混沌控制理论在船舶电力系统中的应用
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摘要
混沌控制理论是混沌理论的重要组成部分,也是非线性理论中的不可缺少的一部分,它具有初始条件极度敏感,非周期性的运行轨道,存在混沌吸引子等特点,很好地描述了非线性一类运动的规律和特征。因此混沌理论已经逐渐为人们所应用到诸多非线性科学中去。
船舶电力系统是典型的非线性系统,随着电力系统的规模增大,其非线性特征也越来越复杂和明显,在一定条件下甚至会发生混沌振荡现象。这种振荡如果不加以控制,极易直接导致发电机组电压崩溃或是机组解列,对系统的安全稳定运行形成一定威胁。并且这些混沌振荡现象具有对初始值极度敏感性,存在奇异吸引子,内部随机性等等。这些特性非一般非线性系统所具有的,用一般非线性控制方法无法将系统稳定到目标轨道上,所以研究混沌控制理论在船舶电力系统中的应用具有重大的意义。因此本论文针对电力系统中在一定条件下发生的混沌行为,以船舶电力系统二阶模型为例进行深入的混沌控制研究,主要研究内容如下所示：
第一,分析研究了船舶电力系统具有的混沌特性。研究了混沌的本质和相空间重构理论,重点研究相空间重构的参数选择；其次研究混沌判别理论,分别从定量和定性去对船舶电力系统进行判别,重点研究李亚普诺夫指数判别方法；最后用MATLAB平台进行仿真得出结论,继而为混沌控制研究拉开序幕。
第二,总结了船舶电力系统的数学模型。分析船舶电力系统的运行原理并总结船舶电力系统从二阶到七阶的数学模型,并对模型的相关参数进行深入的剖析,重点研究船舶电力系统的二阶数学模型,在此模型的基础上进行混沌控制研究。
第三,设计输出延迟反馈控制方法设计反馈控制器。利用梅尔尼科夫方法确定控制器的控制参数,分别选取500个点和5000个点对船舶电力系统进行仿真；在精确反馈线性化控制方面,将系统经过精确线性化处理,在通过最优控制原理设计最优控制器,将设计好的控制器加入到模型中,结果表明该控制器能有效地抑制混沌振荡。
第四,设计RBF神经网络控制器。船舶电力系统易受外界干扰的影响和RBF神经网络较强的逼近特性,设计RBF神经网络逼近器,同时在MATLAB平台上加入设计好的输出延迟反馈控制器,并将仿真结果与其他两种控制器的控制效果进行比较,经分析说明该联合控制器能将系统的动态行为更好地稳定下来。
Chaos control theory is a important part of Chaos theory, and it is also a indispensable part of nonlinear theory. It has many characteristics, such as extremely sensitive to initial conditions, aperiodicity orbits, existing chaos attractor and so on. These characteristics definitely descript Rules and characteristics of Nonlinear movement. so Chaos theory has already applied to a lot of nonlinear science.
Ship power system is a typical nonlinear system. With the scale of the power system increasing, it's nonlinear characteristics also become more and more complex and obvious. Under certain conditions, even Chaos oscillation phenomena occurs. If we don't control the oscillation, it may directly lead to Generator voltage collapse or unit solution columns, and it also form a certain threat of the safe and stable operation of the system. Furthermore, the chaos phenomena is very sensitive to the initial value and common method of nonlinear control can't keep the system running stably. Hence it is of grate significance that we should study the chaos control of ship power system. Concerned with the chaotic behavior of the power system under certain conditions, ship power system of second order model have been studied as a example of chaos control in this paper. The main research contents are shown:
(1) Research on chaotic characters of ship power system. Exploring nature of chaos, reconstruction theory and choosing the parameters of phase space reconstruction. Separately using the quantitative and qualitative method identify the ship power system; Focusing on Lyapunov index identifying method. And using MATLAB to simulate and obtain the results. Consequently, preparing for the research of chaos control.
(2) Research on Ship model of power system. According to the analysis of The operation principle and research material of ship power system, we research Ship power system mathematical model from second order to seven order. The parameters of the model were discussed in the paper, and focusing on the ship power system of second order model.
(3) Design of feedback controller. Using Melnikov's method to determine the parameters of the controller,500points and5000points were separately selected to simulate the ship power system; In the aspect of accurate feedback linear controlling, the system was accurately linearizated and optimal controller was designed with the optimal control theory. The results show that the controller can effectively suppress the chaotic oscillations. The designed controller was added to the model and MATLAB was used to simulate.
(4) Design of RBF neural network controller. Ship power system is easily affected by external interference and hence it is similar to the RBF neural network.Designing approximation operator and adding designed output time delay feedback controller into it. It shows that the dynamic behavior of the system can be stabilized better by the joint controller.
船舶电力系统是典型的非线性系统,随着电力系统的规模增大,其非线性特征也越来越复杂和明显,在一定条件下甚至会发生混沌振荡现象。这种振荡如果不加以控制,极易直接导致发电机组电压崩溃或是机组解列,对系统的安全稳定运行形成一定威胁。并且这些混沌振荡现象具有对初始值极度敏感性,存在奇异吸引子,内部随机性等等。这些特性非一般非线性系统所具有的,用一般非线性控制方法无法将系统稳定到目标轨道上,所以研究混沌控制理论在船舶电力系统中的应用具有重大的意义。因此本论文针对电力系统中在一定条件下发生的混沌行为,以船舶电力系统二阶模型为例进行深入的混沌控制研究,主要研究内容如下所示：
第一,分析研究了船舶电力系统具有的混沌特性。研究了混沌的本质和相空间重构理论,重点研究相空间重构的参数选择；其次研究混沌判别理论,分别从定量和定性去对船舶电力系统进行判别,重点研究李亚普诺夫指数判别方法；最后用MATLAB平台进行仿真得出结论,继而为混沌控制研究拉开序幕。
第二,总结了船舶电力系统的数学模型。分析船舶电力系统的运行原理并总结船舶电力系统从二阶到七阶的数学模型,并对模型的相关参数进行深入的剖析,重点研究船舶电力系统的二阶数学模型,在此模型的基础上进行混沌控制研究。
第三,设计输出延迟反馈控制方法设计反馈控制器。利用梅尔尼科夫方法确定控制器的控制参数,分别选取500个点和5000个点对船舶电力系统进行仿真；在精确反馈线性化控制方面,将系统经过精确线性化处理,在通过最优控制原理设计最优控制器,将设计好的控制器加入到模型中,结果表明该控制器能有效地抑制混沌振荡。
第四,设计RBF神经网络控制器。船舶电力系统易受外界干扰的影响和RBF神经网络较强的逼近特性,设计RBF神经网络逼近器,同时在MATLAB平台上加入设计好的输出延迟反馈控制器,并将仿真结果与其他两种控制器的控制效果进行比较,经分析说明该联合控制器能将系统的动态行为更好地稳定下来。
Chaos control theory is a important part of Chaos theory, and it is also a indispensable part of nonlinear theory. It has many characteristics, such as extremely sensitive to initial conditions, aperiodicity orbits, existing chaos attractor and so on. These characteristics definitely descript Rules and characteristics of Nonlinear movement. so Chaos theory has already applied to a lot of nonlinear science.
Ship power system is a typical nonlinear system. With the scale of the power system increasing, it's nonlinear characteristics also become more and more complex and obvious. Under certain conditions, even Chaos oscillation phenomena occurs. If we don't control the oscillation, it may directly lead to Generator voltage collapse or unit solution columns, and it also form a certain threat of the safe and stable operation of the system. Furthermore, the chaos phenomena is very sensitive to the initial value and common method of nonlinear control can't keep the system running stably. Hence it is of grate significance that we should study the chaos control of ship power system. Concerned with the chaotic behavior of the power system under certain conditions, ship power system of second order model have been studied as a example of chaos control in this paper. The main research contents are shown:
(1) Research on chaotic characters of ship power system. Exploring nature of chaos, reconstruction theory and choosing the parameters of phase space reconstruction. Separately using the quantitative and qualitative method identify the ship power system; Focusing on Lyapunov index identifying method. And using MATLAB to simulate and obtain the results. Consequently, preparing for the research of chaos control.
(2) Research on Ship model of power system. According to the analysis of The operation principle and research material of ship power system, we research Ship power system mathematical model from second order to seven order. The parameters of the model were discussed in the paper, and focusing on the ship power system of second order model.
(3) Design of feedback controller. Using Melnikov's method to determine the parameters of the controller,500points and5000points were separately selected to simulate the ship power system; In the aspect of accurate feedback linear controlling, the system was accurately linearizated and optimal controller was designed with the optimal control theory. The results show that the controller can effectively suppress the chaotic oscillations. The designed controller was added to the model and MATLAB was used to simulate.
(4) Design of RBF neural network controller. Ship power system is easily affected by external interference and hence it is similar to the RBF neural network.Designing approximation operator and adding designed output time delay feedback controller into it. It shows that the dynamic behavior of the system can be stabilized better by the joint controller.
引文
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[2]刘丙泉.船舶人因事故预警管理研究：[博士学位论文].哈尔滨：哈尔滨工程大学,2009.
[3]罗乐.船舶电力系统建模与控制：[硕士学位论文].武汉：武汉理工大学,2011
[4]郭玉祥.含一个非线性混沌系数的脉冲控制及反馈.物理学报.2010,8.
[5]白椿.超混沌系统的同步研究：[硕士学位论文].河北工业大学,2010.
[6]胡静波.混沌控制理论及其发展方向.宝鸡文理学院学报,2007(4).
[7]E.Ott.C.Grebogi, J.A.Yorke. Controlling chaos. Physics Letters,1990,64(11):1196-1199.
[8]张化光,王智良,黄伟.混沌系统的控制理论[M].沈阳：东北大学出版社,2003：110-172.
[9]赵光宙.混沌控制理论及其应用.电工技术学报,2001(5).
[10]黄波.基于混沌优化的火电厂经济负荷分配.华北电力大学.2005.
[11]Yu Y. Electric power system dynamics. New York: Academic Press,1983.
[12]Lu Q, Sun Y, Mei S. Nonlinear control systems and power system dynamics. Boston:Kluwer Academic Publishers,2001.
[13]黄健.船舶电力系统混沌现象研究.上海：上海海事大学,2005.
[14]蒋传文.电力负荷预报理论及其新方法的研究-混沌理论及应用.武汉：华中科技大学,2000.
[15]马敏.船舶电力系统混沌控制的研究[D].哈尔滨：哈尔滨工程大学,2009.
[16]华清.船舶交通事故混沌预测研究：[硕士学位论文].武汉：武汉理工大学,2008.
[17]周金勇.混沌时间序列预测模型研究：[硕士学位论文].武汉：武汉理工大学,2009.
[18]杨姝.激光混沌的相空间重构：[硕士学位论文].长春理工大学,2008.
[19]王雪萍.P-N结中的混沌研究：[硕十学位论文].长春理工大学,2006.
[20]田聪.基于混沌理论的短期电力负荷预测.哈尔滨：哈尔滨理工大学,2007.
[21]Wolf A.etal. Determining Lyapunov exponents from a time series, Physica D,16, 1985:285-317.
[22]汤龙坤.利用最大Lyapunov指数检验混沌时间序列降噪效果.重庆科技学院学报自然科学版,2011,13(2).
[23]华东东.短时交通流的混沌性分析及其基于神经网络的预测模型研究.南京：东南大学,2005.
[24]张晓丹.一类基于奇异值分解的Lyapunov指数计算方法.北京科技大学学报,2005(3).
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