大型油轮艏摇混沌现象的仿真与滑模控制

doi:10.16183/j.cnki.jsjtu.2019.104

摘要/Abstract

摘要：

为了合理解释并控制大型油轮操纵过程中出现的船首异常摆动现象，采用驾驶员模型替代原有的比例模型，结合非线性响应型数学模型，建立了驾驶员操纵大型油轮的闭环系统数学方程，发现其与Duffing方程形似，且在一定的参数配置下系统的Lyapunov指数为正，说明可以用混沌理论解释船首异常摆动的现象．为实现航向保持的稳定控制并增强对参数不确定的鲁棒性，基于反步法提出了与模型对应的滑模控制率．仿真结果表明，当混沌艏摇处于理论最大值时，受控系统的稳态舵角仍小于5°，航向偏差小于0.07°，所设计的控制器很好地消除了混沌现象．建立人在回路中的混沌系统的思路较为新颖，借助滑模解决反步法参数不确定的方法简单而有效．

关键词: 混沌, 驾驶员模型, 混沌系统建模, 反步法, 滑模控制, 航向保持控制

Abstract:

In order to explain and control the unexpected yawing phenomenon of large oil tankers, a pilot model is used to replace the original proportional model and is combined with the nonlinear ship responding model to construct a model of the whole closed-loop maneuvering system, which is found to be similar to the chaotic Duffing equation, and to be able to have a positive Lyapunov exponent after parameter adjustment, indicating that the chaotic theory can be used to explain this unexpected yawing phenomenon. In order to realize course keeping control with robustness to parameter uncertainty, based on the model built and the backstepping method, a sliding mode control scheme is proposed. The simulation illustrates that the static state rudder angle is smaller than 5° and course deviation is smaller than 0.07° when the chaotic yawing is at the theoretical maximum. Chaotic yawing is eliminated. The idea of establishing man-in-the-loop chaotic system is novel, and the method of solving backstepping parameter uncertainty through sliding mode is easy and effective.

Key words: chaos, pilot model, chaotic system modeling, backstepping method, sliding mode control, course keeping control

中图分类号:

U661.32

张显库, 韩旭. 大型油轮艏摇混沌现象的仿真与滑模控制[J]. 上海交通大学学报, 2021, 55(1): 40-47.

ZHANG Xianku, HAN Xu. Modeling and Sliding Mode Control for Chaotic Yawing Phenomenon of Large Oil Tanker[J]. Journal of Shanghai Jiao Tong University, 2021, 55(1): 40-47.

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参考文献 18

[1]	LIU Y, HU A, HAN F, et al. Numerical method research on nonlinear roll system of large container ship[C]∥34th International Conference on Ocean, Offshore and Arctic Engineering (ASME 2015). New York: The American Society of Mechanical Engineers, 2015: 2-22.
[2]	SPYROU K J, THOMPSON J M T. The nonlinear dynamics of ship motions: A field overview and some recent developments[J]. Philosophical Transactions Mathematical Physical & Engineering Sciences, 2000, 358(1771): 1735-1760.
[3]	SPYROU K J, THEMELIS N, KONTOLEFAS I. Nonlinear surge motions of a ship in bi-chromatic following waves[J]. Communications in Nonlinear Science & Numerical Simulations, 2018, 56: 296-313.
[4]	KONTOLEFAS I, SPYROU K J. Coherent structures in phase space, governing the nonlinear surge motions of ships in steep waves[J]. Ocean Engineering, 2016, 120: 339-345.
[5]	苏宁．混沌学与船舶控制应用[D]. 大连：大连海事大学，1996.
	SU Ning. Chaos and ship motion control[D]. Dalian: Dalian Maritime University, 1996.
[6]	朱璐．船舶航向保持中的混沌及鲁棒控制[D]. 大连：大连海事大学，2009.
	ZHU Lu. Chaos in the course keeping control of ships and robust control method[D]. Dalian: Dalian Maritime University, 2009.
[7]	毕宁宁．参数不确定Liu混沌系统的鲁棒控制[D]．大连：大连海事大学，2009.
	BI Ningning. Robust control of parameter uncertain Liu chaotic system[D]. Dalian: Dalian Maritime University, 2009.
[8]	于黎明，王占林，裘丽华．人机控制与驾驶员模型研究[J]. 电光与控制，2000(1): 1-8.
	YU Liming, WANG Zhanlin, QIU Lihua. The study on pilot/flight control system and pilot model[J]. Electronics Optics & Control, 2000(1): 1-8.
[9]	蒋维安. 多维比例微分非线性飞行员模型及仿真应用[J]. 系统仿真学报，2018, 30(10): 100-107.
	JIANG Weian. Multi-dimension proportion-differential nonlinear pilot model and simulation application[J]. Journal of System Simulation, 2018, 30(10): 100-107.
[10]	YUCELEN T, YILDIZ Y, SIPAHI R, et al. Stability limit of human-in-the-loop model reference adaptive control architectures[J]. International Journal of Control, 2017, 91(10): 1-36.
[11]	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.
[12]	LI T, HUANG Q, GUO J, et al. A valid adaptive sliding mode control method for chaotic ship steering[C]∥Control & Decision Conference. New York: IEEE, 2015: 3221-3224.
[13]	ZHANG X, YANG G, ZHANG Q, et al. Improved concise backstepping control of course keeping for ships using nonlinear feedback technique[J]. Journal of Navigation, 2017, 70(6): 1401-1414.
[14]	刘金琨. 滑模变结构控制MATLAB仿真[M]. 第3版. 北京：清华大学出版社，2015: 4-10.
	LIU Jinkun. Sliding mode control design and MATLAB simulation[M]. 3rd ed. Beijing: Tsinghua University Press, 2015: 4-10.
[15]	张显库，金一丞. 控制系统建模与数字仿真[M]. 第2版. 大连：大连海事大学出版社，2013: 108-145.
	ZHANG Xianku, JIN Yicheng. Control system modeling and digital simulation[M]. 2nd ed. Dalian: Dalian Maritime University Press, 2013: 108-145.
[16]	MCCUE L S, TROESCH A W. Use of Lyapunov exponents to predict chaotic vessel motions[J]. Fluid Mechanics and Its Applications, 2011, 97: 415-432.
[17]	孙克辉，谈国强，盛利元. Lyapunov指数计算算法的设计与实现[J]. 计算机工程与应用，2004, 40(35): 12-14.
	SUN Kehui, TAN Guoqiang, SHENG Liyuan. Design and implementation of Lyapunov exponents calculating algorithm[J]. Computer Engineering and Applications, 2004, 40(35): 12-14.
[18]	闵颖颖，刘允刚. Barbalat引理及其在系统稳定性分析中的应用[J]. 山东大学学报(工学版), 2007, 37(1): 51-55.
	MIN Yingying, LIU Yungang. Barbalat lemma and its application in analysis of system stability[J]. Journal of Shandong University (Engineering Science), 2007, 37(1): 51-55.

参数	取值	参数	取值
两柱间长/m	234	重心距中心距离/m	8.536
船宽/m	42	航速/kn	14.8
吃水/m	14.9	舵叶面积/m²	65.04
方形系数	0.817	排水量/m³	122 945
K	0.07	T₃	28.43
T₁	179.4	α	26.59
T₂	12.17	β	152 406.7

(λ₁,λ₂,λ₃)	系统稳定性
(－，－，－)	稳定不动点
(0，－，－)	极限环
(0, 0，－)	二维环面
(+，+，0)	不稳极限环
(+，0, 0)	不稳二维环面
(+，0，－)	混沌吸引子