基于反馈线性化的超空泡航行体控制研究
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摘要
水下超空泡航行体在空泡的包裹下,其所受阻力大幅度减小,航行速度实现质的飞跃,超空泡技术可使鱼雷像导弹一样在水中“飞行”。然而,超空泡技术在水下航行体减阻方面取得巨大成果的同时,也给超空泡航行体的稳定与控制带来严峻的挑战。因航行体被空泡包裹,其流体动力特性发生了深刻的变化,对控制策略提出了更为严格的要求。本论文就是在对超空泡航行体进行受力分析的基础上,根据动量定理与动量矩定理完成运动方程组的建立,并据此完成对超空泡航行体的机动控制,主要研究内容如下:
完成超空泡航行体的动力学建模。为描述超空泡航行体的运动规律定义了相关坐标系,选取运动参数,并推导坐标系之间的转换关系;对超空泡航行体在水中的稳定航行方案进行比对分析,并确定航行体尾部在空泡内壁稳定滑行方案;选取空泡模型方程,并对空泡形态的影响因素进行研究;确定航行体的几何模型,对航行体各部分的流体动力及力矩进行分析计算;最终建立了超空泡航行体六自由度的动力学与运动学方程。
建立超空泡航行体纵向运动模型与侧向无横滚运动模型,并对模型的开环特性、动态耦合特性、操纵耦合特性进行分析。在模型的建立过程中,依据相关化简准则,对运动模型进行简化处理。在侧向运动模型的建立过程中,考虑到横滚角对纵向运动与侧向运动的交连,选择在横滚得到有效控制的情况下,建立侧向无横滚运动模型。
完成超空泡航行体的非线性控制。在超空泡航行体动力学建模与动态特性分析的基础上,分别采用滑模变结构控制理论与LQR最优控制理论实现对超空泡航行体的定深控制、俯仰控制、侧移控制与偏航控制。基于模型本身的非线性与动态耦合、操纵耦合严重的特点,采取反馈线性化方法分别对纵向模型与侧向无横滚模型进行线性化与解耦处理。最后对滑模控制与LQR最优控制的控制效果进行比对分析。
The supercavitating vehicle surrounded by gas surface can attain very high speed while it is traveling underwater, because the vehicle has very small skin friction drag. Supercavitation technology can make the torpedo actually fly in the water like a missile. Supercavitation technology makes great achievements in drag reduction but also poses technical challenges in system stability and control. Because the vehicle is surrounded by cavity, its fluid dynamic characteristics have a great changes, the control strategy was also proposed more stringent requirements. The article completes equations of motion according to theorem of momentum and theorem of angular momentum based on the force analysis of the supercavitating vehicle, and makes motor control and attitude control for supercavitating vehicle. The main works are:
Complete supercavitating vehicle dynamics modeling. In order to describe the movement of vehicle, the coordinate systems are defined, parameters of the motion are selected, and the transform relationships between the coordinate systems are reckoned. By contrasting the stable navigation programs of underwater supercavitating vehicle, we select the appropriate program. We select the equation of cavity model and research the morphology factors of the cavity. We determine the geometrical model of vehicle, analyse the fluid force and moment. Finally, according to theorem of momentum and theorem of angular momentum, we establish six degree of freedom supercavitating nonlinear dynamic and kinematic equations.
Establish vertical motion model and lateral movement without roll motion model of supercavitating vehicle and analyse the open-loop characteristics, dynamic coupling characteristics, manipulation of coupling characteristics of the two models. In the process of establishing models, we simplify motion models according to the relevant guidelines. In the process of establishing lateral movement model, taking into account the influence of the roll angle on the cross-connect between the vertical movement and lateral movement, establishe the lateral motion model without roll when the roll has been effectively controlled.
Complete nonlinear control of supercavitating vehicle. Based on dynamic modeling and dynamic analysis of supercavitating vehicle, sliding mode variable structure control and LQR control are used on depth control, pitch control, lateral control and yaw control. Because of the nonlinear, dynamic coupling and control coupling characteristics of the models are serious, the feedback linearization is respectively used on vertical model and lateral motion model without roll. Finally, sliding mode variable structure control and LQR control are compared to analyse.
完成超空泡航行体的动力学建模。为描述超空泡航行体的运动规律定义了相关坐标系,选取运动参数,并推导坐标系之间的转换关系;对超空泡航行体在水中的稳定航行方案进行比对分析,并确定航行体尾部在空泡内壁稳定滑行方案;选取空泡模型方程,并对空泡形态的影响因素进行研究;确定航行体的几何模型,对航行体各部分的流体动力及力矩进行分析计算;最终建立了超空泡航行体六自由度的动力学与运动学方程。
建立超空泡航行体纵向运动模型与侧向无横滚运动模型,并对模型的开环特性、动态耦合特性、操纵耦合特性进行分析。在模型的建立过程中,依据相关化简准则,对运动模型进行简化处理。在侧向运动模型的建立过程中,考虑到横滚角对纵向运动与侧向运动的交连,选择在横滚得到有效控制的情况下,建立侧向无横滚运动模型。
完成超空泡航行体的非线性控制。在超空泡航行体动力学建模与动态特性分析的基础上,分别采用滑模变结构控制理论与LQR最优控制理论实现对超空泡航行体的定深控制、俯仰控制、侧移控制与偏航控制。基于模型本身的非线性与动态耦合、操纵耦合严重的特点,采取反馈线性化方法分别对纵向模型与侧向无横滚模型进行线性化与解耦处理。最后对滑模控制与LQR最优控制的控制效果进行比对分析。
The supercavitating vehicle surrounded by gas surface can attain very high speed while it is traveling underwater, because the vehicle has very small skin friction drag. Supercavitation technology can make the torpedo actually fly in the water like a missile. Supercavitation technology makes great achievements in drag reduction but also poses technical challenges in system stability and control. Because the vehicle is surrounded by cavity, its fluid dynamic characteristics have a great changes, the control strategy was also proposed more stringent requirements. The article completes equations of motion according to theorem of momentum and theorem of angular momentum based on the force analysis of the supercavitating vehicle, and makes motor control and attitude control for supercavitating vehicle. The main works are:
Complete supercavitating vehicle dynamics modeling. In order to describe the movement of vehicle, the coordinate systems are defined, parameters of the motion are selected, and the transform relationships between the coordinate systems are reckoned. By contrasting the stable navigation programs of underwater supercavitating vehicle, we select the appropriate program. We select the equation of cavity model and research the morphology factors of the cavity. We determine the geometrical model of vehicle, analyse the fluid force and moment. Finally, according to theorem of momentum and theorem of angular momentum, we establish six degree of freedom supercavitating nonlinear dynamic and kinematic equations.
Establish vertical motion model and lateral movement without roll motion model of supercavitating vehicle and analyse the open-loop characteristics, dynamic coupling characteristics, manipulation of coupling characteristics of the two models. In the process of establishing models, we simplify motion models according to the relevant guidelines. In the process of establishing lateral movement model, taking into account the influence of the roll angle on the cross-connect between the vertical movement and lateral movement, establishe the lateral motion model without roll when the roll has been effectively controlled.
Complete nonlinear control of supercavitating vehicle. Based on dynamic modeling and dynamic analysis of supercavitating vehicle, sliding mode variable structure control and LQR control are used on depth control, pitch control, lateral control and yaw control. Because of the nonlinear, dynamic coupling and control coupling characteristics of the models are serious, the feedback linearization is respectively used on vertical model and lateral motion model without roll. Finally, sliding mode variable structure control and LQR control are compared to analyse.
引文
[1]徐双华.超空泡技术的结晶——“风雪”鱼雷[J].海军世界:35.
[2]闫璞,池建文,茹呈瑶.从伊朗试射超空泡鱼雷看世界超空泡武器的发展[J].国防,2006(7):68-70.
[3]李凝,杨飚.德国轻型超空泡鱼雷研发现状及展望[J].鱼雷技术,2008(4)第16卷第2期:1-4.
[4]钱东,张起.欧洲反鱼雷鱼雷研发展望[J].鱼雷技术,2006(12)第14卷第5期:1-5.
[5]王献孚.空化泡和超空化泡流动理论与应用[M].北京:国防工业出版社,2009:1-210.
[6] Y N Savchenko, V N Semenenko and V V Serebryakov. Experimental Study of the Supercavitation Flows at Subsonic Flow Velocities. Doklady AN Ukrainy. 1992, (2): 64-69.
[7] S I Putiliu. Numerical Simulation of Cavitating Flows by Single-phase Flow Approach. 3rd International Symposium on Cavitation, Grenoble, France, 1998.
[8] N Fine. Six Degree-of-Freedom Fin Forces for the ONR Supercavitating Test Bed Vehicle. Anteon Corporation, 2000, http://www.anteon.com, accessed: September 2000.
[9] A May. Water Entry and Cavity-Running Behavior of Missiles. Arlington, VA, SEAHAC TR 75-2, Naval Sea Systems Command, 1975.
[10] H Wagner. Uber Stoss und Gleitvarangange an der Oberflache von Flussigkaiten, Berlin,ZAMM,12(4),193215.
[11]ГВЛогвинович.Некоторыевопросыглиссированияикавитации,ТрудыЦАГИ.-Вып. 2052.-1980.-С:3-12.
[12] S E Hassan. Analysis of Hydrodynamic Planing Forces Associated with Cavity Riding Vehicles, NUWC-NOT Technical Memorandum 90085, July.1999.
[13] S Kulkarni, R Pratap. Studies on Dynamics of a Supercavitating Projectile. Applied Mathematical Modeling, 2000, 24(2):113-129.
[14] F R Kunz, W J Lindau, H J Gibeling, M Jason, M J Dennis, Bieryla, Erica A. Reese. Unsteady Three-Dimensional Multiphase CFD Analysis Of Maneuvering High Speed Supercavitating Vehicles, 41st Aerospace Sciences Meeting and Exhibit,6-9 January 2003, Reno, Nevada, AIAA 2003-841.flows over cavitating projectiles. Euro J Mech B/Fluids, 2004, 23: 339-351.
[16]袁续龙,张宇文,刘乐华.水下航行体通气超空泡形态实验研究[J].应用力学学报,2004(9)第21卷第3期:33-37.
[17]袁续龙,张宇文,王育才.水下航行体通气超空泡非对称性研究[J].力学学报,2004(3)第36卷第2期:146-150.
[18]王海斌,张嘉钟,魏英杰.空泡形态与典型空化器参数关系的研究——小空泡数下的发展空泡形态[J].水动力学研究与进展,2005(3)第20卷第2期:251-257.
[19]王海斌,张嘉钟,魏英杰.水下航行体通气超空泡减阻特性实验研究[J].船舶工程,2006(3)第28卷:14-17.
[20]贾力平,张嘉钟,于开平.空化器线形与超空泡减阻效果关系研究[J].船舶工程,2006(2)第28卷:20-23.
[21]黄海龙,王聪,黄文虎.变攻角圆盘空化器生成自然超空泡数值模拟[J].北京理工大学学报,2008(2)第28卷第2期:100-103.
[22]隗喜斌,刘海军,于开平.通气参数影响超空泡形态的研究[J].哈尔滨商业大学学报(自然科学版),2007(8)第23卷第4期:442-445.
[23]周景军,于开平.空化器倾斜角对超空泡流影响的三维数值仿真研究[J].船舶力学,2011(2)第15卷第1-2期:74-80.
[24]张学伟,张亮,王聪.基于Logvinovich独立膨胀原理的超空泡形态计算方法[J].兵工学报,2009(3)第30卷第3期:361-365.
[25]邓飞,张宇文,陈伟政.头形对细长体超空泡生成与外形影响的实验研究[J].西北工业大学学报,2004(6)第22卷第3期:269-273.
[26]马琳,祁江涛,俞圣杰.水下高速航行体空泡外形的近似计算[C].第九届全国水动力学学术会议暨第二十二届全国水动力学研讨会文集:693-699.
[27]杨武刚,张宇文.攻角空化器的超空泡形态非对称研究特性研究[J].船舶工程,2007(6)总第29卷:80-83.
[28]孟庆昌,张志宏,刘巨斌.海洋环境扰动对水下航行体超空泡形态的影响[J].弹道学报,2010(12)第22卷第4期:31-35.
[29]邹启明,张西建.超空泡航行器流体动力仿真[J].舰船科学技术,2008(10)第30卷第5期:106-110.
[30]罗凯,党建军,王育才,张宇文.超高速水下航行器纵平面运动特性分析[J].鱼雷技术,2007(10)第15卷第5期:37-40.
[31] ZHOU Jing-jun,YU Kai-ping,ZHANG Guang. Numerical Simulation on the Process of Supercavity Development and the Planing State of Supercavitating Vehicle[J]. Journal of Ship Mechanics,2011 Mar,Vol.15 No.3.
[32]邓飞,张宇文,袁绪龙,陈伟政,杨武刚.水下超空泡航行体流体动力设计原理研究[J].西北工业大学学报,2004(12)第22卷第6期:806-810.
[33]孟庆昌,张志宏,顾建农,刘巨斌.超空泡射弹尾拍分析与计算[J].爆炸与冲击,2009(1)第29卷第1期:56-60.
[34]杨传武,王安稳.超空泡水下航行体振动特性分析[J].海军工程大学学报,2008(8)第20卷第4期:30-32.
[35]高永琪,顾建农.超空泡鱼雷有关流体动力分析[J].海军工程大学学报,2005(6)第17卷第3期:57-60.
[36]曹伟,魏英杰,韩万金.超空泡航行体阻力系数的数值模拟研究[J].工程力学,2008(12)第25卷第12期:208-212.
[37]熊永亮,郜冶,杨丹.不同攻角运动的水下导弹表面空泡流场数值研究[J].哈尔滨工程大学学报,2007(7)第28卷第7期:738-742.
[38] Kirschner I N, Neal E F, James S, et al. Numerical modeling of supercavitating flows. In: the RTO AVT Lecture Series on“Supercavitating Flows”, Brussels, 2001-2-12-16. Belgium, RTO EN-010,2001:133-167.
[39] Lin G J, Balachandran B, Abed E. Supercavitating body dynamics, bifurcation and control. In: Lee H K, ed. American Control Conference, 2005, 24th American Control Conference Port-land Oregon USA 2005-06-08-10. USA,AACC, 2005: 691-696.
[40] Shao, Mesbahi Y M, Balas G J. Planing, switching, and supercavitating flight control. In: AAIA. Guidance, Navigation and Control Conference and Exhibit, Austin, TeXas, 2003-08-11-14. America, American Institute of Aeronautics and Astronautics Inc, 2003: 5724.
[41] Vanek B, Bokor J, Balas G. Theoretical aspects of high speed supercavitation vehicle control. In: Eduardo Misawa ed. Proceedings of the 2006 American Control Conference, Minneapolis, Minnesota, USA, 2006-06-14-16:5263-5268.
[42] Geol. Control strategies for supercavitating vehicles[M]. Florida :University Of Florida,2002:7-9.
[43]赵新华.水下超高速航行体动力学建模与控制研究[D].哈尔滨:哈尔滨工程大学,2007:13-15.
[44]王茂励.超空泡航行体的数学建模与控制方法研究[D].哈尔滨:哈尔滨工程大学,2008:14-16.
[45]吕瑞.超空泡航行体动力学建模与姿态机动鲁棒控制方法研究[D].哈尔滨:哈尔滨工业大学,2010:14-15.
[46]魏英杰,王京华.水下超空泡航行体非线性动力学与控制[J].振动与冲击, 2009第28卷第6期:179-182.
[47]王京华,魏英杰.超空泡高速航行体动力学建模与控制设计[J].哈尔滨工业大学学报,2010(9)第42卷第9期:1351-1355.
[48]范辉,张宇文.超空泡航行器稳定性分析及其非线性切换控制[J].控制理论与应用,2009(11)第26卷第11期:1211-1217.
[49]范加利,吕小龙,赵国良.超空泡航行体的自适应模糊滑模控制研究[J].计算机工程与应用,2011,47(3):218-211.
[50]陈艳艳,罗凯,王璐.超高速水下航行器横滚控制研究[J].计算机测量与控制,2009,17(1):129-131.
[51]陈艳艳,罗凯.超高速水下航行器纵平面姿态控制研究[J].计算机仿真,2009(1)第26卷第1期:50-54.
[52]曹伟,魏英杰,王聪,邹振祝,黄文虎.超空泡技术现状、问题与应用[J].力学进展,2006,36(4):571-579.
[53]于开平,隗喜斌,蒋增辉.俄罗斯和乌克兰超空泡减阻技术研究进展[J].飞航导弹,2007(8):5-11.
[54]于开平,蒋增辉.超空泡形状计算及相关试验研究[J].飞航导弹,2005(12):15-22.
[55]周杰,王树宗.超空泡鱼雷推进系统相关问题设计初探[J].鱼雷技术,2006(12)第14卷第5期:27-30.
[56]严卫生.鱼雷航行力学[M].西安:西北工业大学出版社,2005:3-4.
[57] Y N Savchenko. Control of Supercavitation Flow and Stability of Supercavitating Motion of Bodies. RTO AVT Lecture Series on“Supercavitation Flows”. Held at VKI.2001,2.
[58] G V Logvinovich. Hydrodynamics of Flows with Free Boundaries. Kiev, Russian: Naukova Dumka Publishing House, 1969.
[59] V N Buyvol. Slender Cavities in Flows with Perturbations. Kiev, Russian: Naukova Dumka Publishing House, 1980.
[60] I N Kirschner, N E Fine. Supercavitation Research and Development. PRO Undersea Defense Technologies, Hawaii,2002(1).
[61] J Dzielski, A Kurdila. A benchmark control problem for Supercavitating Vehicles and an Initial Investigation of Solutions. Journal of Vibration and Control. 2003, 9(7):791-804.
[62]钱杏芳.导弹飞行力学[M].北京:北京理工大学出版社,2008:1-285.
[63]徐德民.鱼雷自动控制系统[M].西安:西北工业大学出版社,2001:1-375.
[64] G J Lin, Balachandran and E H Abed. Nonlinear Dynamics and Control of Supercavitating Bodies. AIAA Guidance, Navigation, and Control Conference 2006, Keystone, Colorado. 2006:3151-3164.
[65] G J Lin, Balachandran and E H Abed. Nonlinear Dynamics and Bifurcations of a Supercavitating Vehicle. IEEE Journal of Oceanic Engineering, 2007,32(4): 753-761.
[66] G J Lin, Balachandran and E H Abed. Dynamics and Control of Supercavitating Vehicles. Journal of Dynamics System, Measurement and Control, 2008,130 (2): 0210031-02100311.
[67] B Vanek. Control Methods for High-Speed Supercavitating Vehicles. Doctor’s Thesis, University of Minnesota, 2008.
[68] B Vanek, G Balas. Theoretical Aspects of High-Speed Supercavitation Vehicle Control. American Control Conference, Minneapolis: Institute of Electrical and Electronics Engineers Inc, 2006:5263-5268.
[69] B Vanek, G Balas. Longitudinal Motion Control of a High-Speed Supercavitation Vehicle. Journal of Vibration and Control, 2007 13(2):159-184.
[70]胡跃明.非线性控制系统理论与应用[M].国防工业出版社,2005:68.
[2]闫璞,池建文,茹呈瑶.从伊朗试射超空泡鱼雷看世界超空泡武器的发展[J].国防,2006(7):68-70.
[3]李凝,杨飚.德国轻型超空泡鱼雷研发现状及展望[J].鱼雷技术,2008(4)第16卷第2期:1-4.
[4]钱东,张起.欧洲反鱼雷鱼雷研发展望[J].鱼雷技术,2006(12)第14卷第5期:1-5.
[5]王献孚.空化泡和超空化泡流动理论与应用[M].北京:国防工业出版社,2009:1-210.
[6] Y N Savchenko, V N Semenenko and V V Serebryakov. Experimental Study of the Supercavitation Flows at Subsonic Flow Velocities. Doklady AN Ukrainy. 1992, (2): 64-69.
[7] S I Putiliu. Numerical Simulation of Cavitating Flows by Single-phase Flow Approach. 3rd International Symposium on Cavitation, Grenoble, France, 1998.
[8] N Fine. Six Degree-of-Freedom Fin Forces for the ONR Supercavitating Test Bed Vehicle. Anteon Corporation, 2000, http://www.anteon.com, accessed: September 2000.
[9] A May. Water Entry and Cavity-Running Behavior of Missiles. Arlington, VA, SEAHAC TR 75-2, Naval Sea Systems Command, 1975.
[10] H Wagner. Uber Stoss und Gleitvarangange an der Oberflache von Flussigkaiten, Berlin,ZAMM,12(4),193215.
[11]ГВЛогвинович.Некоторыевопросыглиссированияикавитации,ТрудыЦАГИ.-Вып. 2052.-1980.-С:3-12.
[12] S E Hassan. Analysis of Hydrodynamic Planing Forces Associated with Cavity Riding Vehicles, NUWC-NOT Technical Memorandum 90085, July.1999.
[13] S Kulkarni, R Pratap. Studies on Dynamics of a Supercavitating Projectile. Applied Mathematical Modeling, 2000, 24(2):113-129.
[14] F R Kunz, W J Lindau, H J Gibeling, M Jason, M J Dennis, Bieryla, Erica A. Reese. Unsteady Three-Dimensional Multiphase CFD Analysis Of Maneuvering High Speed Supercavitating Vehicles, 41st Aerospace Sciences Meeting and Exhibit,6-9 January 2003, Reno, Nevada, AIAA 2003-841.flows over cavitating projectiles. Euro J Mech B/Fluids, 2004, 23: 339-351.
[16]袁续龙,张宇文,刘乐华.水下航行体通气超空泡形态实验研究[J].应用力学学报,2004(9)第21卷第3期:33-37.
[17]袁续龙,张宇文,王育才.水下航行体通气超空泡非对称性研究[J].力学学报,2004(3)第36卷第2期:146-150.
[18]王海斌,张嘉钟,魏英杰.空泡形态与典型空化器参数关系的研究——小空泡数下的发展空泡形态[J].水动力学研究与进展,2005(3)第20卷第2期:251-257.
[19]王海斌,张嘉钟,魏英杰.水下航行体通气超空泡减阻特性实验研究[J].船舶工程,2006(3)第28卷:14-17.
[20]贾力平,张嘉钟,于开平.空化器线形与超空泡减阻效果关系研究[J].船舶工程,2006(2)第28卷:20-23.
[21]黄海龙,王聪,黄文虎.变攻角圆盘空化器生成自然超空泡数值模拟[J].北京理工大学学报,2008(2)第28卷第2期:100-103.
[22]隗喜斌,刘海军,于开平.通气参数影响超空泡形态的研究[J].哈尔滨商业大学学报(自然科学版),2007(8)第23卷第4期:442-445.
[23]周景军,于开平.空化器倾斜角对超空泡流影响的三维数值仿真研究[J].船舶力学,2011(2)第15卷第1-2期:74-80.
[24]张学伟,张亮,王聪.基于Logvinovich独立膨胀原理的超空泡形态计算方法[J].兵工学报,2009(3)第30卷第3期:361-365.
[25]邓飞,张宇文,陈伟政.头形对细长体超空泡生成与外形影响的实验研究[J].西北工业大学学报,2004(6)第22卷第3期:269-273.
[26]马琳,祁江涛,俞圣杰.水下高速航行体空泡外形的近似计算[C].第九届全国水动力学学术会议暨第二十二届全国水动力学研讨会文集:693-699.
[27]杨武刚,张宇文.攻角空化器的超空泡形态非对称研究特性研究[J].船舶工程,2007(6)总第29卷:80-83.
[28]孟庆昌,张志宏,刘巨斌.海洋环境扰动对水下航行体超空泡形态的影响[J].弹道学报,2010(12)第22卷第4期:31-35.
[29]邹启明,张西建.超空泡航行器流体动力仿真[J].舰船科学技术,2008(10)第30卷第5期:106-110.
[30]罗凯,党建军,王育才,张宇文.超高速水下航行器纵平面运动特性分析[J].鱼雷技术,2007(10)第15卷第5期:37-40.
[31] ZHOU Jing-jun,YU Kai-ping,ZHANG Guang. Numerical Simulation on the Process of Supercavity Development and the Planing State of Supercavitating Vehicle[J]. Journal of Ship Mechanics,2011 Mar,Vol.15 No.3.
[32]邓飞,张宇文,袁绪龙,陈伟政,杨武刚.水下超空泡航行体流体动力设计原理研究[J].西北工业大学学报,2004(12)第22卷第6期:806-810.
[33]孟庆昌,张志宏,顾建农,刘巨斌.超空泡射弹尾拍分析与计算[J].爆炸与冲击,2009(1)第29卷第1期:56-60.
[34]杨传武,王安稳.超空泡水下航行体振动特性分析[J].海军工程大学学报,2008(8)第20卷第4期:30-32.
[35]高永琪,顾建农.超空泡鱼雷有关流体动力分析[J].海军工程大学学报,2005(6)第17卷第3期:57-60.
[36]曹伟,魏英杰,韩万金.超空泡航行体阻力系数的数值模拟研究[J].工程力学,2008(12)第25卷第12期:208-212.
[37]熊永亮,郜冶,杨丹.不同攻角运动的水下导弹表面空泡流场数值研究[J].哈尔滨工程大学学报,2007(7)第28卷第7期:738-742.
[38] Kirschner I N, Neal E F, James S, et al. Numerical modeling of supercavitating flows. In: the RTO AVT Lecture Series on“Supercavitating Flows”, Brussels, 2001-2-12-16. Belgium, RTO EN-010,2001:133-167.
[39] Lin G J, Balachandran B, Abed E. Supercavitating body dynamics, bifurcation and control. In: Lee H K, ed. American Control Conference, 2005, 24th American Control Conference Port-land Oregon USA 2005-06-08-10. USA,AACC, 2005: 691-696.
[40] Shao, Mesbahi Y M, Balas G J. Planing, switching, and supercavitating flight control. In: AAIA. Guidance, Navigation and Control Conference and Exhibit, Austin, TeXas, 2003-08-11-14. America, American Institute of Aeronautics and Astronautics Inc, 2003: 5724.
[41] Vanek B, Bokor J, Balas G. Theoretical aspects of high speed supercavitation vehicle control. In: Eduardo Misawa ed. Proceedings of the 2006 American Control Conference, Minneapolis, Minnesota, USA, 2006-06-14-16:5263-5268.
[42] Geol. Control strategies for supercavitating vehicles[M]. Florida :University Of Florida,2002:7-9.
[43]赵新华.水下超高速航行体动力学建模与控制研究[D].哈尔滨:哈尔滨工程大学,2007:13-15.
[44]王茂励.超空泡航行体的数学建模与控制方法研究[D].哈尔滨:哈尔滨工程大学,2008:14-16.
[45]吕瑞.超空泡航行体动力学建模与姿态机动鲁棒控制方法研究[D].哈尔滨:哈尔滨工业大学,2010:14-15.
[46]魏英杰,王京华.水下超空泡航行体非线性动力学与控制[J].振动与冲击, 2009第28卷第6期:179-182.
[47]王京华,魏英杰.超空泡高速航行体动力学建模与控制设计[J].哈尔滨工业大学学报,2010(9)第42卷第9期:1351-1355.
[48]范辉,张宇文.超空泡航行器稳定性分析及其非线性切换控制[J].控制理论与应用,2009(11)第26卷第11期:1211-1217.
[49]范加利,吕小龙,赵国良.超空泡航行体的自适应模糊滑模控制研究[J].计算机工程与应用,2011,47(3):218-211.
[50]陈艳艳,罗凯,王璐.超高速水下航行器横滚控制研究[J].计算机测量与控制,2009,17(1):129-131.
[51]陈艳艳,罗凯.超高速水下航行器纵平面姿态控制研究[J].计算机仿真,2009(1)第26卷第1期:50-54.
[52]曹伟,魏英杰,王聪,邹振祝,黄文虎.超空泡技术现状、问题与应用[J].力学进展,2006,36(4):571-579.
[53]于开平,隗喜斌,蒋增辉.俄罗斯和乌克兰超空泡减阻技术研究进展[J].飞航导弹,2007(8):5-11.
[54]于开平,蒋增辉.超空泡形状计算及相关试验研究[J].飞航导弹,2005(12):15-22.
[55]周杰,王树宗.超空泡鱼雷推进系统相关问题设计初探[J].鱼雷技术,2006(12)第14卷第5期:27-30.
[56]严卫生.鱼雷航行力学[M].西安:西北工业大学出版社,2005:3-4.
[57] Y N Savchenko. Control of Supercavitation Flow and Stability of Supercavitating Motion of Bodies. RTO AVT Lecture Series on“Supercavitation Flows”. Held at VKI.2001,2.
[58] G V Logvinovich. Hydrodynamics of Flows with Free Boundaries. Kiev, Russian: Naukova Dumka Publishing House, 1969.
[59] V N Buyvol. Slender Cavities in Flows with Perturbations. Kiev, Russian: Naukova Dumka Publishing House, 1980.
[60] I N Kirschner, N E Fine. Supercavitation Research and Development. PRO Undersea Defense Technologies, Hawaii,2002(1).
[61] J Dzielski, A Kurdila. A benchmark control problem for Supercavitating Vehicles and an Initial Investigation of Solutions. Journal of Vibration and Control. 2003, 9(7):791-804.
[62]钱杏芳.导弹飞行力学[M].北京:北京理工大学出版社,2008:1-285.
[63]徐德民.鱼雷自动控制系统[M].西安:西北工业大学出版社,2001:1-375.
[64] G J Lin, Balachandran and E H Abed. Nonlinear Dynamics and Control of Supercavitating Bodies. AIAA Guidance, Navigation, and Control Conference 2006, Keystone, Colorado. 2006:3151-3164.
[65] G J Lin, Balachandran and E H Abed. Nonlinear Dynamics and Bifurcations of a Supercavitating Vehicle. IEEE Journal of Oceanic Engineering, 2007,32(4): 753-761.
[66] G J Lin, Balachandran and E H Abed. Dynamics and Control of Supercavitating Vehicles. Journal of Dynamics System, Measurement and Control, 2008,130 (2): 0210031-02100311.
[67] B Vanek. Control Methods for High-Speed Supercavitating Vehicles. Doctor’s Thesis, University of Minnesota, 2008.
[68] B Vanek, G Balas. Theoretical Aspects of High-Speed Supercavitation Vehicle Control. American Control Conference, Minneapolis: Institute of Electrical and Electronics Engineers Inc, 2006:5263-5268.
[69] B Vanek, G Balas. Longitudinal Motion Control of a High-Speed Supercavitation Vehicle. Journal of Vibration and Control, 2007 13(2):159-184.
[70]胡跃明.非线性控制系统理论与应用[M].国防工业出版社,2005:68.
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