高超声速飞行器再入段的最优制导
摘要
本文以X-33飞行器为研究对象,首先根据飞行器再入过程的特点,在半速度坐标系中建立了三维再入运动方程,确定以高度、经度和纬度在终点时刻的误差平方和为最小的目标函数,详细分析了再入过程中所需要满足的过载、动压及热流率约束条件,设计了以高度-速度为剖面的再入走廊。
论文详细介绍了高斯伪谱法(GPM)的基本原理及特点,并且基于高斯伪谱法将研究的最优控制问题成功转化成非线性规划问题,通过实例仿真分析了该优化算法的收敛速度、精度以及实时性。
在采用高斯伪谱法(GPM)进行飞行器轨迹优化设计时,结合仿真数据得出了不同情况下的航向角,航迹角、经度及纬度等状态变量的变化曲线,以及在终端时刻的落点误差数据,通过仿真分析了初值估计、配置点个数等因素对轨迹优化的影响。
本文通过仿真分析了存在初始误差和气动系数误差情况下的落点误差,结合仿真数据得出了两种情况下的实际轨迹曲线与参考轨迹曲线,最终采用线性二次型调节器(LQR)对参考轨迹进行跟踪,并通过仿真分析了其鲁棒性。
In this paper, it chooses the X-33 aircraft as the research object. Firstly, according to the characteristics of the reentry process, it creates the reentry equations of motion in the half-speed coordinate system. It gives the objective function that makes the errors of the height, longitude and latitude minimum at the end of time. Meanwhile it analyses the constraints of the overload, dynamic pressure and heating rate. Finally it establishes the reentry corridor of the height-speed profile.
This paper introduces the basic principles of the Gaussian pseudo-spectral method (GPM) and transforms the optimal control problems into solving the parametric problem of state variables and control variables. Ultimately it analyses the convergence speed and accuracy of the Gaussian pseudo-spectral method (GPM) when solving optimal control problems.
During the design of aircraft trajectory optimization, it draws the curves of the flight path angle, longitude, latitude and other state variables and gives the errors at the terminal time through the simulation analysis. Meanwhile it analyses the effects of the initial estimates of the value, the number of collocation points on the trajectory optimization.
This paper analyzes the errors at the end point in the presence of aerodynamic coefficients errors and initial errors through the simulation analysis. At the same time it gives the curves of the actual trajectory and the reference trajectory. Ultimately it uses the linear quadratic regulator (LQR) to track the reference trajectory and analyses its robust characteristics.
论文详细介绍了高斯伪谱法(GPM)的基本原理及特点,并且基于高斯伪谱法将研究的最优控制问题成功转化成非线性规划问题,通过实例仿真分析了该优化算法的收敛速度、精度以及实时性。
在采用高斯伪谱法(GPM)进行飞行器轨迹优化设计时,结合仿真数据得出了不同情况下的航向角,航迹角、经度及纬度等状态变量的变化曲线,以及在终端时刻的落点误差数据,通过仿真分析了初值估计、配置点个数等因素对轨迹优化的影响。
本文通过仿真分析了存在初始误差和气动系数误差情况下的落点误差,结合仿真数据得出了两种情况下的实际轨迹曲线与参考轨迹曲线,最终采用线性二次型调节器(LQR)对参考轨迹进行跟踪,并通过仿真分析了其鲁棒性。
In this paper, it chooses the X-33 aircraft as the research object. Firstly, according to the characteristics of the reentry process, it creates the reentry equations of motion in the half-speed coordinate system. It gives the objective function that makes the errors of the height, longitude and latitude minimum at the end of time. Meanwhile it analyses the constraints of the overload, dynamic pressure and heating rate. Finally it establishes the reentry corridor of the height-speed profile.
This paper introduces the basic principles of the Gaussian pseudo-spectral method (GPM) and transforms the optimal control problems into solving the parametric problem of state variables and control variables. Ultimately it analyses the convergence speed and accuracy of the Gaussian pseudo-spectral method (GPM) when solving optimal control problems.
During the design of aircraft trajectory optimization, it draws the curves of the flight path angle, longitude, latitude and other state variables and gives the errors at the terminal time through the simulation analysis. Meanwhile it analyses the effects of the initial estimates of the value, the number of collocation points on the trajectory optimization.
This paper analyzes the errors at the end point in the presence of aerodynamic coefficients errors and initial errors through the simulation analysis. At the same time it gives the curves of the actual trajectory and the reference trajectory. Ultimately it uses the linear quadratic regulator (LQR) to track the reference trajectory and analyses its robust characteristics.
引文
[1]汤一华,余梦伦,杨勇,等.第二代可重复使用运载器及其再入制导技术[J].导弹与航天运载技术, 2010(1):1-6.
[2] Betts J.T. Survey of Numerical Methods for Trajectory Optimization[C]. Journal of Guidance, Control and Dynamics, 1998.
[3]雍恩米.高超声速滑翔式再入飞行器轨迹优化与制导方法研究[D].国防科学技术大学, 2008:71-90.
[4] Kang wei. The Rate of Convergence for a Pseudo spectral Optimal Control Method[C]. Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, Dec.9-11, 2008.
[5]胡建学,陈克俊,赵汉元,等. RLV再入标准轨道制导与轨道预测指导方法比较分析[J].国防科技大学学报, 2007,29(1):1-5.
[6]胡建学,陈克俊,赵汉元,等. RLV再入标准轨道制导与设计[J].航天控制,2007, 25(6):1-4.
[7] Dukeman GA. Profile-following Entry Guidance Using Linear Quadratic Regulator Theory[C]. AIAA 2002-4457, 2002.
[8] Youssef H, Chowdhry RS, Lee H, et al. Predictor-Corrector Entry Guidance for Reusable Launch Vehicles[C]. AIAA 2001-4043, 2001.
[9] Schierman JD, Hull JR, Ward DG. Flight Test Results of an Adaptive Guidance System for Reusable Launch Vehicles[C]. AIAA 2004-4771, 2004.
[10] Bollino KP, Ross IM. Optimal Nonlinear Feedback Guidance for Reentry Vehicles[C]. AIAA 2006-6074, 2006.
[11] Ross IM, Sekhavat P, Fleming A, et al. Pseudo spectral Feedback Control: Foundations, Examples and Experimental Results[C]. AIAA 2006-6354, 2006.
[12] Shen Zuojun, Lu Ping. Onboard Generation of Three-Dimensional Constrained Entry Trajectories[C]. Journal of Guidance, Control and Dynamics, 2003, 26(1):1-11.
[13]王光伦.高超声速飞行器再入段预测校正制导研究[D].哈尔滨工业大学,2010:10-21.
[14]赵汉元.飞行器再入动力学和制导[M].国防科技大学出版社, 1997:23-97.
[15] Singh B, Bhattacharya R. Optimal Guidance of Hypersonic Vehicles Using B-Splines and Galerkin Projection[C]. AIAA 2008-7263, 2008.
[16] Fahroo F, Ross IM. Advances in Pseudo spectral Methods for Optimal Control[C]. AIAA 2008-7309, 2008.
[17] Garg D, Patterson MA, Darby CL, et al. Patterson. Direct TrajectoryOptimization and Costate Estimation of General Optimal Control Problems Using a Radau Pseudo spectral Method[C]. AIAA 2009-5989, 2009.
[18] Jorris RT, Schulz CS, Friedl FR, et al. Constrained Trajectory Optimization Using Pseudo spectral Methods[C]. AIAA 2008-6218, 2009.
[19] Bollino KP, Lewis LR, Sekhavat P, et al. Pseudo spectral Optimal Control: A Clear Road for Autonomous Intelligent Path Planning[C]. AIAA 2007-2831, 2007.
[20] Chartres JT, Michael H, Schneider G. Optimization of the Terminal Flight Phase for a Future Reusable Launch Vehicle[C]. AIAA2005-6060, 2005.
[21]雍恩米,唐国金,陈磊.基于Gauss伪谱方法的高超声速飞行器再入轨迹快速优化[J].宇航学报, 2008, 29(6):1-7.
[22] Schierman JD, Hull JR, Ward DG. On-Line Trajectory Command Reshaping for Reusable Launch Vehicles[C]. AIAA 2003-5439, 2003.
[23] Allwine DA, Fisher JE, Strahler JA. On-Line Trajectory Generation for Hypersonic Vehicles[C]. AIAA 2005-6435, 2005.
[24] Lee YI, Ryoo CK, Kim E. Optimal Guidance with Constraints on Impact Angle and Terminal Acceleration[C]. AIAA 2003-5795, 2003.
[25] Hill AD, Anderson DM, Coughlin DJ, et al. X-33 Trajectory Optimization and Design[C].AIAA-98-4408, 1998.
[26] Oppenheimer MW, Doman DB. Reconfigurable Control Design for the X-40A with In-Flight Simulation Results[C]. AIAA 2004-5017, 2004.
[27] Harl N, Balakrishnan SN. Reentry Terminal Guidance through Sliding Mode Control[C]. Journal of Guidance, Control and Dynamics, 2010, 33(1):1-14.
[28]孙春贞,黄一敏.重复使用运载器末端区域能量管理轨迹鲁棒性分析[J].兵工学报, 2008,29(3):1-5.
[29] Iris F.A. Vis. Survey of research in the design and control of automated guided vehicle systems [J]. European Journal of Operational Research, 2006:677-709.
[30] S. De Ridder, E. Mooij. Terminal area trajectory planning using the energy-tube concept for reusable launch vehicles [J]. Acta Astronautica, 2010.
[31] C.A. Kluever. Terminal Guidance for an Unpowered Reusable Launch Vehicle with Bank Constraints [J]. Journal of Guidance, Control and Dynamics, 2007, 30(1):1-7.
[32]钱杏芳,林瑞雄,赵亚男.导弹飞行力学[M].北京理工大学出版社, 2008:160-165.
[33]胡寿松,王执铨,胡维礼.最优控制理论与系统[M].科学出版社, 1994:162-189.
[34] E. Mooij. Linear Quadratic Regulator re-entry control: performance assessmentusing a taguchi approach[C]. AIAA-98-1629, 1998.
[35] Bryson A E, Ho Y C. Applied Optimal Control [M]. Hemisphere publishing corporation, Washington, D C, 1975.
[36] Shinar Josef, Shima Tal, Kebke Alexei. On the Validity of Linearized Analysis in the Interception of Reentry Vehicles[C]. AIAA-98-4303, 1998.
[37]李佳峰,姜欢,陈万春.基于拟勒让德谱变换的防空导弹弹道优化[J].弹道学报, 2009,21(3):1-7.
[38]赵红.高超声速飞行器跳跃飞行轨道优化研究[D].哈尔滨工业大学, 2008.
[39] Tian, bailing, Zong qun. Optimal Guidance for Reentry Vehicles Based on Indirect Legendre Pseudo spectral method [J]. Acta Astronautica, 2011:1176-1184.
[40] E. Mooij. Aerospace-Plane Flight Dynamics Analysis of Guidance and Control Concepts [M]. Delft University of Technology, 1998.
[41]马丽娟.LQR系统最优控制器设计的MATLAB实现及应用.石河子大学学报,2005,23(4):1-3.
[2] Betts J.T. Survey of Numerical Methods for Trajectory Optimization[C]. Journal of Guidance, Control and Dynamics, 1998.
[3]雍恩米.高超声速滑翔式再入飞行器轨迹优化与制导方法研究[D].国防科学技术大学, 2008:71-90.
[4] Kang wei. The Rate of Convergence for a Pseudo spectral Optimal Control Method[C]. Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, Dec.9-11, 2008.
[5]胡建学,陈克俊,赵汉元,等. RLV再入标准轨道制导与轨道预测指导方法比较分析[J].国防科技大学学报, 2007,29(1):1-5.
[6]胡建学,陈克俊,赵汉元,等. RLV再入标准轨道制导与设计[J].航天控制,2007, 25(6):1-4.
[7] Dukeman GA. Profile-following Entry Guidance Using Linear Quadratic Regulator Theory[C]. AIAA 2002-4457, 2002.
[8] Youssef H, Chowdhry RS, Lee H, et al. Predictor-Corrector Entry Guidance for Reusable Launch Vehicles[C]. AIAA 2001-4043, 2001.
[9] Schierman JD, Hull JR, Ward DG. Flight Test Results of an Adaptive Guidance System for Reusable Launch Vehicles[C]. AIAA 2004-4771, 2004.
[10] Bollino KP, Ross IM. Optimal Nonlinear Feedback Guidance for Reentry Vehicles[C]. AIAA 2006-6074, 2006.
[11] Ross IM, Sekhavat P, Fleming A, et al. Pseudo spectral Feedback Control: Foundations, Examples and Experimental Results[C]. AIAA 2006-6354, 2006.
[12] Shen Zuojun, Lu Ping. Onboard Generation of Three-Dimensional Constrained Entry Trajectories[C]. Journal of Guidance, Control and Dynamics, 2003, 26(1):1-11.
[13]王光伦.高超声速飞行器再入段预测校正制导研究[D].哈尔滨工业大学,2010:10-21.
[14]赵汉元.飞行器再入动力学和制导[M].国防科技大学出版社, 1997:23-97.
[15] Singh B, Bhattacharya R. Optimal Guidance of Hypersonic Vehicles Using B-Splines and Galerkin Projection[C]. AIAA 2008-7263, 2008.
[16] Fahroo F, Ross IM. Advances in Pseudo spectral Methods for Optimal Control[C]. AIAA 2008-7309, 2008.
[17] Garg D, Patterson MA, Darby CL, et al. Patterson. Direct TrajectoryOptimization and Costate Estimation of General Optimal Control Problems Using a Radau Pseudo spectral Method[C]. AIAA 2009-5989, 2009.
[18] Jorris RT, Schulz CS, Friedl FR, et al. Constrained Trajectory Optimization Using Pseudo spectral Methods[C]. AIAA 2008-6218, 2009.
[19] Bollino KP, Lewis LR, Sekhavat P, et al. Pseudo spectral Optimal Control: A Clear Road for Autonomous Intelligent Path Planning[C]. AIAA 2007-2831, 2007.
[20] Chartres JT, Michael H, Schneider G. Optimization of the Terminal Flight Phase for a Future Reusable Launch Vehicle[C]. AIAA2005-6060, 2005.
[21]雍恩米,唐国金,陈磊.基于Gauss伪谱方法的高超声速飞行器再入轨迹快速优化[J].宇航学报, 2008, 29(6):1-7.
[22] Schierman JD, Hull JR, Ward DG. On-Line Trajectory Command Reshaping for Reusable Launch Vehicles[C]. AIAA 2003-5439, 2003.
[23] Allwine DA, Fisher JE, Strahler JA. On-Line Trajectory Generation for Hypersonic Vehicles[C]. AIAA 2005-6435, 2005.
[24] Lee YI, Ryoo CK, Kim E. Optimal Guidance with Constraints on Impact Angle and Terminal Acceleration[C]. AIAA 2003-5795, 2003.
[25] Hill AD, Anderson DM, Coughlin DJ, et al. X-33 Trajectory Optimization and Design[C].AIAA-98-4408, 1998.
[26] Oppenheimer MW, Doman DB. Reconfigurable Control Design for the X-40A with In-Flight Simulation Results[C]. AIAA 2004-5017, 2004.
[27] Harl N, Balakrishnan SN. Reentry Terminal Guidance through Sliding Mode Control[C]. Journal of Guidance, Control and Dynamics, 2010, 33(1):1-14.
[28]孙春贞,黄一敏.重复使用运载器末端区域能量管理轨迹鲁棒性分析[J].兵工学报, 2008,29(3):1-5.
[29] Iris F.A. Vis. Survey of research in the design and control of automated guided vehicle systems [J]. European Journal of Operational Research, 2006:677-709.
[30] S. De Ridder, E. Mooij. Terminal area trajectory planning using the energy-tube concept for reusable launch vehicles [J]. Acta Astronautica, 2010.
[31] C.A. Kluever. Terminal Guidance for an Unpowered Reusable Launch Vehicle with Bank Constraints [J]. Journal of Guidance, Control and Dynamics, 2007, 30(1):1-7.
[32]钱杏芳,林瑞雄,赵亚男.导弹飞行力学[M].北京理工大学出版社, 2008:160-165.
[33]胡寿松,王执铨,胡维礼.最优控制理论与系统[M].科学出版社, 1994:162-189.
[34] E. Mooij. Linear Quadratic Regulator re-entry control: performance assessmentusing a taguchi approach[C]. AIAA-98-1629, 1998.
[35] Bryson A E, Ho Y C. Applied Optimal Control [M]. Hemisphere publishing corporation, Washington, D C, 1975.
[36] Shinar Josef, Shima Tal, Kebke Alexei. On the Validity of Linearized Analysis in the Interception of Reentry Vehicles[C]. AIAA-98-4303, 1998.
[37]李佳峰,姜欢,陈万春.基于拟勒让德谱变换的防空导弹弹道优化[J].弹道学报, 2009,21(3):1-7.
[38]赵红.高超声速飞行器跳跃飞行轨道优化研究[D].哈尔滨工业大学, 2008.
[39] Tian, bailing, Zong qun. Optimal Guidance for Reentry Vehicles Based on Indirect Legendre Pseudo spectral method [J]. Acta Astronautica, 2011:1176-1184.
[40] E. Mooij. Aerospace-Plane Flight Dynamics Analysis of Guidance and Control Concepts [M]. Delft University of Technology, 1998.
[41]马丽娟.LQR系统最优控制器设计的MATLAB实现及应用.石河子大学学报,2005,23(4):1-3.
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