N_{\rm{t}}}\dot z + 2{\rho _{\rm{t}}}g{S_0}z - \\ {\rho _{\rm{t}}}{S_0}{b^2}\ddot \phi - 2{\rho _{\rm{t}}}g{S_0}R\phi = 0 \end{array} \right.$ (1)
 $\left\{ \begin{array}{l} A = {l_{\rm{f}}}{\rho _{\rm{t}}}{V^2}{A_{\rm{F}}}{K_{\rm{h}}}{K_{\rm{I}}}\left( {\partial Cy/\partial \alpha } \right)\\ B = {l_{\rm{f}}}{\rho _{\rm{t}}}{V^2}{A_{\rm{F}}}{K_{\rm{h}}}{K_{\rm{P}}}\left( {\partial Cy/\partial \alpha } \right)\\ C = {l_{\rm{f}}}{\rho _{\rm{t}}}{V^2}{A_{\rm{F}}}{K_{\rm{h}}}{K_{\rm{D}}}\left( {\partial Cy/\partial \alpha } \right) \end{array} \right.$ (2)

 $\left\{ \begin{array}{l} {K_{\rm{P}}} = \frac{{2{N_\phi }F}}{{{l_{\rm{f}}}{\rho _{\rm{t}}}{A_{\rm{F}}}{V^2}\left( {\partial Cy/\partial \alpha } \right)}}\\ {K_{\rm{I}}} = \frac{{DhF}}{{{l_{\rm{f}}}{\rho _{\rm{t}}}{A_{\rm{F}}}{V^2}\left( {\partial Cy/\partial \alpha } \right)}}\\ {K_{\rm{D}}} = \frac{{{I_1}F}}{{{l_{\rm{f}}}{\rho _{\rm{t}}}{A_{\rm{F}}}{V^2}\left( {\partial Cy/\partial \alpha } \right)}} \end{array} \right.$ (3)

 $\left\{ \begin{array}{l} \ddot \phi + 2{v_\phi }\dot \phi + \omega _\phi ^2\phi - \beta \ddot z - {a_{\rm{t}}}z = {K_\omega }\\ \ddot z + 2{v_{\rm{t}}}\dot z + \omega _{\rm{t}}^2z - {b_{\rm{t}}}\ddot \phi - R\omega _{\rm{t}}^2\phi = 0 \end{array} \right.$ (4)

${x_1} = \phi, {x_2} = \dot \phi, {x_3} = z, {x_4} = \dot z$，将方程式(4) 转化为微分方程模型[10-11]

 $\left\{ \begin{array}{l} {{\dot x}_1} = {x_2}\\ {{\dot x}_2} = \left[{{K_\omega } + \left( {{a_{\rm{t}}}-\beta \omega _{\rm{t}}^2} \right){x_3}-2{v_\phi }{x_2} + } \right.\\ \;\;\;\;\;\;\;\left. {\left( {\beta R\omega _{\rm{t}}^2-\omega _\phi ^2} \right){x_1} - 2\beta {v_{\rm{t}}}{x_4}} \right] \times {\left( {1 - \beta {b_{\rm{t}}}} \right)^{ - 1}}\\ {{\dot x}_3} = {x_4}\\ {{\dot x}_4} = \left[{{b_{\rm{t}}}{K_\omega } + \left( {{a_{\rm{t}}}{b_{\rm{t}}}-\omega _{\rm{t}}^2} \right){x_3}-2{v_{\rm{t}}}{x_4} + } \right.\\ \;\;\;\;\;\;\;\left. {\left( {R\omega _{\rm{t}}^2-\omega _\phi ^2{b_{\rm{t}}}} \right){x_1} - 2{v_\phi }{b_{\rm{t}}}{x_2}} \right] \times {\left( {1 - \beta {b_{\rm{t}}}} \right)^{ - 1}} \end{array} \right.$ (5)
1.2 综合减摇系统混沌行为发生条件 1.2.1 综合减摇系统混沌行为

 图 1 综合减摇系统混沌的Lyapunov指数动态变化图 Fig.1 Dynamic change figure of Lyapunov index of the integrated stabilization chaotic system

 $\mathit{\boldsymbol{J}} = \left[{\begin{array}{*{20}{c}} 0&1&0&0\\ {1.6953}&{-0.0599}&{0.0097}&{0.00092}\\ 0&0&0&1\\ {1.8955}&{-0.564}&{-0.6954}&{ - 3.883} \end{array}} \right]$ (6)

 图 2 综合减摇混沌系统的三维混沌吸引子相图 Fig.2 Three-dimensional chaotic attractor phase diagram of integrated stabilization chaotic system
1.2.2 非线性反馈控制下混沌行为

 图 3 Lyapunov指数随K变化曲线 Fig.3 Graph of the Lyapunov index with the change of K
 $\left\{ \begin{array}{l} {{\dot x}_1} = {x_2}\\ {{\dot x}_2} = \left[{{K_\omega } + \left( {{a_{\rm{t}}}-\beta \omega _{\rm{t}}^2} \right){x_3}-2\beta {v_{\rm{t}}}{x_4} + } \right.\\ \;\;\;\;\;\;\;\left. {\left( {\beta R\omega _{\rm{t}}^2-\omega _\phi ^2} \right){x_1} - 2{v_\phi }{v_2}} \right] \times {\left( {1 -\beta {b_{\rm{t}}}} \right)^{ -1}} + K{x_2}\left| {{x_2}} \right|\\ {{\dot x}_3} = {x_4}\\ {{\dot x}_4} = \left( {{b_{\rm{t}}}{K_\omega } + \left( {{a_{\rm{t}}}{b_{\rm{t}}} -\omega _{\rm{t}}^2} \right){x_3} - 2{v_{\rm{t}}}{x_4} + } \right.\\ \;\;\;\;\;\;\;\left. {\left( {R\omega _{\rm{t}}^2 - \omega _\phi ^2{b_{\rm{t}}}} \right){x_1} - 2{v_\phi }{b_{\rm{t}}}{x_2}} \right] \times {\left( {1 - \beta {b_{\rm{t}}}} \right)^{ - 1}} \end{array} \right.$ (7)

 图 4 非线性反馈控制后综合减摇混沌系统的三维混沌子相图 Fig.4 Three-dimensional chaotic attractor phasediagram after nonlinear feedback control

2 混沌蚁群算法的综合减摇系统PID控制参数寻优 2.1 混沌蚁群优化算法

 图 5 混沌蚁群算法流程图 Fig.5 Flow chart of chaos ant colony algorithm
2.2 混沌蚁群算法对综合减摇系统PID参数优化

 图 6 混沌蚁群算法优化原理图 Fig.6 Optimization schematic of chaos ant colony algorithm

1) PID控制参数优化问题转化为蚁群算法适用的组合优化问题

2) 目标函数的建立

 ${\rm{ITAE}} = \left\{ \begin{array}{l} \int_0^{{t_i}} {\left| {y\left( t \right) - {y_{ * p}}\left( t \right)} \right|{\rm{d}}t}, \;\;\;\;\;y\left( t \right) \ge {y_{ * p}}\left( t \right)\\ \int_0^{{t_i}} {\left| {y\left( t \right) - {y_{ * p}}\left( t \right)} \right|{\rm{d}}t}, \;\;\;\;\;y\left( t \right) < {y_{ * p}}\left( t \right) \end{array} \right.$ (8)

3) 路径的构建

 ${P_k}\left( {{c_i}, {y_j}, t} \right) = \frac{{{\tau ^a}\left( {{c_i}, {y_j}, t} \right){\eta ^\beta }\left( {{c_i}, {y_j}, t} \right)}}{{\sum\limits_{j = 0}^9 {{\tau ^a}\left( {{c_i}, {y_j}, t} \right){\eta ^\beta }\left( {{c_i}, {y_j}, t} \right)} }}$ (9)

4) 信息素的更新

 $\tau \left( {{c_i}, {y_j}, t + 15} \right) = \rho \tau \left( {{c_i}, {y_j}, t} \right) + \Delta \tau \left( {{c_i}, {y_j}} \right)$ (10)
 $\Delta \tau \left( {{c_i}, {y_j}} \right) = \sum\limits_k^m {\Delta {\tau _k}\left( {{c_i}, {y_j}} \right)}$ (11)
 $\Delta {\tau _k}\left( {{c_i}, {y_j}} \right) = \left\{ \begin{array}{l} Q/{F_k}\\ 0 \end{array} \right.$ (12)

2.3 仿真及结果分析

 图 7 基于遗传算法的PID控制系统的响应 Fig.7 Responses of PID control system based on genetic algorithm
 图 8 基于混沌蚁群算法的PID控制系统的响应 Fig.8 Responses of PID control system based on chaos ant colony optimization

3 结束语

 [1] 李天伟, 刘晓光, 彭伟骅, 等. 船舶航向保持中的混沌运动控制[J]. 计算机应用, 2013, 33(1): 234-238. LI Tianwei, LIU Xiaoguang, PENG Weihua, et al. Chaotic ship maneuvering control in course-keeping[J]. Journal of computer applications, 2013, 33(1): 234-238. (0) [2] 于立君, 陈佳, 刘繁明, 等. 改进粒子群算法的PID神经网络解耦控制[J]. 智能系统学报, 2015, 10(5): 699-704. YU Lijun, CHEN Jia, LIU Fanming, et al. An improved particle swarm optimization for PID neural network decoupling control[J]. CAAI transactions on intelligent systems, 2015, 10(5): 699-704. (0) [3] YU Lijun, LIU Shaoying, LIU Fanming, et al. Energy optimization of the fin/rudder roll stabilization system based on the multi-objective genetic algorithm(MOGA)[J]. Journal of marine science and application, 2015, 14(2): 202-207. DOI:10.1007/s11804-015-1292-z (0) [4] 刘胜, 孔琳. 基于工控机的船舶航向/横摇控制信息处理系统[J]. 智能系统学报, 2011, 6(3): 268-271. LIU Sheng, KONG Lin. An information processing system of ship course/roll control based on an industrial computer[J]. CAAI transactions on intelligent systems, 2011, 6(3): 268-271. (0) [5] FAIEGHI M R, NADERI M, JALALI A A. Design of fractional-order PID for ship roll motion control using chaos embedded PSO algorithm[C]//Proceedings of 2011 2nd International Conference on Control, Instrumentation and Automation (ICCIA). Shiraz: IEEE, 2011: 606-610. http://ieeexplore.ieee.org/document/6356727/ (0) [6] 黄谦, 李天伟, 王书晓, 等. 舰船混沌运动的单输入自适应变结构控制[J]. 动力学与控制学报, 2015, 13(6): 443-448. HUANG Qian, LI Tianwei, WANG Shuxiao, et al. Chaos control of ship steering via single input adaptive sliding mode control method[J]. Journal of dynamics and control, 2015, 13(6): 443-448. (0) [7] 胡开业, 丁勇, 王宏伟, 等. 船舶在随机横浪中的全局稳定性[J]. 哈尔滨工程大学学报, 2011, 32(6): 719-723. HU Kaiye, DING Yong, WANG Hongwei, et al. Global stability of ship motion in stochastic beam seas[J]. Journal of Harbin engineering university, 2011, 32(6): 719-723. (0) [8] 金鸿章, 赵卫平, 綦志刚, 等. 大型船舶综合减摇系统的研究[J]. 中国造船, 2005, 46(1): 29-35. JIN Hongzhang, ZHAO Weiping, QI Zhigang, et al. Research on integrated roll stabilization system for large ships[J]. Shipbuilding of China, 2005, 46(1): 29-35. (0) [9] 于立君, 孙经广, 刘繁明, 等. 广义预测算法在综合减摇系统控制器设计中的应用[J]. 船舶工程, 2013, 35(6): 76-79. YU Lijun, SUN Jingguang, LIU Fanming, et al. Application of generalized prediction algorithm in designing integrated stabilization system controller[J]. Ship engineering, 2013, 35(6): 76-79. (0) [10] MATOUK A E. Stability conditions, hyperchaos and control in a novel fractional order hyperchaotic system[J]. Physics letters A, 2009, 373(25): 2166-2173. DOI:10.1016/j.physleta.2009.04.032 (0) [11] LI C W, DU Yichun, WU Jianxing, et al. Synchronizing chaotification with support vector machine and wolf pack search algorithm for estimation of peripheral vascular occlusion in diabetes mellitus[J]. Biomedical signal processing and control, 2014, 9: 45-55. DOI:10.1016/j.bspc.2013.10.001 (0) [12] WALDNER F, KLAGES R. Symmetric jacobian for local Lyapunov exponents and Lyapunov stability analysis revisited[J]. Chaos, solitons and fractals, 2012, 45(3): 325-340. DOI:10.1016/j.chaos.2011.12.014 (0) [13] BARRIO R, MARTÍNEZ M A, SERRANO S, et al. When chaos meets hyperchaos: 4D Rössler model[J]. Physics letters A, 2015, 379(38): 2300-2305. DOI:10.1016/j.physleta.2015.07.035 (0) [14] WANG Junwei, XIONG Xiaohua, ZHAO Meichun, et al. Fuzzy stability and synchronization of hyperchaos systems[J]. Chaos, solitons and fractals, 2008, 35(5): 922-930. DOI:10.1016/j.chaos.2006.05.087 (0) [15] KAKMENI F M M, BOWONG S, TCHAWOUA C, et al. Strange attractors and chaos control in a Duffing-Van der Pol oscillator with two external periodic forces[J]. Journal of sound and vibration, 2004, 277(4/5): 783-799. (0) [16] 张文娟, 俞建宁, 张建刚, 等. 利用非线性反馈控制一类振动系统的振动[J]. 重庆理工大学学报:自然科学, 2013, 27(1): 27-31. ZHANG Wenjuan, YU Jianning, YANG Jiangang, et al. Using nonlinear feedback control for the vibration of a nonlinear vibration system[J]. Journal of Chongqing university of technology: natural science, 2013, 27(1): 27-31. (0) [17] LIU Yajuan, LEE S M. Synchronization criteria of chaotic Lur'e systems with delayed feedback PD control[J]. Neurocomputing, 2016, 189: 66-71. DOI:10.1016/j.neucom.2015.12.058 (0) [18] 陈烨. 变尺度混沌蚁群优化算法[J]. 计算机工程与应用, 2007, 43(3): 68-70. CHEN Ye. Scaleable chaotic ant colony optimization[J]. Computer engineer and applications, 2007, 43(3): 68-70. (0) [19] 朱洪华, 黄永华. 基于遗传算法的减摇鳍PID控制器优化[J]. 电脑知识与技术, 2011, 7(11): 2642-2644. ZHU Honghua, HUANG Yonghua. Optimization the PID controller of fin stabilizer based on genetic algorithm[J]. Computer knowledge and technology, 2011, 7(11): 2642-2644. DOI:10.3969/j.issn.1009-3044.2011.11.067 (0) [20] 李士勇, 柏继云. 连续函数寻优的改进量子扩展蚁群算法[J]. 哈尔滨工程大学学报, 2012, 33(1): 80-84. LI Shiyong, BAI Jiyun. Extended quantum ant colony algorithm for continuous function optimization[J]. Journal of Harbin engineering university, 2012, 33(1): 80-84. (0) [21] 王辉, 王科俊, 于立君. 减摇鳍模糊免疫自适应PID控制器设计及仿真研究[J]. 海军工程大学学报, 2007, 19(4): 17-21, 29. WANG Hui, WANG Kejun, YU Lijun. Design and simulation of fuzzy immune self-adaptation PID controller of fin stabilizer[J]. Journal of naval university of engineering, 2007, 19(4): 17-21, 29. (0) [22] 冯铁城, 陶尧森. 可控被动水舱研究[J]. 中国造船, 1997(1): 8-14. FENG Tiecheng, TAO Yaosen. A study on passive controlled antiroll tank[J]. Ship building of China, 1997(1): 8-14. (0)