区域防洪系统模拟模型及其控制运用研究
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摘要
在遍及全球的各种自然灾害中，洪涝灾害是发生频率最大、危害也最大的一种。人必须学会与洪水和平共处、和谐发展，在谋求社会经济发展的同时，尽量减少洪水所造成的灾害损失，遵循洪水的自然规律，尽力保持其在自然生态环境中所能发挥的洗涤净化地表与河流、补充地下水、维持湖沼及改良土壤等有益的作用。防洪减灾，需工程与非工程措施并举，硬软件环境相配合，建立有效的防汛指挥系统。
本研究以淮河入江水道和入海水道为研究对象，讨论入江水道和入海水道水动力学洪水演进模拟及其控制运用问题。论文建立了其洪水演进模拟模型，模型采用常用的一维非恒定流水动力学模拟模型，用追赶法求解按Preissmann四点加权格式离散的Saint-Venant方程组所得的线性方程组。
论文采用最优控制中的鲁棒H∞控制理论对防洪系统进行反馈控制。为便于解决问题，首先将圣维南方程组离散化和线性化，在此基础上用现代控制理论的概念建立了河道防洪模拟及控制系统的状态空间方程。论文运用鲁棒H∞控制方法对防洪控制系统进行了稳定性分析、权函数选取、增广矩阵计算及系统最优控制器的设计，求解鲁棒H∞反馈控制律实现对系统的反馈控制。以入海水道和入江水道为例，验证了控制系统的可行性。应用中，采用塔姆勒的纯时延模型考虑水流状态的时延。
鲁棒H∞控制应用于河道防洪系统中是较前沿的课题，有不少人对此课题进行了研究，但目前尚没有工程应用实例。本文作了初步探讨，希望对以后的相关研究有所帮助。
Among various disasters in the world, flood disaster happens in a high frequency and causes great damage to human society. So when seeking for the vigorous socio-economic development, flood should be coped with to minimize the losses caused by it, to make full use of the flood, i.e. cleaning the ground surface and rivers, supplying ground water, maintaining lakes and meliorate soil, etc.. All the approaches should be done through following the natural rules of flood. Therefore, flood control should consider both the project-related approaches and non-project measure, together with the hardware and the software development. Only by attaining so, can the efficient flood prevention commanding centre be realized.
This dissertation discusses the simulation and control of flood in Rujiang River and Ruhai River based on the flood simulation models. Saint-venant equations describe the channel flow movement, and the solution of the nonlinear algebraic equations was obtained through discretization of Pressman weighted implicit four-point genre with the matching pursuit method.
The dissertation reveals the application of robust H_∞control theory, one of the optimized control theories, to the flood control process to seek for an easier way to explain the application of robust control theory in resolving the flood control issue, the subject was demenstrated with the state space methodology which is followed by discretizing and linearzing the St.Venant Equation based on the flood simulation and control model. In order to apply the robust control theory into the river, system stability was analyzed, weight function and augmented matrix, as well as the design of optimized H_∞control devices, were selected and calculated. And then the feedback matrix can be obtained. The flood of Ruhai River and Rujiang River was taken as a case study to validate the model's feasibility. Tamura's model was also used to consider the time lag of water in the two rivers.
The application of robust H_∞control theory to the flood prevention system is still immature without a precedent in real application after a great many of researcher's hard work and hence requires further research. A primary exploration on the subject was made in this study, hoping it could be inspiring for the future research.
本研究以淮河入江水道和入海水道为研究对象，讨论入江水道和入海水道水动力学洪水演进模拟及其控制运用问题。论文建立了其洪水演进模拟模型，模型采用常用的一维非恒定流水动力学模拟模型，用追赶法求解按Preissmann四点加权格式离散的Saint-Venant方程组所得的线性方程组。
论文采用最优控制中的鲁棒H∞控制理论对防洪系统进行反馈控制。为便于解决问题，首先将圣维南方程组离散化和线性化，在此基础上用现代控制理论的概念建立了河道防洪模拟及控制系统的状态空间方程。论文运用鲁棒H∞控制方法对防洪控制系统进行了稳定性分析、权函数选取、增广矩阵计算及系统最优控制器的设计，求解鲁棒H∞反馈控制律实现对系统的反馈控制。以入海水道和入江水道为例，验证了控制系统的可行性。应用中，采用塔姆勒的纯时延模型考虑水流状态的时延。
鲁棒H∞控制应用于河道防洪系统中是较前沿的课题，有不少人对此课题进行了研究，但目前尚没有工程应用实例。本文作了初步探讨，希望对以后的相关研究有所帮助。
Among various disasters in the world, flood disaster happens in a high frequency and causes great damage to human society. So when seeking for the vigorous socio-economic development, flood should be coped with to minimize the losses caused by it, to make full use of the flood, i.e. cleaning the ground surface and rivers, supplying ground water, maintaining lakes and meliorate soil, etc.. All the approaches should be done through following the natural rules of flood. Therefore, flood control should consider both the project-related approaches and non-project measure, together with the hardware and the software development. Only by attaining so, can the efficient flood prevention commanding centre be realized.
This dissertation discusses the simulation and control of flood in Rujiang River and Ruhai River based on the flood simulation models. Saint-venant equations describe the channel flow movement, and the solution of the nonlinear algebraic equations was obtained through discretization of Pressman weighted implicit four-point genre with the matching pursuit method.
The dissertation reveals the application of robust H_∞control theory, one of the optimized control theories, to the flood control process to seek for an easier way to explain the application of robust control theory in resolving the flood control issue, the subject was demenstrated with the state space methodology which is followed by discretizing and linearzing the St.Venant Equation based on the flood simulation and control model. In order to apply the robust control theory into the river, system stability was analyzed, weight function and augmented matrix, as well as the design of optimized H_∞control devices, were selected and calculated. And then the feedback matrix can be obtained. The flood of Ruhai River and Rujiang River was taken as a case study to validate the model's feasibility. Tamura's model was also used to consider the time lag of water in the two rivers.
The application of robust H_∞control theory to the flood prevention system is still immature without a precedent in real application after a great many of researcher's hard work and hence requires further research. A primary exploration on the subject was made in this study, hoping it could be inspiring for the future research.
引文
[1] 李光炽．流域洪水演进模型及其参数反问题研究[D]．河海大学，2001．4
[2] 程海云，葛守西，李玉荣．水动力学模型实时校正方法研究[J]．人民长江，2005(36)2
[3] 李家星，赵振兴．水力学[M]．南京：河海大学出版社，2001．
[4] Cunge J A. On the subject of a flood propagation computation method[J]. Journal of HydraulicResource, 1969, 7 (2):205-230.
[5] Ponce V M, Li R M, Simons D B. Applicability of kinematic and diffusion models [J]. Journalof Hydraulic Div., 1978, 104(3):353-360.
[6] Liggett J A, Woolhiser D A. Difference solution of the shallow-water equation [J]. J. Engng. Mech. Div. 1967, 95 (2):39-71.
[7] Strelkoff T. Numericalsolution of Saint-Venant equations [J]. J. HydraulicDiv, 1970, 96(1):223-252.
[8] Abott M B, Lonescu F. On the numerical computation of nearly horizontal flows[J]. J. Hydraulic Res., 1967, 5 (2):97-117.
[9] Amein M, Fang C S. Implicit flood routing in natural channels [J]. J. Hydraulic Div., 1970, 96(12):2481-2500.
[10] Fread D L. Technique for implicit dynamic routing in rivers with tributaries [J].Water Resources Res., 1973, 9(4):918-926.
[11] 徐小明，张静怡，丁健，汪德燧．河网水力数值模拟的松弛迭代法及水位的可视化显示[J]．水文，2000，20(6)：1-4．
[12] 徐小明，何建京，汪德爟．求解大型河网非恒定流的非线性方法[J]．水动力学研究与进展，2001，16(1)：18-24．
[13] 王船海，李光炽．实用河网水流计算[M]．河海大学出版社，2003．
[14] 李岳生等．河网不恒定流隐式方程组的稀疏矩阵解法[J]．中山大学学报(自然科学版)，1977(3)：25-37．
[15] Dronkers J J．河流近海区和外海的潮汐计算[J]．水利水运科技情况，1976(增刊)：24-67．
[16] Naidu B J, Murty Bhallamudi S, and Narasimhan S, GVF Computation in tree-type channel Networks. [J]。J. Hydr Engrg, 1997, (8):700-708.
[17] 张二骏，张东生，李挺．河网非恒定流三级联合解法[J]．华东水利学院学报，1982，10(1)：1-13．
[18] 吴寿红．河网非恒定流四级解法[J]．水利学报，1985(8)：42-50．
[19] 芮孝芳，冯平．多支流河道洪水演算方法的探讨[J]．水利学报，1990(2)：26-32．
[20] 李义天．河网非恒定流隐式方程组的汊点分组解法[J]．水利学报，1997(3)：49-57．
[21] 韩龙喜，张书全，金忠青．复杂河网非恒定流计算模型——单元划分法[J]．水利学报，1994，2：52-56．
[22] 姚琪等．运河水网水量数学模型的研究应用[J]．河海大学学报，1991，4：9-17．
[23] 徐小明，汪德罐。河网非恒定流分级解法与松弛迭代解法比较[J]．河海大学学报，2000(增刊)：68-70．
[24] Cruz, J.B. and Perkins, W. K. A new approach to the sensitivity problem in multivariable feedback systems. IEEE Trans. Automat. Contr., 1964, Vol. AC-9:216-223.
[25] 褚健，俞立，苏宏业．鲁棒控制理论与应用[M]．浙江大学出版社．1998，4
[26] 芮孝芳，洪水预报理论的新进展及现行方法的适用性[J]．水利水电科技进展，2001(21)5
[27] 伍宁．一维圣维南方程组在非恒定流计算中的应用[J]．武汉：人民长江，2001(32)11
[28] 汪德罐．计算水力学[M]．南京：河海大学出版社，1989，9
[29] 王船海，李光炽．实用河网水流计算[M]．南京：河海大学水资源水文系，2003
[30] 王显正，陈正航，王旭永．控制理论基础[M]．北京：科学出版社，2000．
[31] 王划一，杨西侠，林家恒．现代控制理论基础[M]．国防工业出版社，2004．9．
[32] 薛亚莉，城市河流水量水质自适应控制模型研究[D]．河海大学，2006，6
[33] 王朝珠，秦化淑．最优控制理论[M]．北京：科学出版社，2003．9
[34] [英]M．G．辛，[法]A．铁托里．大系统的最优化及控制[M]．机械工业出版社，1983．7
[35] M．G．辛格．大系统的动态递阶控制[M]．北京：科学出版社，1983
[36] 褚健，俞立，苏宏业．鲁棒控制理论与应用[M]．浙江大学出版社．1998，4
[37] 尚涛，安宁，刘勇．渠道自动运行鲁棒控制的理论及其动态仿真研究[J]．武汉大学学报(工学版)，2004(37)，2．
[38] 单毅．渠道运行过程鲁棒控制研究及动态仿真[D]．武汉大学．2005
[39] 吴旭东，解学书．H∞鲁棒控制中的加权阵选择[J]．清华大学学报(自然科学版)，1997(37)，1．
[40] 解学书，钟宜生．H∞控制理论[M]．北京：清华大学出版社，1994．
[41] ZamesG.On the input-output stability of time varying nonlinear feedback systems: parts Ⅰ and Ⅱ. IEEETranAC,1966,11(2,3):228～238,465～476
[42] Tsai M C,Geddes EJM, Postlethwaite I. Pole-zero Cancellations and closed-loop properties of an H∞mixed sensitivity ydesign problem.Automatica, 1992,28(3): 519～530
[43] Kwakernaak Hilbert. Robust control and H∞ optimiza-tion: tutorial paper. Automatica, 1993,28(3):255～273
[44] Postlethwaite I, Tsai Miching, GuDawei. Weighting Function selection in Hoodesign.11th IFAC, 1990, Tallinn: 104～109
[45] 冯纯伯，田玉平，忻欣．鲁棒控制系统设计[M]．南京：东南大学出版社，1995
[46] 陈永春．MATLAB M语言高级编程[M]．北京：清华大学出版社．2004
[47] Zames, G.. Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms and.approximate inverses. IEEE Trans. Automat. Contr., 1981, Vol. AC-26:301-320.
[48] Francis, B. A.. A course in H_∞ control theory. Lecture Notes in Control and Information Sciences, Springer-Verleg, 1987.
[49] Doyle, J. C., Glover, K., Khargonekor, P.P. and Francis, B. A.. State-space solutions to standard H_2 and H_∞ control problems. IEEE Trans. Automat. Contr., 1989, Vol. 30:1307-1317.
[50] 梅生伟，申铁龙，刘康志．现代鲁棒控制理论与应用，北京：清华大学出版社，2003，9
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[2] 程海云，葛守西，李玉荣．水动力学模型实时校正方法研究[J]．人民长江，2005(36)2
[3] 李家星，赵振兴．水力学[M]．南京：河海大学出版社，2001．
[4] Cunge J A. On the subject of a flood propagation computation method[J]. Journal of HydraulicResource, 1969, 7 (2):205-230.
[5] Ponce V M, Li R M, Simons D B. Applicability of kinematic and diffusion models [J]. Journalof Hydraulic Div., 1978, 104(3):353-360.
[6] Liggett J A, Woolhiser D A. Difference solution of the shallow-water equation [J]. J. Engng. Mech. Div. 1967, 95 (2):39-71.
[7] Strelkoff T. Numericalsolution of Saint-Venant equations [J]. J. HydraulicDiv, 1970, 96(1):223-252.
[8] Abott M B, Lonescu F. On the numerical computation of nearly horizontal flows[J]. J. Hydraulic Res., 1967, 5 (2):97-117.
[9] Amein M, Fang C S. Implicit flood routing in natural channels [J]. J. Hydraulic Div., 1970, 96(12):2481-2500.
[10] Fread D L. Technique for implicit dynamic routing in rivers with tributaries [J].Water Resources Res., 1973, 9(4):918-926.
[11] 徐小明，张静怡，丁健，汪德燧．河网水力数值模拟的松弛迭代法及水位的可视化显示[J]．水文，2000，20(6)：1-4．
[12] 徐小明，何建京，汪德爟．求解大型河网非恒定流的非线性方法[J]．水动力学研究与进展，2001，16(1)：18-24．
[13] 王船海，李光炽．实用河网水流计算[M]．河海大学出版社，2003．
[14] 李岳生等．河网不恒定流隐式方程组的稀疏矩阵解法[J]．中山大学学报(自然科学版)，1977(3)：25-37．
[15] Dronkers J J．河流近海区和外海的潮汐计算[J]．水利水运科技情况，1976(增刊)：24-67．
[16] Naidu B J, Murty Bhallamudi S, and Narasimhan S, GVF Computation in tree-type channel Networks. [J]。J. Hydr Engrg, 1997, (8):700-708.
[17] 张二骏，张东生，李挺．河网非恒定流三级联合解法[J]．华东水利学院学报，1982，10(1)：1-13．
[18] 吴寿红．河网非恒定流四级解法[J]．水利学报，1985(8)：42-50．
[19] 芮孝芳，冯平．多支流河道洪水演算方法的探讨[J]．水利学报，1990(2)：26-32．
[20] 李义天．河网非恒定流隐式方程组的汊点分组解法[J]．水利学报，1997(3)：49-57．
[21] 韩龙喜，张书全，金忠青．复杂河网非恒定流计算模型——单元划分法[J]．水利学报，1994，2：52-56．
[22] 姚琪等．运河水网水量数学模型的研究应用[J]．河海大学学报，1991，4：9-17．
[23] 徐小明，汪德罐。河网非恒定流分级解法与松弛迭代解法比较[J]．河海大学学报，2000(增刊)：68-70．
[24] Cruz, J.B. and Perkins, W. K. A new approach to the sensitivity problem in multivariable feedback systems. IEEE Trans. Automat. Contr., 1964, Vol. AC-9:216-223.
[25] 褚健，俞立，苏宏业．鲁棒控制理论与应用[M]．浙江大学出版社．1998，4
[26] 芮孝芳，洪水预报理论的新进展及现行方法的适用性[J]．水利水电科技进展，2001(21)5
[27] 伍宁．一维圣维南方程组在非恒定流计算中的应用[J]．武汉：人民长江，2001(32)11
[28] 汪德罐．计算水力学[M]．南京：河海大学出版社，1989，9
[29] 王船海，李光炽．实用河网水流计算[M]．南京：河海大学水资源水文系，2003
[30] 王显正，陈正航，王旭永．控制理论基础[M]．北京：科学出版社，2000．
[31] 王划一，杨西侠，林家恒．现代控制理论基础[M]．国防工业出版社，2004．9．
[32] 薛亚莉，城市河流水量水质自适应控制模型研究[D]．河海大学，2006，6
[33] 王朝珠，秦化淑．最优控制理论[M]．北京：科学出版社，2003．9
[34] [英]M．G．辛，[法]A．铁托里．大系统的最优化及控制[M]．机械工业出版社，1983．7
[35] M．G．辛格．大系统的动态递阶控制[M]．北京：科学出版社，1983
[36] 褚健，俞立，苏宏业．鲁棒控制理论与应用[M]．浙江大学出版社．1998，4
[37] 尚涛，安宁，刘勇．渠道自动运行鲁棒控制的理论及其动态仿真研究[J]．武汉大学学报(工学版)，2004(37)，2．
[38] 单毅．渠道运行过程鲁棒控制研究及动态仿真[D]．武汉大学．2005
[39] 吴旭东，解学书．H∞鲁棒控制中的加权阵选择[J]．清华大学学报(自然科学版)，1997(37)，1．
[40] 解学书，钟宜生．H∞控制理论[M]．北京：清华大学出版社，1994．
[41] ZamesG.On the input-output stability of time varying nonlinear feedback systems: parts Ⅰ and Ⅱ. IEEETranAC,1966,11(2,3):228～238,465～476
[42] Tsai M C,Geddes EJM, Postlethwaite I. Pole-zero Cancellations and closed-loop properties of an H∞mixed sensitivity ydesign problem.Automatica, 1992,28(3): 519～530
[43] Kwakernaak Hilbert. Robust control and H∞ optimiza-tion: tutorial paper. Automatica, 1993,28(3):255～273
[44] Postlethwaite I, Tsai Miching, GuDawei. Weighting Function selection in Hoodesign.11th IFAC, 1990, Tallinn: 104～109
[45] 冯纯伯，田玉平，忻欣．鲁棒控制系统设计[M]．南京：东南大学出版社，1995
[46] 陈永春．MATLAB M语言高级编程[M]．北京：清华大学出版社．2004
[47] Zames, G.. Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms and.approximate inverses. IEEE Trans. Automat. Contr., 1981, Vol. AC-26:301-320.
[48] Francis, B. A.. A course in H_∞ control theory. Lecture Notes in Control and Information Sciences, Springer-Verleg, 1987.
[49] Doyle, J. C., Glover, K., Khargonekor, P.P. and Francis, B. A.. State-space solutions to standard H_2 and H_∞ control problems. IEEE Trans. Automat. Contr., 1989, Vol. 30:1307-1317.
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